# Hybrid III-V diamond photonic platform for quantum nodes based on neutral
silicon vacancy centers in diamond

Ding Huang  1,† Alex Abulnaga  1,† Sacha Welinski  1 Mouktik Raha  1 Jeff D.
Thompson  1 and Nathalie P. de Leon1  1Department of Electrical Engineering,
Princeton University, New Jersey 08544, USA  †These authors contributed
equally to this work<EMAIL_ADDRESS>
###### Abstract

Integrating atomic quantum memories based on color centers in diamond with on-
chip photonic devices would enable entanglement distribution over long
distances. However, efforts towards integration have been challenging because
color centers can be highly sensitive to their environment, and their
properties degrade in nanofabricated structures. Here, we describe a
heterogeneously integrated, on-chip, III-V diamond platform designed for
neutral silicon vacancy (SiV0) centers in diamond that circumvents the need
for etching the diamond substrate. Through evanescent coupling to SiV0 centers
near the surface of diamond, the platform will enable Purcell enhancement of
SiV0 emission and efficient frequency conversion to the telecommunication
C-band. The proposed structures can be realized with readily available
fabrication techniques.

††journal: oe††articletype: Research Article

##  1 Introduction

Color centers in diamond combine optical addressability with long spin
coherence times, making them promising candidates for repeater-based quantum
networks [1]. Recent proof-of-principle demonstrations of key ingredients for
quantum networks using color centers in diamond include on-demand remote
entanglement generation [2], coherent control of multiple nearby nuclear spin
memories [3], entanglement distillation [4], and memory-enhanced quantum
communication [5]. However, building larger quantum networks that incorporate
more than two nodes and span longer distances will require new technological
breakthroughs. Currently known platforms suffer from either degraded optical
coherence when incorporating into nanophotonic devices [6, 7], or limited
electron spin coherence times of milliseconds combined with the requirement to
work at millikelvin temperatures [8]. The recently reported SiV0 center in
diamond has the potential to overcome many of these challenges [9, 10, 11,
12]. The unique combination of stable optical transitions and long spin
coherence times at liquid helium temperature makes the SiV0 center an
attractive building block for nodes in quantum networks.

One proposal for enhancing the entanglement generation rate in color-center-
based quantum networks is to integrate color centers with nanophotonic
devices. In particular, optical cavities greatly enhance atom-photon
interaction, which improves spin readout and spin-photon entanglement
fidelity. Recent progress in diamond nanofabrication techniques has enabled
record single-emitter cooperativities up to 105 [5], as well as interfaces
with multiple color centers [13]. Furthermore, nanophotonic devices can enable
other functionality such as on-chip quantum frequency conversion (QFC), which
is key to achieving long-distance quantum communication. The small mode volume
offers an opportunity for highly efficient nonlinear optical interactions even
with low pump powers, which increases the signal-to-noise ratio for single
photon level signals [14].

Monolithic fabrication techniques of diamond nanophotonic cavities require
milling or etching bulk single crystal diamond, which leads to low yield [15]
and precludes the on-chip integration of photonic components with other
functionality, such as QFC and active devices. Furthermore, there is currently
no method for high purity, wafer-scale synthesis of single crystal diamond
[16], limiting the scalability of this approach.

By contrast, nanofabrication techniques in III-V semiconductor systems are
fairly mature. Nanophotonic components with diverse functionalities have been
fabricated in III-V semiconductors such as gallium arsenide (GaAs) [17] and
gallium phosphide (GaP) [18]. GaAs photonic crystal cavities with quality
factors exceeding $10^{4}$ have been demonstrated at wavelengths close to the
zero-phonon line of the SiV0 center ($\sim$ 946 nm) [19, 20]. More recently,
surface passivation schemes helped to push the quality factors of state-of-
the-art cavities to be above $10^{5}$ [21]. Other recent efforts in GaP
photonics have been spurred by its large optical nonlinearities and
transparency over a wide wavelength range [18]. GaP cavities with high quality
factors have been reported using microdisks [22], one-dimensional photonic
crystal cavities [23] and ring resonators [18].

A promising method to mitigate the constraints imposed by diamond
nanofabrication is heterogeneous integration of diamond and a separate device
layer material [24]. Instead of fabricating devices directly on single crystal
diamond, the photonic device is fabricated in a high-index photonic layer on
top of the diamond substrate such that photons can evanescently couple to
color centers that are close to the diamond surface (Fig.1). This scheme has
previously been used to demonstrate Purcell enhancement of optical emission
from the negatively charged nitrogen vacancy (NV) center in diamond [25, 26,
27] and Er3+ ions in yttrium orthosilicate [28, 29, 30]. For NV centers,
previous work has involved fabricating GaP waveguides or microdisks on top of
diamond, and then subsequently etching into the diamond to realize a high
quality factor structure [26, 31, 27]. This subsequent etching step leads to
significant spectral diffusion of the NV center optical transition [7, 32].

Figure 1: Schematic illustration of the hybrid III-V diamond photonic
platform. III-V material (pink) is patterned on top of the diamond substrate
(grey). The SiV0 center near the diamond surface is evanescently coupled to a
nanobeam photonic crystal cavity with a width of $w_{\text{y}}$ and a
thickness of $w_{\text{z}}$. The emitted photon is routed to an on-chip
frequency conversion module, where FWM-BS scheme is used to translate the
signal to single photon at the telecommunication C-band.

Here, we develop a design for heterogeneously integrated nanophotonic devices
to build quantum nodes based on the SiV0 center, using a hybrid III-V diamond
platform. One-dimensional photonic crystal cavities enhance the optical
emission from single SiV0 centers, and the emission can then be routed on-chip
to a microresonator-based frequency converter based on a four-wave mixing
Bragg scattering (FWM-BS) scheme. In contrast to previous demonstrations, our
design does not require etching into the diamond, avoiding deleterious effects
on the color center.

##  2 Photonic crystal cavity design

Photonic crystal cavities provide mode confinement to a small volume on the
order of a cubic wavelength, enabling enhanced coupling between a single color
center and the cavity mode [33]. The key figure of merit is the Purcell
enhancement factor of the spontaneous emission rate, $P$, which is given by
$P=4g(\vec{r})^{2}/\kappa\Gamma_{0}$. Here, the rate of interaction between
the cavity mode and a single SiV0 center at the position $\vec{r}$ is
characterized by the single-photon Rabi frequency,
$g(\vec{r)}=\vec{\mu}\cdot\vec{E}(\vec{r})/\hbar$, where $\vec{\mu}$ is the
electric dipole moment of the optical transition for the SiV0 center and
$\vec{E}(\vec{r})$ is the electric field strength at the position of the SiV0
center associated with a single photon in the cavity mode. The cavity decay
rate, $\kappa$, is related to the quality factor of the cavity, Q, and the
cavity resonance frequency, $\omega$, by $\kappa=\omega/Q$. The spontaneous
emission rate of the optical transition of interest, $\Gamma_{0}$, is an
intrinsic property of the SiV0 center that can be characterized independent of
the cavity.

This points to two parameters to optimize to build an efficient spin-photon
interface: high Q and concentrated electric field with a good overlap between
the color center and the cavity mode to maximize $\vec{E}(\vec{r})$. Here, we
optimize the design for a heterogeneously integrated GaP-on-diamond photonic
crystal cavity. Suspended GaP photonic crystal cavities with high Q resonances
at telecommunication wavelengths have been demonstrated [23]. The large
bandgap of GaP minimizes absorption losses at near-infrared wavelengths and
allows for cavities with high Q. The diamond substrate has a moderately high
refractive index ($n_{\text{Dia}}\sim 2.4$), presenting a design challenge for
achieving high Q. In contrast to suspended photonic crystal devices, a diamond
substrate expands the light cone into which photons can radiate out of the
cavity [Fig.2(c)]. We propose a one-dimensional photonic crystal nanobeam
cavity, where high Q resonances can be supported. For realistic beam width and
height, the proposed heterogeneously integrated structure supports resonant
modes with quality factors $\sim 10^{5}$, on par with state-of-the-art
freestanding GaP photonic crystal cavities.

Figure 2: Design of a GaP nanobeam cavity on a diamond substrate. (a) Mirror
strength for different values of $w_{\text{y}}$ and $w_{\text{z}}$ with
$n_{\text{eff}}=2.55$. (b) Maximum mirror strength at different
$n_{\text{eff}}$ values. (c) Band diagram for a nanobeam waveguide with
$(w_{\text{y}},w_{\text{z}},h_{\text{x}},h_{\text{y}},a)=(400,380,59,128,184)$
nm. TE modes and TM modes are indicated by solid black lines and dashed blue
lines respectively. The region above the diamond light line is shaded in grey
and the fundamental TE bandgap is indicated by the pink shaded area. The
target frequency is marked by the dashed red line. (d) Normalized electric
field $|E|^{2}$ distribution (left) in the yz-plane at x = 0 with a line cut
of the electric field at y = 0 nm (right). (e) Normalized $E_{\text{y}}$ field
profile of the fundamental cavity mode of the GaP nanobeam cavity. The xy
slice is taken at the center of the cavity (i.e. z = 190 nm).

We first consider a GaP nanobeam with waveguide width $w_{\text{y}}$ and
waveguide thickness $w_{\text{z}}$. As illustrated by Fig.1, the high
refractive index of GaP ($n_{\text{GaP}}\sim 3.13$) provides the optical mode
confinement along the y- and z-direction. The cavity is defined by a one-
dimensional lattice of elliptical air holes with lattice constant $a$ and
diameters $h_{\text{x}}$ and $h_{\text{y}}$ along the x- and y-directions
respectively [Fig.2(e), inset]. Starting with the design that maximizes the
bandgap, the nanobeam cavity is formed by locally perturbing the periodic
array to form a defect [34]. An adiabatic shift of the band-edge frequencies
moves the target frequency from the dielectric band-edge at the defect to the
middle of bandgap in the Bragg mirror regions. This can be achieved by either
tapering the size of the holes or the lattice constant. As an example, we
employ the latter approach to design a symmetric cavity where the lattice
constant is gradually increased from $a_{\text{cav}}$ in the middle of the
cavity to $a_{\text{mirr}}$ in the mirror regions on both sides.

To find the design with maximum mirror strength, we choose a lattice constant
according to $a=\lambda_{0}/2n_{\text{eff}}$, where $\lambda_{0}$ is the
target wavelength and $n_{\text{eff}}$ is the effective mode index of the
cavity. In the case of the GaP-on-diamond system, the effective indices of the
cavity modes have to lie in between the refractive index of diamond and that
of GaP, i.e. $n_{\text{eff}}\in(2.4,3.13)$. Using MIT Photonic Bands [35], we
calculate the band structure of the GaP nanobeam on a diamond substrate for
different structural parameters. As modes above the diamond light line are
unconfined, we are only interested in those below the light line at
$k_{\text{x}}=\pi/a$.

We define the mirror strength as the separation between the target frequency
and the nearest quasi-transverse-electric (TE) guided mode normalized by the
target frequency. The TE modes and the quasi-transverse-magnetic (TM) modes
are defined as modes with most of their electric field components along the
y-axis and the z-axis respectively. Fig.2(a) shows the largest mirror strength
at different combinations of $w_{\text{y}}$ and $w_{\text{z}}$ for
$n_{\text{eff}}=2.55$. At each point on the two-dimensional sweep, we optimize
the mirror strength with different combinations of hole diameters (i.e.
$h_{\text{x}}$ and $h_{\text{y}}$). By repeating the two-dimensional sweep for
different $n_{\text{eff}}$ values, we could identify the cavity design with
the maximum mirror strength at the target frequency. Fig.2(b) shows the
largest mirror strength for different $n_{\text{eff}}$ values. As
$n_{\text{eff}}$ gets closer to the refractive index of diamond
($n_{\text{Dia}}\sim 2.4$), the mirror strength is limited by leaky modes
above the diamond light line. On the other hand as $n_{\text{eff}}$ increases,
more modes are pushed beneath the light line, and the mirror strength
decreases as the modes are pushed closer together. The optimal design (i.e.
$n_{\text{eff}}=2.55$) has an air band-edge frequency slightly below the
diamond light line with structural parameters
$(w_{\text{y}},w_{\text{z}},h_{\text{x}},h_{\text{y}},a)$ = (400, 380, 59,
128, 184) nm. For the cavity design with maximum mirror strength, we plot the
band diagram for different modes in Fig.2(c). The desired resonant frequency
is in the middle of the fundamental TE bandgap. We achieve a bandgap of $\sim
11\%$.

In our cavity design, we keep structural parameters $w_{\text{y}}$,
$w_{\text{z}}$, $h_{\text{x}}$ and $h_{\text{y}}$ to be the same across the
entire nanobeam. By varying the lattice constant from $a_{\text{cav}}$ = 171
nm in the middle of the cavity to $a_{\text{mirr}}$ = 184 nm in the mirror
region, we adiabatically move the dielectric band-edge such that the target
resonance frequency is in the middle of the fundamental TE bandgap.

The Purcell enhancement factor depends on the overlap between the transition
dipole moment for the SiV0 center and the resonant mode. To examine the
efficacy of our cavity design approach, we study the cavity mode profile using
three-dimensional finite-difference time-domain (FDTD) simulations. As an
example, we perform FDTD simulations on a cavity where the lattice constant is
parabolically tapered from $a_{\text{mirr}}$ to $a_{\text{cav}}$ across 10
holes on a single side (20 holes in total in the cavity region). In order to
further increase the mirror strength, we add 20 Bragg mirror holes on both
ends of the cavity. The normalized $E_{\text{y}}$ field components for the
fundamental localized cavity mode are plotted in Fig.2(e). Most of the field
strength is concentrated in the adiabatically tapered cavity region. The
electric field strength at the position of the SiV0 center varies depending on
its location in the diamond substrate [Fig.2(d), left]. At around 50 nm into
the diamond substrate, where we observed SiV0 centers with stable optical
properties and long spin coherence [9], the electric field energy density,
$|E(\vec{r})|^{2}$, is $9.6\%$ of its maximum value in the center of the
cavity [Fig.2(d), right].

Figure 3: (a) Geometry of the symmetric photonic crystal cavity design. In the
cavity region, the hole spacing is adiabatically tapered from $a_{\text{cav}}$
to $a_{\text{mirr}}$. In the mirror regions on both sides, the hole spacing is
held constant at $a_{\text{mirr}}$. The schematic shows a design with 20
cavity holes and 12 mirror pairs. Dependence of the GaP nanobeam (b) and the
GaAs nanobeam (c) cavity Q on the number of mirror pairs for 10 (purple), 12
(red), 16 (green), 20 (orange) and 30 (blue) holes in the cavity region.

We evaluate the scaling of Q with different design parameters using 3D FDTD.
The nanobeam cavity can be divided into a cavity region and two Bragg mirror
regions [Fig.3(a)]. In the cavity region, the lattice constant tapers
parabolically from $a_{\text{cav}}$ in the middle to $a_{\text{mirr}}$ on both
ends. As the cavity is symmetric with respect to x = 0, the total number of
holes in the entire cavity region is twice the number of holes on a single
side. For simplicity, we will refer to different designs based on the total
number of holes in the cavity region in the following discussions. The mirror
segments consist of periodic arrays of holes where the lattice constant is
fixed at $a_{\text{mirr}}$. Since our cavity design is symmetric, an
additional mirror hole on one end of the cavity implies an extra mirror hole
on the opposite side. We define the addition of a pair of Bragg mirror holes
as an additional "mirror pair".

First we calculate the Q for different cavity designs. Fig.3(b) shows the
scaling of Q with the number of mirror pairs. For small numbers of holes in
the mirror regions, the Q of the cavity increases with the mirror strength. At
higher numbers of mirror holes, Q is limited by radiation loss in the cavity
region. In order to further push up the quality factor, we taper the lattice
constant over more holes in the cavity region. For 30 cavity holes, the Q is
saturated over $10^{6}$ with 20 mirror pairs, and for 20 cavity holes, the
saturated Q exceeds $10^{5}$, which is the current demonstrated state of the
art in suspended GaP cavities [23].

Our method for designing hybrid photonic platforms can be applied to other
material systems with a higher refractive index than diamond. Using the
aforementioned design principles, we demonstrate that a similar evanescent
coupling scheme can be realized using GaAs-on-diamond. Epitaxially grown GaAs
has a higher refractive index ($n_{\text{GaAs}}\sim 3.55$) compared to GaP.
The optimized GaAs nanobeam cavity has structural parameters
$(w_{\text{y}},w_{\text{z}},h_{\text{x}},h_{\text{y}},a_{\text{cav}},a_{\text{mirr}})$
= (350, 220, 70, 136, 162, 180) nm with a bandgap of $\sim 15.7\%$ in the
mirror region. Using 3D FDTD simulations, we can similarly evaluate the
scaling of Q for different GaAs photonic crystal cavity designs [Fig.3(c)]. We
find that for the optimized structure, a smaller number of mirror pairs is
required to saturate the Q because the mirror strength is larger.

For the optimized cavity designs, we can evaluate the expected Purcell factor
for SiV0 located at different locations. After taking local-field correction
of the spontaneous emission rate into account [36], we can extract the dipole
moment for the SiV0 center ($\vec{\mu}$) using the following expression:

$\Gamma_{0}=\frac{1}{\beta}\cdot\left(\frac{3n_{\text{Dia}}^{2}}{2n_{\text{Dia}}^{2}+1}\right)^{2}n_{\text{Dia}}\cdot\frac{|\vec{\mu}|^{2}\omega^{3}}{3\pi\epsilon_{0}\hbar
c^{3}}$ (1)

where $\beta$ is the fraction of the decay rate caused by spontaneous emission
at the transition coupled to the cavity.

Here, we make the assumptions that the SiV0 center can be treated as a perfect
two-level atom and $\beta=1$. Using the bulk spontaneous emission rate for
SiV0 centers $\Gamma_{0}=2\pi\times 88$ MHz [9], we arrive at the calculated
$|\vec{\mu}|=6.027\times 10^{-29}$ C-m. If we further assume that the dipole
moment is parallel to the electric field polarization of the cavity resonant
mode, we can estimate the Purcell factor. The inset of Fig.4(a) shows the
distribution of expected Purcell factor inside the diamond substrate for GaP-
on-diamond. At a depth of 50 nm, the maximum Purcell factor is 743 for a GaP
nanobeam cavity with 20 cavity holes and a saturated quality factor of $\sim
10^{5}$. We also study the sensitivity of Purcell factor to displacements in
the xy-plane. The maximum Purcell factor can be achieved when the SiV0 is
placed directly under the electric field energy density maximum. As Fig.4(a)
shows, the Purcell factor is more sensitive to misalignments along the
nanobeam direction (i.e. x-direction). Similar results can be obtained for a
GaAs nanobeam cavity with 20 cavity holes and a saturated quality factor of
$\sim 3.5\times 10^{5}$ [Fig.4(b)]. As we will discuss in Section 4, a Purcell
factor above 200 for GaP-on-diamond and a Purcell factor above 1000 for GaAs-
on-diamond are practical and attainable using widely available fabrication
techniques.

Figure 4: Variations of expected Purcell factors for GaP cavity design with 20
cavity holes and 20 mirror pairs (a) and GaAs cavity design with 20 cavity
holes and 12 mirror pairs (b). At a depth of 50 nm in the diamond substrate,
the maximum attainable Purcell factor for GaP design is 743 and that for GaAs
design is 3921. The displacements, in the x-direction (blue) and y-direction
(orange), are defined relative to the optimal position. (Inset) Distribution
of Purcell factor inside the diamond substrate, y-z plane at x = 0.

##  3 On-chip quantum frequency conversion

Low-loss optical fibers provide a scalable way to connect nodes in a long-
distance quantum network. To utilize the fiber network, the emission
wavelengths of color centers in diamond need to be shifted to overlap with the
transparency window of silica fibers. QFC of single photons requires
simultaneously achieving high conversion efficiency and low noise. Despite
these challenges, recent demonstrations were able to show that the spin-photon
entanglement is preserved after the QFC process for NV centers in diamond [37,
38]. These experiments used free-space optics in combination with centimeter-
long, second-order optically nonlinear ($\chi^{(2)}$) waveguides to perform
spectral translations of single photons from the NV emission wavelength (637
nm) to the telecommunication L-band (1588 nm). In addition to leveraging the
benefits of low-loss optical fibers, QFC presents a solution to inhomogeneous
broadening of color center emission. By detuning the pump laser, the disparate
color center emission wavelengths can be shifted to the same telecommunication
wavelength, and therefore identical telecom photons can be generated from
multiple color-center-based quantum nodes.

We propose a compact and power-efficient QFC scheme that can be realized on
the hybrid III-V diamond platform. Leveraging the large third order optical
nonlinearities ($\chi^{(3)}$) of III-V semiconductors such as GaAs and GaP, we
show that a microresonator-based FWM-BS scheme can efficiently translate the
emitted photons from SiV0 centers to the telecommunication C-band (1550 nm).
In the FWM-BS scheme, two pump fields, $\omega_{\text{p1}}$ and
$\omega_{\text{p2}}$, create an effective modulation of $\chi^{(3)}$ and
scatter an input signal photon ($\omega_{\text{s}}$) to the idler frequency
$\omega_{\text{i}}$ [Fig.5(a)]. In principle, this enables noise-free
frequency translation of the signal photon by an amount set by the difference
between the two pump frequencies [39]. QFC based on FWM-BS has recently been
demonstrated to convert the emission of InAs/GaAs quantum dots using
Si${}_{\text{3}}$N${}_{\text{4}}$ micro-ring resonators [40]. Owing to their
large $\chi^{(3)}$, III-V semiconductors are promising material platforms in
realizing efficient frequency conversion with low pump powers [41, 18]. Here,
we extend the functionalities of the hybrid III-V diamond system and outline
our design of an integrated QFC module based on GaP.

Because nonlinear optical effects are generally quite weak, appreciable
conversion efficiency requires long interaction times between the pumps and
the signal, as well as high pump powers [42, 43]. By employing a resonant
optical structure such as a whispering gallery mode (WGM) microring resonator,
strong interactions can be achieved with small device footprints, allowing for
high conversion efficiencies in a scalable platform [44, 45, 46]. These
resonant structures additionally allow for smaller mode areas than bulk
crystals, resulting in enhanced nonlinearities at low pump powers [47, 48]. We
consider here a 25 $\mu$m radius ring resonator with coupling of 946 nm and
1550 nm TE modes using separate point waveguide couplers as shown in Fig.5(b).

To design a ring resonator geometry for QFC of SiV0 emission using FWM-BS, we
consider the case of a weak continuous-wave field with frequency
$\omega_{\text{s}}$ as the input signal. When combined with pumps at
frequencies $\omega_{\text{p1, p2}}$ the fields interact to scatter the signal
into two new signals, the "idlers", at frequencies
$\omega_{\text{i$\pm$}}=\omega_{\text{p2}}\pm|\omega_{\text{p1}}-\omega_{\text{s}}|$
where $\omega_{\text{p1}}$ is the pump in the 946 nm band, and
$\omega_{\text{p2}}$ is the pump in the 1550 nm band. In a WGM resonator there
are discrete resonances, so it is critical that the converted idlers lie on
cavity resonances to achieve appreciable conversion efficiency. Within a given
frequency band, the cavity resonances can be described by a Taylor series
expansion in orders of the integer mode number $\mu$ relative to some central
cavity resonance frequency $\hat{\omega}_{\text{0}}$ as described by Eq. (2)
[49].

$\hat{\omega}_{\mu}=\hat{\omega}_{0}+D_{\text{1}}\mu+\frac{1}{2}D_{\text{2}}\mu^{2}+\frac{1}{6}D_{\text{3}}\mu^{3}+...$
(2)

where the coefficients
$D_{\text{n}}\equiv(1/R^{n})(\partial^{n}\omega/\partial\beta^{n})|_{\omega_{0}}$
describe the dispersion of the device at the central resonance. The
propagation constant is given by $\beta=2\pi n_{\text{eff}}(\lambda)/\lambda$,
and R is the ring radius. Following the treatment and notation in [14], we
denote the cavity resonances nearest the signal, pump, and idler frequencies
by $\hat{\omega}_{\text{s,p1,p2,i$\pm$}}$. For a given pump-signal separation
$|\mu|$ in the 946 nm band, the detuning of the converted idlers from their
nearest cavity resonance in the 1550 nm band is given by

$\delta\hat{\omega}_{i\pm,|\mu|}=\pm(D_{1}^{1550}-D_{1}^{946})|\mu|+\frac{1}{2}(D_{\text{2}}^{1550}\mp
D_{\text{2}}^{946})|\mu|^{2}\pm\frac{1}{6}(D_{\text{3}}^{1550}-D_{\text{3}}^{946})|\mu|^{3}+...$
(3)

The superscripts denote the dispersion coefficients evaluated at the central
resonances in the 946 nm and 1550 nm bands respectively.

To minimize the idler detuning we seek a device geometry with similar
dispersion in both bands. Since $D_{\text{1}}=(1/R)c/n_{\text{g}}$, where
$n_{\text{g}}$ is the group index, this can be achieved to first order in
$|\mu|$ by designing a ring resonator cross-section for which $n_{\text{g}}$
at 946 nm and 1550 nm is matched. To find such a design, we perform 2D
eigenmode simulations of a rectangular GaP waveguide on diamond. The waveguide
is defined by its width, $w_{\text{y}}$, and thickness, $w_{\text{z}}$, as
defined in the previous section. We perform a parameter sweep over the
waveguide aspect ratio (AR), defined as $AR=w_{\text{y}}/w_{\text{z}}$, and
the total cross-sectional area, $A=w_{\text{y}}w_{\text{z}}$. In general, we
observe that at smaller ARs and smaller areas we achieve greater group index
dispersion and better matching between the fundamental TE modes at 946 nm and
1550 nm as shown in Fig.5(c). The AR and area cannot be reduced arbitrarily,
however, because the telecom mode is pushed into cut-off for very small areas
and extreme ARs. To avoid cut-off, smaller ARs can be compensated with a
larger device area, and smaller device areas can be similarly compensated by a
larger AR. As such, there is a tradeoff between AR and area which can be
optimized to achieve group index matching without cut-off. In Fig.5(d) we
present simulations for a 25 $\mu$m radius ring resonator, sweeping the
resonator width for different thicknesses, from which we select a cross-
section geometry with $w_{\text{z}}$ = 640 nm, $w_{\text{y}}$ = 500 nm. The
group velocity dispersion of the device, shown in Fig.5(e), exhibits normal
dispersion at both 946 nm and 1550 nm.

Figure 5: (a) Four-wave-mixing Bragg-scattering frequency conversion scheme.
The two pump fields, $\omega_{\text{p1}}$ at 946 nm, and $\omega_{\text{p2}}$
at 1550nm, combine in a $\chi^{(3)}$ medium to scatter the input SiV0 photon
($\omega_{\text{s}}$) to idlers $\omega_{\text{i$\pm$}}$ in the 1550 nm band.
(b) The QFC module consists of a microring resonator with two point-couplers
to separately couple 946 nm and 1550 nm TE modes. A high-Q resonator allows
for prolonged interactions between the fields in a small mode volume, leading
to enhanced nonlinear interactions. (c) Group index of the TE modes as a
function of wavelength for different waveguide areas and ARs. Solid lines
represent a total cross-sectional area of $A=0.35\mu m^{2}$, dashed lines are
for $A=0.55\mu m^{2}$. For each cross-sectional area, ARs of 0.75 (blue), 1
(orange) and 1.5 (red) are plotted. (d) Simulated group index mismatch $\Delta
n_{\text{g}}=n_{\text{g}}^{946}-n_{\text{g}}^{1550}$ as a function of
resonator width, $w_{\text{y}}$ and thickness, $w_{\text{z}}$. We achieve
$\Delta n_{\text{g}}=0$ for several cross-sections, and the geometries are
relatively insensitive to small variations in width and thickness. (e)
Dispersion of the selected ring resonator cross-section ($w_{\text{z}}=640$
nm, $w_{\text{y}}=500$ nm) with zero-crossings, i.e. $\text{D}=0$, at 1155 nm
and 1536 nm. (f) Coupling quality factor as a function of wavelength for two
separate point couplers. The red line represents a 640 nm $\times$ 500nm
coupling waveguide at a gap of 210 nm. The blue line represents a 380 nm
$\times$ 300 nm coupling waveguide at a gap of 10 nm.

To couple light into the ring resonator, we design two separate point couplers
as described in Fig.5(f) [50]. A coupler waveguide with cross-section 640 nm
$\times$ 500 nm and 210 nm gap is utilized to couple the mode at 1550 nm with
coupling quality factor $Q_{\text{C,2}}(1550\text{ nm})=7.71\times 10^{4}$. As
the 946 nm mode is much more strongly confined than the telecom mode, there is
minimal mode overlap between the 946 nm mode in the coupler and ring
resonator, resulting in a severely undercoupled quality factor
$Q_{\text{C,2}}(946\text{ nm})=3.52\times 10^{8}$. To couple the 946 nm signal
we utilize a point coupler with cross-section 380 nm $\times$ 300 nm with a 10
nm gap from the resonator, resulting in a coupling quality factor
$Q_{\text{C,1}}(946\text{ nm})=7.64\times 10^{4}$. The thickness of the 946 nm
coupler is chosen to match that of the photonic crystal cavity design from the
previous section, and a tapering of the width is introduced to achieve the
desired coupling Q. Due to the small cross-sectional area, the telecom mode is
in cut-off for this coupler [51], and as such there is very weak coupling of
the telecom mode from the resonator into the waveguide, leading to a coupling
quality factor $Q_{\text{C,1}}(1550\text{ nm})=2.70\times 10^{7}$. For both
modes we calculate an effective coupling quality factor defined as
$1/Q_{\text{C}}=1/Q_{\text{C,1}}+1/Q_{\text{C,2}}$ leading to
$Q_{\text{C}}(946\text{ nm})=7.64\times 10^{4}$ and $Q_{\text{C}}(1550\text{
nm})=7.69\times 10^{4}$.

To evaluate the FWM-BS conversion efficiency in our designed coupler-resonator
system, we study analytic coupled mode equations (4) - (7) for the fields
inside a resonator with a $\chi^{(3)}$ as described in detail in [14]. In
addition to our pumps, signal, and idlers, we consider mixing between the
signal and the 946 nm band pump which scatters the signal into an auxiliary
signal $\omega_{\text{s'}}=2\omega_{\text{p1}}-\omega_{\text{s}}$ as shown in
Fig.6(a).

$t_{\text{R}}\frac{dE_{\text{s}}}{dt}=-(\alpha_{\text{p1}}+i\Delta\phi_{\text{s}})E_{\text{s}}+i\gamma_{\text{p1}}LE^{2}_{\text{p1}}E^{*}_{\text{s'}}+i2\gamma_{\text{p1}}LE_{\text{p1}}(E_{\text{p2}}E^{*}_{\text{i-}}+E_{\text{p2}}^{*}E_{\text{i+}})+i\sqrt{\theta_{\text{1}}P_{\text{s}}}$
(4)

$t_{\text{R}}\frac{dE_{\text{s'}}}{dt}=-(\alpha_{\text{p1}}+i\Delta\phi_{\text{s'}})E_{\text{s'}}+i\gamma_{\text{p1}}LE^{2}_{\text{p1}}E^{*}_{\text{s}}+i2\gamma_{\text{p1}}LE_{\text{p1}}(E_{\text{p2}}E^{*}_{\text{i+}}+E_{\text{p2}}^{*}E_{\text{i-}})$
(5)

$t_{\text{R}}\frac{dE_{\text{i+}}}{dt}=-(\alpha_{\text{p2}}+i\Delta\phi_{\text{i+}})E_{\text{i+}}+i\gamma_{\text{p2}}LE^{2}_{\text{p2}}E^{*}_{\text{i-}}+i2\gamma_{\text{p2}}LE_{\text{p2}}(E_{\text{p1}}E^{*}_{\text{s'}}+E_{\text{p1}}^{*}E_{\text{s}})$
(6)

$t_{\text{R}}\frac{dE_{\text{i-}}}{dt}=-(\alpha_{\text{p2}}+i\Delta\phi_{\text{i-}})E_{\text{i-}}+i\gamma_{\text{p2}}LE^{2}_{\text{p2}}E^{*}_{\text{i+}}+i2\gamma_{\text{p2}}LE_{\text{p2}}(E_{\text{p1}}E^{*}_{\text{s}}+E_{\text{p1}}^{*}E_{\text{s'}})$
(7)

Where $\text{p}1$ and $\text{p}2$ denote the pumps at 946 nm and 1550 nm
respectively, $L=2\pi R$ is the cavity round-trip length,
$t_{\text{R}}=2\pi/D_{\text{1}}$ is the round-trip time, and
$\alpha_{m}=\hat{\omega}_{\text{m}}t_{\text{R}}/2Q_{\text{L,m}}$ is the cavity
loss for a resonance $m$ with loaded quality factor $Q_{\text{L,m}}$. The
effective nonlinear parameter is given by
$\gamma=n_{2}\omega/cA_{\text{eff}}$. $P_{\text{s}}$ is the power of the
signal at the waveguide input which is coupled into the resonator with power
coupling ratio
$\theta_{\text{1}}=\hat{\omega}_{\text{p1}}t_{\text{R}}/Q_{\text{C}}(946\text{
nm})$. Here we neglect nonlinear effects arising from the signal and auxiliary
signal. The round trip loss, nonlinear parameters, and power coupling ratios
are assumed to be constant within the 946 nm and 1550 nm bands. The
$\Delta\phi_{\text{m}}$ terms describe the effective detuning of the modes
from their nearest cavity resonance, including the effects of Kerr nonlinear
frequency shifts of the cavity resonances caused by the strong pumps, given
by:

$\Delta\phi_{\text{s,s'}}=(\hat{\omega}_{\text{s,s'}}-\omega_{\text{s,s'}})t_{\text{R}}-2\gamma_{\text{p1}}L(|E_{\text{p1}}|^{2}+|E_{\text{p2}}|^{2})$
(8)

$\Delta\phi_{\text{i$\pm$}}=(\hat{\omega}_{\text{i$\pm$}}-\omega_{\text{i$\pm$}})t_{\text{R}}-2\gamma_{\text{p2}}L(|E_{\text{p1}}|^{2}+|E_{\text{p2}}|^{2})$
(9)

To calculate $\gamma_{\text{p1,p2}}$ we first perform 2D eigenmode simulations
of the ring cross-section to extract the TE field profiles at 946 nm and 1550
nm. We then calculate the effective mode area, A${}_{\text{eff}}$, as defined
in Eq. (10) where the integral in the denominator is evaluated over the
resonator cross-section only:

$A_{\text{eff}}=\frac{\left(\int\int\epsilon_{\text{r}}(x,y)|E(x,y)|^{2}dxdy\right)^{2}}{\int\int_{\text{Ring}}\epsilon_{\text{r}}^{2}(x,y)|E(x,y)|^{4}dxdy}$
(10)

We determine the central resonance in the 946 nm and 1550 nm bands via 2D
eigenmode simulations of the effective index of the TE modes, yielding
resonances at $\hat{\omega}_{\text{p1}}=2\pi c/946.6\text{ nm}$ and
$\hat{\omega}_{\text{p2}}=2\pi c/1547.8\text{ nm}$ respectively. We solve Eq.
(4) - (7) in the steady state and compute the conversion efficiency,
$\eta_{\text{\text{conv}}}$, in terms of idler photon flux at the output of
the coupling waveguide relative to the signal photon flux at the input:

$\eta_{\text{conv}}=\frac{\theta_{\text{2}}|E_{\text{i$\pm$}}|^{2}/\hbar\omega_{\text{i$\pm$}}}{P_{\text{s}}/\hbar\omega_{\text{s}}}$
(11)

Where
$\theta_{\text{2}}=\hat{\omega}_{\text{p2}}t_{\text{R}}/Q_{\text{C}}(1550\text{
nm})$. Table 1 summarizes the constants used in the analysis.

Wavelength Band |  $D_{1}/2\pi$ (MHz) |  $D_{2}/2\pi$ (MHz) |  $D_{3}/2\pi$ (MHz) |  $Q_{i}$ ($10^{4}$) |  $Q_{\text{C}}$ ($10^{4}$) |  $n_{2}$ ($10^{-17}m^{2}W^{-1}$) |  $A_{\text{eff}}$ ($\mu m^{2}$)
---|---|---|---|---|---|---|---
946 nm | 531 | -122 | -0.964 | 7.5 | 7.64 | 0.85 [52] | 0.196
1550 nm | 531 | -44.2 | 13.1 | 7.5 | 7.69 | 1.1 [18] | 0.292

Table 1: Constants used for solving the coupled mode equations Figure 6: (a)
Signal, pump, and idler frequencies are shown as arrows, relative to their
nearest cavity resonances. Mixing between the signal, telecom pump, and 946 nm
pump leads to conversion into idlers which are offset from the telecom pump by
an amount equal to the frequency difference between the signal and 946 nm
pump. The frequency shift can occur either to the red (i-) or to the blue
(i+). In addition to the idlers, FWM-BS between the signal and 946 nm pump
leads to conversion into an auxiliary signal s’ with frequency
$\omega_{\text{s'}}=\omega_{\text{p1}}+(\omega_{\text{p1}}-\omega_{\text{s}})$
(b) Conversion efficiency of the i+ idler as a function of signal detuning,
$\delta\lambda_{\text{s}}$, normalized by FWHM of the signal resonance,
$\Delta\lambda_{\text{s}}$, for different total pump power values. The ratio
of total power in each pump is kept equal. The signal wavelength is swept near
the cavity resonance $\mu=1$. (c) Conversion efficiency bandwidth of the
i$\pm$ idlers. As the pump-signal separation $\mu$ is increased, the converted
idler frequencies are correspondingly shifted further from the 1550 nm pump.
The top (bottom) x-axis indicates the conversion efficiency of the i- (i+)
idler at a given output wavelength. Conversion efficiency drops for larger
$\mu$ as the idlers become increasingly detuned from their nearest cavity
resonance. The conversion efficiency for i$\pm$ is non-symmetric because the
resonance spacing is not identical at wavelengths greater than 1550 nm and
wavelengths smaller than 1550 nm. (d) Conversion efficiency for the i+ idler
as a function of the ring total quality factor $Q_{\text{L}}$ and total pump
power, under the assumption of critical coupling at both 946 nm and 1550 nm
for a pump-signal separation $\mu=1$. The vertical dashed line indicates a
loaded quality factor $Q_{\text{L}}=3.75\times 10^{4}$.

In Fig.6(b) we analyze the conversion efficiency for the i+ idler as a
function of normalized signal detuning from the $\mu=1$ cavity resonance for
different total pump powers. We assume a ring with intrinsic quality factor
$Q_{\text{i}}=7.5\times 10^{4}$, yielding loaded quality factors
$Q_{\text{L}}^{946}=3.78\times 10^{4}$ and $Q_{\text{L}}^{1550}=3.80\times
10^{4}$ using the coupler design from Fig.5(f). As GaP microring resonators
with loaded quality factors in excess of $10^{5}$ have been experimentally
demonstrated in the telecom band [53, 18] we believe this to be a conservative
estimate. We achieve a near-unity conversion efficiency of $-0.21$ dB for i+
at a total pump power of $50$ mW and signal detuning of
$0.95\Delta\lambda_{s}$, where $\Delta\lambda_{s}$ is the full width at half
maximum (FWHM) of the signal resonance. At higher pump powers the signal
cavity resonance experiences a nonlinear Kerr shift which requires the signal
frequency to be correspondingly shifted to achieve maximal conversion
efficiency.

Fig.6(c) shows the conversion efficiency into both idlers as a function of
signal-pump separation $\mu$. At larger values of $\mu$ conversion efficiency
is reduced due to dispersion in the resonator: the resonances are not equally
spaced with the same magnitude for both wavelength bands, and this difference
increases with larger detuning from the central pump resonance. The efficiency
for i$\pm$ is not symmetric because the dispersion differs at wavelengths
below the central resonance as compared to wavelengths above the central
resonance. As such, the detuning for i- is not the same as the detuning for
i+.

In Fig.6(d) we analyze conversion efficiency into i+ as a function of the ring
loaded quality factor $Q_{\text{L}}$ for different total pump powers under the
assumption of critical coupling $Q_{\text{C}}=Q_{\text{i}}$. For a total pump
power of 30 mW, we predict unity conversion efficiency for
$Q_{\text{L}}=4.9\times 10^{4}$ at the optimal signal detuning, and for 10 mW
we require $Q_{\text{L}}=8.6\times 10^{4}$. Moving to lower pump powers is
favorable for reducing the effects of nonlinear and thermal frequency shifts
of the cavity resonances which can make it difficult for the pumps and signal
to be simultaneously on-resonance with the cavity modes [14]. In addition to
the assumptions of critical coupling, we neglect pump depletion and parasitic
nonlinear processes such as higher order idler generations in the 1550 nm
band. These processes serve to deplete the primary idlers and thereby reduce
the conversion efficiency [14].

##  4 Discussion

In this paper, we have demonstrated the potential of hybrid III-V diamond
platforms for quantum networks based on SiV0 centers in diamond. We show that
a heterogeneously integrated nanobeam cavity can enhance the photon emission
from a single SiV0 center, and the emitted photon can be subsequently
converted to the telecommunication C-band on chip via a FWM-BS scheme,
providing an efficient interface between the SiV0 center and photons at
telecommunication wavelengths. In a fully integrated platform, the system will
require joint optimization between Purcell enhancement and frequency
conversion. Specifically, there will be a trade-off between the photon
collection efficiency into the cavity (i.e. $P/(P+1)$) and the maximum
conversion efficiency achievable with the frequency converter because the
optical linewidth will radiatively broaden beyond the bandwidth of the
microresonator-based frequency converter [40]. For the system presented here,
the linewidth of SiV0 emission (88 MHz) is narrow compared to the loaded
linewidth of the ring resonator in Section 3 ($\sim 8.4$ GHz), which allows
for a Purcell factor of around 100 before the broadened optical linewidth
reaches the bandwidth of the ring resonator. An example of such a device would
utilize a large number of cavity holes (greater than 20) to suppress far-field
scattering and a small number of mirror segments (less than 5) to allow for
decay into the waveguide mode, with a total Purcell factor of less than 100
and a collection efficiency over 90$\%$.

The proposed platform can be experimentally realized using widely available
existing fabrication techniques. Here, we comment on practical implementation
of the hybrid platform. Heterogeneous integration of quantum photonic elements
with different functionalities has been demonstrated in a wide variety of
material platforms [46]. Among different fabrication approaches to assemble
the elements, epitaxial lift-off, in which the III-V membrane layer is
released from the heteroepitaxially-grown substrate through selective wet
etching and subsequently transferred onto diamond [27], and transfer printing,
where suspended photonic devices can be picked up and transferred using a
rubber stamp [54, 28], are promising routes towards large-scale integration.
The two techniques differ in the method for aligning photonic elements to the
color centers. With the epitaxial lift-off approach, the nanobeam cavity and
the micro-resonator for QFC can be defined by lithography with sub-50 nm
alignment accuracy. In principle, this would enable large-scale photonic
circuit elements with more complex functionality [55]. However, the
applicability of this technique may be limited by the inhomogeneous
distribution of SiV0 centers and the spectral variation of nanobeam cavities
resulting from fabrication imperfections. On the other hand, transfer printing
allows the integration of pre-selected color centers in diamond with pre-
characterized photonic devices. Previous work has demonstrated similar
alignment accuracy to the epitaxial lift-off approach [54]. Despite the
challenges in achieving large-scale photonic device integration, this method
promises a robust and reproducible way to couple individual SiV0 centers to
high-performance photonic devices.

While our hybrid platform design targets SiV0 centers in diamond with an
emission wavelength of 946 nm, our general design approach for designing the
bandgap for the nanobeam cavity and the dispersion for miroresonator-based
FWM-BS can be applied to a wide variety of color centers in diamond and other
host materials. For example, the GaP-on-diamond platform could be applied to
the negatively charged silicon vacancy centers in diamond due to the wide
transparancy window of GaP. Furthermore, while the proposed FWM-BS QFC scheme
is not feasible for SiV0 in the GaAs-on-diamond platform due to the band edge
absorption feature which dominates the index dispersion at 946 nm, GaAs could
be used for color centers in silicon carbide that emit in the near-infrared
wavelength ranges [56, 57].

## Acknowledgements

The authors would like to thank Kartik Srinivasan, Alejandro Rodriguez, Zi-
Huai Zhang, and Paul Stevenson for helpful discussions about the photonic
crystal cavity design and FWM-BS scheme. This work was primarily supported by
DARPA under Young Faculty Award (award number D18AP00047), and work on the
neutral silicon vacancy center was supported by the NSF under the EFRI ACQUIRE
program (grant 1640959) and the Air Force Office of Scientific Research under
award number FA9550-17-0158. M. R. and J. D. T. were additionally supported by
the Air Force Office of Scientific Research (grant FA9550-18-1-0081). D. H.
was supported by a National Science Scholarship from A*STAR, Singapore. A. A.
was supported by a Post Graduate Scholarship from the Natural Sciences and
Engineering Research Council of Canada.

## Disclosures

The authors declare no conflicts of interests.

## References

  * [1] M. Atatüre, D. Englund, N. Vamivakas, S.-Y. Lee, and J. Wrachtrup, “Material platforms for spin-based photonic quantum technologies,” Nature Reviews Materials 3, 38–51 (2018).
  * [2] P. C. Humphreys, N. Kalb, J. P. J. Morits, R. N. Schouten, R. F. L. Vermeulen, D. J. Twitchen, M. Markham, and R. Hanson, “Deterministic delivery of remote entanglement on a quantum network,” Nature 558, 268–273 (2018).
  * [3] C. E. Bradley, J. Randall, M. H. Abobeih, R. C. Berrevoets, M. J. Degen, M. A. Bakker, M. Markham, D. J. Twitchen, and T. H. Taminiau, “A ten-qubit solid-state spin register with quantum memory up to one minute,” Phys. Rev. X 9, 031045 (2019).
  * [4] N. Kalb, A. A. Reiserer, P. C. Humphreys, J. J. W. Bakermans, S. J. Kamerling, N. H. Nickerson, S. C. Benjamin, D. J. Twitchen, M. Markham, and R. Hanson, “Entanglement distillation between solid-state quantum network nodes,” Science 356, 928–932 (2017).
  * [5] M. K. Bhaskar, R. Riedinger, B. Machielse, D. S. Levonian, C. T. Nguyen, E. N. Knall, H. Park, D. Englund, M. Lončar, D. D. Sukachev, and M. D. Lukin, “Experimental demonstration of memory-enhanced quantum communication,” Nature 580, 60–64 (2020).
  * [6] Y. Chu, N. P. de Leon, B. J. Shields, B. Hausmann, R. Evans, E. Togan, M. J. Burek, M. Markham, A. Stacey, A. S. Zibrov, A. Yacoby, D. J. Twitchen, M. Loncar, H. Park, P. Maletinsky, and M. D. Lukin, “Coherent optical transitions in implanted nitrogen vacancy centers,” Nano letters 14, 1982–1986 (2014).
  * [7] M. Ruf, M. IJspeert, S. van Dam, N. de Jong, H. van den Berg, G. Evers, and R. Hanson, “Optically coherent nitrogen-vacancy centers in micrometer-thin etched diamond membranes,” Nano Letters 19, 3987–3992 (2019).
  * [8] D. D. Sukachev, A. Sipahigil, C. T. Nguyen, M. K. Bhaskar, R. E. Evans, F. Jelezko, and M. D. Lukin, “Silicon-vacancy spin qubit in diamond: a quantum memory exceeding 10 ms with single-shot state readout,” Phys. Rev. Lett. 119, 223602 (2017).
  * [9] B. C. Rose, D. Huang, Z.-H. Zhang, P. Stevenson, A. M. Tyryshkin, S. Sangtawesin, S. Srinivasan, L. Loudin, M. L. Markham, A. M. Edmonds, D. J. Twitchen, S. A. Lyon, and N. P. de Leon, “Observation of an environmentally insensitive solid-state spin defect in diamond,” Science 361, 60–63 (2018).
  * [10] B. L. Green, S. Mottishaw, B. G. Breeze, A. M. Edmonds, U. F. S. D’Haenens-Johansson, M. W. Doherty, S. D. Williams, D. J. Twitchen, and M. E. Newton, “Neutral silicon-vacancy center in diamond: Spin polarization and lifetimes,” Phys. Rev. Lett. 119, 096402 (2017).
  * [11] B. C. Rose, G. Thiering, A. M. Tyryshkin, A. M. Edmonds, M. L. Markham, A. Gali, S. A. Lyon, and N. P. de Leon, “Strongly anisotropic spin relaxation in the neutral silicon vacancy center in diamond,” Phys. Rev. B 98, 235140 (2018).
  * [12] Z.-H. Zhang, P. Stevenson, G. Thiering, B. C. Rose, D. Huang, A. M. Edmonds, M. L. Markham, S. A. Lyon, A. Gali, and N. P. de Leon, “Optically detected magnetic resonance in neutral silicon vacancy centers in diamond via bound exciton states,” Physical Review Letters 125, 237402 (2020).
  * [13] R. E. Evans, M. K. Bhaskar, D. D. Sukachev, C. T. Nguyen, A. Sipahigil, M. J. Burek, B. Machielse, G. H. Zhang, A. S. Zibrov, E. Bielejec, H. Park, M. Lončar, and M. D. Lukin, “Photon-mediated interactions between quantum emitters in a diamond nanocavity,” Science 362, 662–665 (2018).
  * [14] Q. Li, M. Davanço, and K. Srinivasan, “Efficient and low-noise single-photon-level frequency conversion interfaces using silicon nanophotonics,” Nature Photonics 10, 406–414 (2016).
  * [15] C. T. Nguyen, D. D. Sukachev, M. K. Bhaskar, B. Machielse, D. S. Levonian, E. N. Knall, P. Stroganov, C. Chia, M. J. Burek, R. Riedinger, H. Park, M. Lončar, and M. D. Lukin, “An integrated nanophotonic quantum register based on silicon-vacancy spins in diamond,” Phys. Rev. B 100, 165428 (2019).
  * [16] R. Nelz, J. Görlitz, D. Herrmann, A. Slablab, M. Challier, M. Radtke, M. Fischer, S. Gsell, M. Schreck, C. Becher, and E. Neu, “Toward wafer-scale diamond nano- and quantum technologies,” APL Materials 7, 011108 (2019).
  * [17] C. P. Dietrich, A. Fiore, M. G. Thompson, M. Kamp, and S. Höfling, “GaAs integrated quantum photonics: towards compact and multi-functional quantum photonic integrated circuits,” Laser & Photonics Reviews 10, 870–894 (2016).
  * [18] D. J. Wilson, K. Schneider, S. Hönl, M. Anderson, Y. Baumgartner, L. Czornomaz, T. J. Kippenberg, and P. Seidler, “Integrated gallium phosphide nonlinear photonics,” Nature Photonics 14, 57–62 (2020).
  * [19] K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot–cavity system,” Nature 445, 896–899 (2007).
  * [20] D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vučković, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
  * [21] K. Kuruma, Y. Ota, M. Kakuda, S. Iwamoto, and Y. Arakawa, “Surface-passivated high-Q GaAs photonic crystal nanocavity with quantum dots,” APL Photonics 5, 046106 (2020).
  * [22] M. Mitchell, A. C. Hryciw, and P. E. Barclay, “Cavity optomechanics in gallium phosphide microdisks,” Applied Physics Letters 104, 141104 (2014).
  * [23] K. Schneider, Y. Baumgartner, S. Hönl, P. Welter, H. Hahn, D. J. Wilson, L. Czornomaz, and P. Seidler, “Optomechanics with one-dimensional gallium phosphide photonic crystal cavities,” Optica 6, 577–584 (2019).
  * [24] N. H. Wan, T.-J. Lu, K. C. Chen, M. P. Walsh, M. E. Trusheim, L. De Santis, E. A. Bersin, I. B. Harris, S. L. Mouradian, I. R. Christen, E. S. Bielejec, and D. Englund, “Large-scale integration of artificial atoms in hybrid photonic circuits,” Nature 583, 226–231 (2020).
  * [25] D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučković, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Letters 10, 3922–3926 (2010).
  * [26] P. E. Barclay, K.-M. Fu, C. Santori, and R. G. Beausoleil, “Hybrid photonic crystal cavity and waveguide for coupling to diamond NV-centers,” Opt. Express 17, 9588–9601 (2009).
  * [27] M. Gould, E. R. Schmidgall, S. Dadgostar, F. Hatami, and K.-M. C. Fu, “Efficient extraction of zero-phonon-line photons from single nitrogen-vacancy centers in an integrated GaP-on-diamond platform,” Phys. Rev. Applied 6, 011001 (2016).
  * [28] A. M. Dibos, M. Raha, C. M. Phenicie, and J. D. Thompson, “Atomic source of single photons in the telecom band,” Phys. Rev. Lett. 120, 243601 (2018).
  * [29] M. Raha, S. Chen, C. M. Phenicie, S. Ourari, A. M. Dibos, and J. D. Thompson, “Optical quantum nondemolition measurement of a single rare earth ion qubit,” Nature Communications 11, 1605 (2020).
  * [30] S. Chen, M. Raha, C. M. Phenicie, S. Ourari, and J. D. Thompson, “Parallel single-shot measurement and coherent control of solid-state spins below the diffraction limit,” Science 370, 592–595 (2020).
  * [31] P. E. Barclay, K.-M. C. Fu, C. Santori, A. Faraon, and R. G. Beausoleil, “Hybrid nanocavity resonant enhancement of color center emission in diamond,” Phys. Rev. X 1, 011007 (2011).
  * [32] E. R. Schmidgall, S. Chakravarthi, M. Gould, I. R. Christen, K. Hestroffer, F. Hatami, and K.-M. C. Fu, “Frequency control of single quantum emitters in integrated photonic circuits,” Nano Letters 18, 1175–1179 (2018).
  * [33] P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87, 347–400 (2015).
  * [34] Q. Quan and M. Loncar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express 19, 18529–18542 (2011).
  * [35] S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
  * [36] H. T. Dung, S. Y. Buhmann, and D.-G. Welsch, “Local-field correction to the spontaneous decay rate of atoms embedded in bodies of finite size,” Phys. Rev. A 74, 023803 (2006).
  * [37] A. Dréau, A. Tchebotareva, A. E. Mahdaoui, C. Bonato, and R. Hanson, “Quantum frequency conversion of single photons from a nitrogen-vacancy center in diamond to telecommunication wavelengths,” Phys. Rev. Applied 9, 064031 (2018).
  * [38] A. Tchebotareva, S. L. N. Hermans, P. C. Humphreys, D. Voigt, P. J. Harmsma, L. K. Cheng, A. L. Verlaan, N. Dijkhuizen, W. de Jong, A. Dréau, and R. Hanson, “Entanglement between a diamond spin qubit and a photonic time-bin qubit at telecom wavelength,” Phys. Rev. Lett. 123, 063601 (2019).
  * [39] C. J. McKinstrie, J. D. Harvey, S. Radic, and M. G. Raymer, “Translation of quantum states by four-wave mixing in fibers,” Opt. Express 13, 9131–9142 (2005).
  * [40] A. Singh, Q. Li, S. Liu, Y. Yu, X. Lu, C. Schneider, S. Höfling, J. Lawall, V. Verma, R. Mirin, S. W. Nam, J. Liu, and K. Srinivasan, “Quantum frequency conversion of a quantum dot single-photon source on a nanophotonic chip,” Optica 6, 563–569 (2019).
  * [41] L. Chang, W. Xie, H. Shu, Q.-F. Yang, B. Shen, A. Boes, J. D. Peters, W. Jin, C. Xiang, S. Liu, G. Moille, S.-P. Yu, X. Wang, K. Srinivasan, S. B. Papp, K. Vahala, and J. E. Bowers, “Ultra-efficient frequency comb generation in AlGaAs-on-insulator microresonators,” Nature Communications 11, 1331 (2020).
  * [42] K. Uesaka, K.-Y. Wong, M. E. Marhic, and L. G. Kazovsky, “Wavelength exchange in a highly nonlinear dispersion-shifted fiber: theory and experiments,” IEEE Journal of Selected Topics in Quantum Electronics 8, 560–568 (2002).
  * [43] M. E. Marhic, Y. Park, F. S. Yang, and L. G. Kazovsky, “Widely tunable spectrum translation and wavelength exchange by four-wave mixing in optical fibers,” Opt. Lett. 21, 1906–1908 (1996).
  * [44] L. Chang, A. Boes, P. Pintus, J. D. Peters, M. Kennedy, X.-W. Guo, N. Volet, S.-P. Yu, S. B. Papp, and J. E. Bowers, “Strong frequency conversion in heterogeneously integrated GaAs resonators,” APL Photonics 4, 036103 (2019).
  * [45] X. Lu, G. Moille, Q. Li, D. A. Westly, A. Singh, A. Rao, S.-P. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Efficient telecom-to-visible spectral translation through ultralow power nonlinear nanophotonics,” Nature Photonics 13, 593–601 (2019).
  * [46] A. W. Elshaari, W. Pernice, K. Srinivasan, O. Benson, and V. Zwiller, “Hybrid integrated quantum photonic circuits,” Nature Photonics 14, 285–298 (2020).
  * [47] P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25, 554–556 (2000).
  * [48] A. Rodriguez, M. Soljačić, J. D. Joannopoulos, and S. G. Johnson, “$\chi^{(2)}$ and $\chi^{(3)}$ harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15, 7303–7318 (2007).
  * [49] S. Fujii and T. Takasumi, “Dispersion engineering and measurement of whispering gallery mode microresonator for Kerr frequency comb generation,” Nanophotonics 9, 1087–1104 (2020).
  * [50] W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser & Photonics Reviews 6, 47–73 (2012).
  * [51] Z.-F. Bi, A. W. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K.-M. Wang, and S. G. Johnson, “High-efficiency second-harmonic generation in doubly-resonant $\chi^{(2)}$ microring resonators,” Opt. Express 20, 7526–7543 (2012).
  * [52] G. Grinblat, M. P. Nielsen, P. Dichtl, Y. Li, R. F. Oulton, and S. A. Maier, “Ultrafast sub–30-fs all-optical switching based on gallium phosphide,” Science Advances 5, 1–6 (2019).
  * [53] D. J. Wilson, S. Hönl, K. Schneider, M. Anderson, T. J. Kippenberg, and P. Seidler, “Gallium phosphide microresonator frequency combs,” in _Conference on Lasers and Electro-Optics,_ (Optical Society of America, 2018), p. SW3A.1.
  * [54] R. Katsumi, Y. Ota, M. Kakuda, S. Iwamoto, and Y. Arakawa, “Transfer-printed single-photon sources coupled to wire waveguides,” Optica 5, 691–694 (2018).
  * [55] M. Gould, S. Chakravarthi, I. R. Christen, N. Thomas, S. Dadgostar, Y. Song, M. L. Lee, F. Hatami, and K.-M. C. Fu, “Large-scale GaP-on-diamond integrated photonics platform for NV center-based quantum information,” J. Opt. Soc. Am. B 33, B35–B42 (2016).
  * [56] B. Diler, S. J. Whiteley, C. P. Anderson, G. Wolfowicz, M. E. Wesson, E. S. Bielejec, F. Joseph Heremans, and D. D. Awschalom, “Coherent control and high-fidelity readout of chromium ions in commercial silicon carbide,” npj Quantum Information 6, 11 (2020).
  * [57] G. Wolfowicz, C. P. Anderson, B. Diler, O. G. Poluektov, F. J. Heremans, and D. D. Awschalom, “Vanadium spin qubits as telecom quantum emitters in silicon carbide,” Science Advances 6, eaaz1192 (2020).


# LLMs for User Interest Exploration in Large-scale Recommendation Systems

Jianling Wang  Google DeepMind<EMAIL_ADDRESS>,  Haokai Lu  Google
DeepMind<EMAIL_ADDRESS>,  Yifan Liu  Google<EMAIL_ADDRESS>,  He Ma
Google<EMAIL_ADDRESS>,  Yueqi Wang  Google<EMAIL_ADDRESS>,  Yang Gu
Google<EMAIL_ADDRESS>,  Shuzhou Zhang  Google<EMAIL_ADDRESS>,
Ningren Han  Google<EMAIL_ADDRESS>,  Shuchao Bi  Google
<EMAIL_ADDRESS>,  Lexi Baugher  Google<EMAIL_ADDRESS>,  Ed H. Chi
Google DeepMind<EMAIL_ADDRESS>and  Minmin Chen  Google DeepMind
<EMAIL_ADDRESS>
(2018)

###### Abstract.

Traditional recommendation systems are subject to a strong feedback loop by
learning from and reinforcing past user-item interactions, which in turn
limits the discovery of novel user interests. To address this, we introduce a
hybrid hierarchical framework combining Large Language Models (LLMs) and
classic recommendation models for user interest exploration. The framework
controls the interfacing between the LLMs and the classic recommendation
models through “interest clusters”, the granularity of which can be explicitly
determined by algorithm designers. It recommends the next novel interests by
first representing “interest clusters” using language, and employs a fine-
tuned LLM to generate novel interest descriptions that are strictly within
these predefined clusters. At the low level, it grounds these generated
interests to an item-level policy by restricting classic recommendation
models, in this case a transformer-based sequence recommender to return items
that fall within the novel clusters generated at the high level. We showcase
the efficacy of this approach on an industrial-scale commercial platform
serving billions of users. Live experiments show a significant increase in
both exploration of novel interests and overall user enjoyment of the
platform.

Large Language Models, Recommendation System, User Interest Exploration

* indicates Equal Contribution

††copyright: acmcopyright††journalyear: 2018††doi:
10.1145/1122445.1122456††conference: Woodstock ’18: ACM Symposium on Neural
Gaze Detection; June 03–05, 2018; Woodstock, NY††booktitle: Woodstock ’18: ACM
Symposium on Neural Gaze Detection, June 03–05, 2018, Woodstock, NY††price:
15.00††isbn: 978-1-4503-XXXX-X/18/06††ccs: Information systems Information
retrieval

##  1\. Introduction

Recommendation systems are indispensable in helping users navigate the vast
and ever-growing content on the web nowadays. These systems however are often
subject to a strong feedback loop (Chaney et al., 2018; Mansoury et al.,
2020), recommending items similar to a user’s past behavior. Classic
recommendation systems infer a user’s next interest based on their historical
interactions. While this can be effective for short-term engagement, it limits
users from discovering novel interests, leading to content fatigue. Recent
research highlights the importance of user interest exploration (Su et al.,
2024; Chen et al., 2021; Chen, 2021; Mahajan et al., 2023; Song et al., 2022),
aiming to introduce diverse content that goes beyond a user’s historical
preferences. Effectively introducing novel interests to users are however
challenging due to the vast interest space and the high uncertainty of a
user’s affinity to previously unseen interests (Chen et al., 2021; Wu et al.,
2024).

Recent breakthroughs in Large Language Models (LLMs) (Anil et al., 2023; Brown
et al., 2020; Touvron et al., 2023) and other foundation models offer exciting
opportunities to revolutionize recommendation systems (Bao et al., 2023; Dai
et al., 2023; Lin et al., 2024; Wang et al., 2024; Christakopoulou et al.,
2023). The pre-trained world knowledge in these models holds the potential to
break recommendation feedback loops by introducing diverse and serendipitous
recommendations, addressing the challenge of user interest exploration. While
prior work (Li et al., 2023b, c; Hou et al., 2023b; Geng et al., 2022) has
demonstrated the potential of using LLMs for recommendation by translating
recommendation problems into natural language processing tasks, deploying
these approaches in real-world industrial recommendation systems remain
extremely challenging as: (1) unlike domain-specific recommendation models,
LLMs lack deep knowledge of the massive, and rapidly evolving item corpus on
industrial-scale online platforms (e.g., more than 500 hours of content are
uploaded to YouTube every minute (Blog, 2023; Hale, 2019), a new track is
uploaded to Spotify every second (Ingham, 2023)); (2) off-the-shelf LLMs are
unaware of the collaborative signals from users, failing to capture domain-
specific user behaviors; and (3) the latency and cost of serving LLMs per user
request are prohibitively large, cannot meet the O(100ms) response time
expected and production Query-Per-Second (QPS) required on industrial
recommendation platforms.

To overcome the above challenges, we introduce a hybrid hierarchical planning
paradigm combining LLMs and classic recommendation models (as shown in Figure
1) for user interest exploration in large-scale recommendation systems. At the
high level, considering the massive number of incoming items in the system,
instead of directly predicting the next item, we use LLMs to infer the next
novel interest. At the low level, to leverage classic recommendation models
with strong personalization, we ground these novel interests to item
recommendations by ”restricting” conventional transformer-based sequence
models (Chen et al., 2019; Shaw et al., 2018) to items within the ”clusters”
defined by those novel interests. By combining the best of both worlds, the
hybrid approach leverages LLMs’ reasoning and generalization capability in
exploring user’s novel interests effectively, at the same time bridges the
knowledge gap by relying on domain-specific models for actual item
recommendation. We further perform supervised fine-tuning (SFT) with real-
world novel consumption behaviors for in-domain user alignment, and also
enable LLMs to perform controlled generation, producing novel interest
descriptions that directly match one of the pre-defined clusters. The
controlled generation allow algorithm designers to easily define the
granularity of the interests generated by LLMs for different applications,
which is critical for effectively exploring the interest space. We find
diversification and label balance treatment while curating the SFT data
significantly mitigate the long-tailed distribution of LLM generation, and
thus improves interest exploration efficiency. To address the LLM inference
challenge, we propose to use topically coherent interest clusters with
cluster-level descriptions to represent recommendation objects, i.e, both the
historical user interests and the recommended next novel interests. By using a
small number of historical consumed clusters as high-level user interest, we
pre-compute the novel interest transitions offline with LLM bulk inference,
which can be then be served online with simple table lookup operations. In
summary, we make the following contributions:

  * $\bullet$

We propose a hybrid hierarchical framework that combines LLM’s reasoning and
generalization capabilities with classic recommendation models with strong
personalization and grounded item corpus knowledge for effective user interest
exploration.

  * $\bullet$

We fine-tune LLMs using a diverse and balanced set of novel interest
transitions curated from real-world user interactions for controlled
generation and user behavior alignment, to ensure LLMs generate novel
interests that match one of the predefined interest ”clusters” and align with
actual user behaviors.

  * $\bullet$

We propose to adopt topical clusters instead of items to represent user’s
high-level interests. The coarser representation allows us to limit the length
of historical cluster sequence used to represent dynamic user interests and
move the expensive LLM inference to offline stage, making it feasible to serve
LLM generated novel interest transitions online.

  * $\bullet$

We validate our method through live experiments on a large commercial
recommendation platform with billions of users. The results clearly show our
approach successfully expands user interests while boosting user enjoyment of
the platform demonstrated through more active users with longer dwell time.

Figure 1. LLM-powered hybrid hierarchical planning diagram for user interest
exploration.

##  2\. Related Work

LLMs for Recommendation Systems. Application of LLMs to recommendation systems
is a rapidly growing research area. Some studies explore using LLMs directly
for generating recommendations (Bao et al., 2023; Dai et al., 2023; Geng et
al., 2023; Hou et al., 2023b; Li et al., 2023c; Liu et al., 2023b), while
others focus on augmenting traditional recommendation models with LLM-powered
feature engineering (Hou et al., 2023a; Yu et al., 2022) or enriched user/item
representations (Li et al., 2023a; Liu et al., 2023a; Xi et al., 2023). The
computational cost of LLMs however presents a critical challenge. Directly
using them for large-scale retrieval is expensive and hinders adoption. Wang
et al. (Wang et al., 2024) use LLMs as data augmenters for conventional
recommendation systems during training, to improve model performance without
additional serving cost. Different from prior work, we focus on directly
incorporating LLM-generated content to break the feedback loop, aiming for
more diverse and serendipitous recommendations while maintaining efficiency.

User Interest Exploration. Prior research has established the benefits of User
Interest Exploration in recommendation systems, demonstrating its ability to
expand user preferences and enhance long-term engagement (Chen et al., 2021;
Chen, 2021; Su et al., 2024). However, a key challenge lies in the inherent
closed-loop nature of existing systems (Chaney et al., 2018; Mansoury et al.,
2020; Chen et al., 2021). Training data is primarily derived from past user-
item interactions, limiting the system’s ability to explore truly novel
interests. While methods like PIE (Mahajan et al., 2023) address this to
certain extent through user-creator affinity and online bandit formulations,
they remain confined by the system’s internal knowledge (Chen et al., 2021).
Our work introduces a novel approach that integrates world knowledge from LLMs
to overcome these limitations.

##  3\. Method

In this section, we introduce the hybrid hierarchical planning paradigm and
the LLM fine-tuning process designed to enable controlled generation and user
behavior alignment, to apply LLMs in real-world large-scale recommenders.

###  3.1. Preliminaries

The sheer number of items and the constant influx of new items on online
platforms make LLM planning at the individual item-level infeasible. Instead,
we leverage the planning capabilities of LLMs at the item interest-level to
reduce the planning space. A prerequisite for efficient hierarchical planning
is a set of high-quality item interest clusters, where items within each
cluster are topically coherent. Following the same procedure as in (Chang et
al., 2024), we group items into $N$ traffic-weighted equal sized clusters
based on their topical coherence, a method proven to scale well to the
magnitude of our problem. To create these clusters, we first represent each
item as a 256-dimensional embedding based on its metadata (title, hashtags,
etc.) and content (frames and audio). Then, we connect items in a graph based
on their similarity and cluster it into traffic-balanced clusters. This
clustering process is repeated multiple times to create a 4-level tree
structure, with each item associated with different tree levels. Higher-level
clusters represent broader topics, while lower-level clusters represent more
specific ones. These clusters in each level, denoted by
$\mathcal{C}^{l}=\\{c_{1}^{l},c_{2}^{l},...,c_{M_{l}}^{l}\\},l=1,2,3,4$,
represent different user interests, with each cluster linked to a set of
keywords describing its theme. Here $M_{l}$ denotes the number of clusters
within level $l$, with $M_{4}>M_{3}>M_{2}>M_{1}$. Each item belongs to a
single interest cluster in each level. As discussed in (Chang et al., 2024),
we focus on level-2 clusters to balance granularity and feasible planning
space111To reduce notation complexity, we drop level $l$ in cluster moving
forward..

###  3.2. Hybrid Hierarchical Planning

The hybrid approach combines a LLM to produce a language policy that generates
novel interests on the high-level, and a classic recommendation models to
produce an item policy that grounds these language-based interests to the low-
level item space. Such a hybrid approach combines the strength of LLMs in
reasoning and generalization, and domain-specific recommendation models in
handling item dynamics and enhanced personalization.

High-level language policy. Given the historical user interest representation
by language, we first use LLM to learn a high-level language policy that
generates novel user interests. Instead of using item descriptions to
represent users, we propose to adopt cluster descriptions (i.e., a set of
keywords) to represent user’s consumption history, i.e., a user’s historical
interest is represented as a sequence of her $K$ most recent interacted unique
clusters, with each cluster represented by its description. Specifically, with
a user’s previously consumed unique clusters, we can ask LLM to generate the
next novel interest with the prompt illustrated in Figure 2.

Figure 2. Prompt for Novel Interest Prediction when $K=2$.

Practical implication. One major challenge of deploying LLM to industrial-
scale recommendation system lies in its prohibitively high inference cost
failing to meet latency and QPS requirements. Empirically, we find that
relying on a small number of historical clusters to represent each user (e.g.,
$K=2$) can effectively balance representation granularity and computation
efficiency. In our experiment, the level-2 clustering produced 761 clusters.
We can therefore enumerate all $761*761=579,121$ cluster pairs and perform a
batch inference with LLM to obtain novel interests for each cluster pair under
just a few hours. These novel interests, together with the input cluster
pairs, could be stored in a table. During online serving as a new user request
comes in, we first represent the user by sampling $K=2$ items from their watch
history22230-day user history are used in sampling, and items with high-
quality interactions are more likely to be sampled., and convert them into the
cluster pair for lookup to determine the recommended novel interest cluster.

Low-level item policy. Once the language based novel user interest is
obtained, the next step is to convert it to item-level recommendation policy.
A straight-forward approach is to rely on search engine (Li et al., 2023c) to
retrieve the most relevant items according to the keywords of the novel
interest. The search results however often lack personalization since these
language based novel interests can still be broad and lack specificity. To
enhance personalization, we propose to reuse domain specific recommendation
models, specifically transformer-based sequential recommender model (Chen et
al., 2019; Shaw et al., 2018), but restrict the items to clusters prescribed
by the language based novel interests. Specifically, we follow the two steps:
(i) map the generated novel interests to cluster ID space, and (ii) restrict
the original item level softmax policy on these cluster IDs, to retrieve items
only from these clusters.

Figure 3. Label (i.e., generated by fine-tuned LLM) Distribution: X-axis
represents label frequency; Y-axis represents the percentage of labels within
each frequency range.

Controlled generation. The remaining challenges are how to specify the
granularity of the LLM generated interests and map the generated novel
interests to cluster IDs. Free-form responses from LLMs can be arbitrary,
which are unlikely to be directly matched to the predefined cluster
descriptions. We control the granularity of the generation through the
hierarchical clustering and picking the cluster level explained in Section
3.1. Furthermore, appropriate finetuning as detailed in Section 3.3 enables
LLMs to speak the language of interest clusters, producing cluster
descriptions that exactly match one of the predefined clusters.

(a) Control Generation Capability & Alignment Learning (b) Novelty (x-axis)
and Quality (y-axis) Comparison (c) Improvement of UCI@N

Figure 4. (a) Model Finetuning Process. (b) and (c) Comparison between
different recommenders in live experiments.

###  3.3. Fine-Tuning for User Behavior Alignment

LLMs trained on massive publicly available data on the Internet contains rich
global knowledge, it however lacks capabilities to perform: 1) controlled
generation (i.e., generate in the interest cluster space) and 2) domain-
specific user behavior alignment. We propose to inject these domain specific
knowledge through supervised fine-tuning using a dataset curated from real
user watch histories on the commercial platform. The quality of data used for
fine-tuning is thus crucial for its success.

Diversified Data Curation. Take K=2 as an example. Each fine-tuning data
sample, denoted as $[(C_{1},C_{2}),C_{L}]$, consists of a cluster pair
$(C_{1},C_{2})$ to form the prompt and the subsequent novel cluster $C_{L}$ as
the finetune label. By definition of novelty, $C_{L}$ must be different from
$C_{1}$ and $C_{2}$. Initially, we gathered approximately 250K
$[(C_{1},C_{2}),C_{L}]$ data samples from our log, focusing solely on high
quality interactions333In other words, these samples are novel interest
transitions existed in the log where a user was successfully introduced a
novel interest.. These samples are then grouped by their labels, and the
top-10 most frequently occurring cluster pairs are selected for each label,
forming the final data samples which is diverse and cover all the labels.
Following these steps, we obtain $761*10=7,610$ data samples (10 per label
cluster) and proceed to perform supervised fine-tuning for the LLM using these
samples.

In Figure 3, we plot the distributions of interest clusters generated by fine-
tuned LLMs on the 579,121 context cluster pairs. When using finetuning data of
low diversity, where we randomly select 7,610 transitions and their
corresponding subsequent clusters from the initial $250K$ to form the data,
the fine-tuned LLM generates interests that are highly-skewed, where a few
generated clusters have very high frequencies (depicted as Region B). When we
increase the diversity of our fine-tuning data, these dominant labels
disappear, and the number of generated clusters with very low frequency
(depicted in Region A) also decreases. Ensuring the fine-tuning data covers
all clusters evenly allows us to address the long-tailed distribution issue in
the model’s generated clusters. This treatment not only mitigates the feedback
loop effect in behavior data but also enhances overall user satisfaction as
shown in Section 4.

Control Generation Capability & User Behavior Alignment. The number of fine-
tuning steps determines the balance between the LLM’s global and task-specific
knowledge. Our fine-tuning process has two main objectives: (1) controlling
LLM generation to speak the language of interest clusters. We evaluate the
match rate of the generation from the fine-tuned LLM to determine if the
output matches exactly with one of the cluster descriptions; and (2) aligning
with real-world user transitions, measured by comparing the fine-tuned LLM’s
output with the successful user interest transition in both fine-tuning and
test set to compute recall. A higher recall indicates LLM learning the domain
specific novel transitions from the fine-tuned data, and aligning with user
behaviors.

In Figure 4 (a), with batch size of 16, we illustrate the changes in match
rate and recall as the fine-tuning steps progress. We note that formatting
learning, i.e., learning the language of intrest clusters, kicks in first,
peaking at around 2,000 steps. With a high match rate (over 99%), we can
efficiently map the generation to cluster ID space and restrict the original
item-level softmax policy on these clusters. Subsequently, the model begins to
align with user behaviors, resulting in a significant increase in recall (on
the fine-tuned set). Moreover, we find that the recall for a separate test set
increases following transition alignment, reaching its peak at around 3,000
steps before gradually decreasing. Therefore, we select models fine-tuned with
3,000 steps. Note that the recall on the test set is much lower than that of
the fine-tuning set, indicating LLM is still relying heavily on its global
knowledge instead of memorizing interest transitions in the log while
generating novel interests.

##  4\. Live Experiments

###  4.1. Experimental Setup

We conduct a series of live experiments on a commercial short-form video
recommendation platform that serves billions of users. Our experiments are
conducted with Gemini-Pro (Gemini Team Google, 2023), but the same fine-tuning
process and pipeline can be readily adapted to other LLMs. We set the number
of historical clusters for LLM inference $K=2$, it however can easily scale to
accommodate larger numbers in future iterations with a sparse table.

Baseline. We compare the proposed method to existing production models: (1)
Exploration-oriented models include: a Novelty-enhanced sequence recommender
(Chen et al., 2021) trained with labels from both positive and novel items
whose clusters have not appeared in user’s consumption history before;
Hierarchical contextual bandit (Song et al., 2022) based on the hierarchical
clusters introduced in 3.1 to explore user’s interests through a tree-based
LinUCB to obtain the next clusters, from which the sequential model is then
used to restrict the retrieval to items. Although these models are tailored to
explore user interests, they are trained on interest transitions existing in
the system and therefore are still subject to the feedback loop. (2)
Exploitation-oriented models include a regular two-tower model (Yang et al.,
2020) and transformer-based (Chen et al., 2019; Shaw et al., 2018) sequential
model trained on all positive user feedback. Our live experimental results
demonstrate our proposed method can lead to recommendation which are more
novel and in better quality compared to these existing models.

###  4.2. Results and Analysis

Novelty and Quality. In Figure 4 (b), we compare the proposed method with
various baseline models currently in production. Using the performance of
Hierarchical contextual bandit (Song et al., 2022) as the reference, we
measure the improvement of the other models. Specifically, we plot the
increase in ratio of novel impressions (considering only impressions from
interest clusters the user has never interacted with) to highlight
recommendation novelty (x-axis), and the increase in positive feedback rate to
demonstrate recommendation quality (y-axis). The proposed method recommends
more novel items compared to all the baseline methods (to the right on
x-axis). Additionally, it achieves much better quality than existing
exploration-oriented methods, comparable to exploitation-oriented methods
(high on x-axis). In other words, the proposed method presents an effective
approach to introduce users to novel interests that are of interests to the
user.

User Interest Exploration. To measure if the recommenders encourage users to
explore new interests, we use a metric called UCI@N, which tracks the number
of users who have consumed items from N unique clustered interests within the
past 7 days. Higher UCI@N indicates more users are consuming N interests. By
monitoring UCI@N for different values of N (20 to 200), we can gauge the
effectiveness of our system for user interest exploration. Figure 4(c)
summarizes the improvement of our method compared to Hierarchical Contextual
Bandit, to evaluate its effectiveness in user interest exploration. Notably,
our proposed method shows very significant improvement compared to the
prominent exploratory model currently deployed in production for different
values of $N$.

User Growth. At the same time, we monitor increase in overall watch time and
number of active users who had total watch time $>=$ 10 minute (in Figure 5),
to measure user growth on the short-form video platform. The x-axis represents
the experiment periods (the exact dates are redacted), and the y-axis shows
the relative percentage difference between the experiment and control, which
excludes the proposed system. Our method successfully broadens user interest
by recommending diverse and novel content, with user growth. This underscores
the quality and relevance of the recommended novel content.

(a) Overall Watch Time

(b) Number of Users watch ¿= 10min

Figure 5. The proposed method drives user growth.

##  5\. Conclusion

We present a hybrid approach to leverage LLMs for user interest exploration.
It combines the strength of LLMs in reasoning and generalization, and the
grounding of classic recommendation models. We showcase a successful recipe to
inject domain-specific recommendation knowledge to LLMs for controlled
generation and user behavior alignment. Extensive testing on a commercial
platform with billions of users has yielded significant improvements in both
exploration of novel interests and user growth. The future work will focus on
taking long-term effects into account to further improve hierarchical planning
with LLMs for recommendation systems.

## References

  * (1)
  * Anil et al. (2023) Rohan Anil, Andrew M Dai, Orhan Firat, Melvin Johnson, Dmitry Lepikhin, Alexandre Passos, Siamak Shakeri, Emanuel Taropa, Paige Bailey, Zhifeng Chen, et al. 2023\.  Palm 2 technical report.  _arXiv preprint arXiv:2305.10403_.
  * Bao et al. (2023) Keqin Bao, Jizhi Zhang, Yang Zhang, Wenjie Wang, Fuli Feng, and Xiangnan He. 2023.  Tallrec: An effective and efficient tuning framework to align large language model with recommendation.  _arXiv preprint arXiv:2305.00447_.
  * Blog (2023) Youtube Official Blog. 2023.  _YouTube by the Number_.  Retrieved January, 2023 from https://blog.youtube/press/
  * Brown et al. (2020) Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. 2020\.  Language models are few-shot learners. In _NeurIPS_.
  * Chaney et al. (2018) Allison JB Chaney, Brandon M Stewart, and Barbara E Engelhardt. 2018.  How algorithmic confounding in recommendation systems increases homogeneity and decreases utility. In _RecSys_.
  * Chang et al. (2024) Bo Chang, Changping Meng, He Ma, Shuo Chang, Yang Gu, Yajun Peng, Jingchen Feng, Yaping Zhang, Shuchao Bi, Ed H Chi, et al. 2024\.  Cluster Anchor Regularization to Alleviate Popularity Bias in Recommender Systems. In _Companion Proceedings of the ACM on Web Conference 2024_. 151–160.
  * Chen (2021) Minmin Chen. 2021.  Exploration in recommender systems. In _RecSys_.
  * Chen et al. (2019) Minmin Chen, Alex Beutel, Paul Covington, Sagar Jain, Francois Belletti, and Ed H Chi. 2019.  Top-k off-policy correction for a REINFORCE recommender system. In _WSDM_.
  * Chen et al. (2021) Minmin Chen, Yuyan Wang, Can Xu, Ya Le, Mohit Sharma, Lee Richardson, Su-Lin Wu, and Ed Chi. 2021.  Values of user exploration in recommender systems. In _RecSys_.
  * Christakopoulou et al. (2023) Konstantina Christakopoulou, Alberto Lalama, Cj Adams, Iris Qu, Yifat Amir, Samer Chucri, Pierce Vollucci, Fabio Soldo, Dina Bseiso, Sarah Scodel, et al. 2023\.  Large language models for user interest journeys.  _arXiv preprint arXiv:2305.15498_ (2023).
  * Dai et al. (2023) Sunhao Dai, Ninglu Shao, Haiyuan Zhao, Weijie Yu, Zihua Si, Chen Xu, Zhongxiang Sun, Xiao Zhang, and Jun Xu. 2023.  Uncovering ChatGPT’s Capabilities in Recommender Systems.  _arXiv preprint arXiv:2305.02182_.
  * Gemini Team Google (2023) Gemini Team Google. 2023.  Gemini: A family of highly capable multimodal models.  _arXiv preprint arXiv:2312.11805_ (2023).
  * Geng et al. (2022) Shijie Geng, Shuchang Liu, Zuohui Fu, Yingqiang Ge, and Yongfeng Zhang. 2022.  Recommendation as language processing (rlp): A unified pretrain, personalized prompt & predict paradigm (p5). In _ResSys_.
  * Geng et al. (2023) Shijie Geng, Juntao Tan, Shuchang Liu, Zuohui Fu, and Yongfeng Zhang. 2023.  VIP5: Towards Multimodal Foundation Models for Recommendation.  _arXiv preprint arXiv:2305.14302_.
  * Hale (2019) James Hale. 2019.  _More Than 500 Hours Of Content Are Now Being Uploaded To YouTube Every Minute_.  Retrieved January, 2023 from https://www.tubefilter.com/2019/05/07/number-hours-video-uploaded-to-youtube-per-minute/
  * Hou et al. (2023a) Yupeng Hou, Zhankui He, Julian McAuley, and Wayne Xin Zhao. 2023a.  Learning vector-quantized item representation for transferable sequential recommenders. In _TheWebConf_.
  * Hou et al. (2023b) Yupeng Hou, Junjie Zhang, Zihan Lin, Hongyu Lu, Ruobing Xie, Julian McAuley, and Wayne Xin Zhao. 2023b.  Large language models are zero-shot rankers for recommender systems.  _ECIR_.
  * Ingham (2023) Tim Ingham. 2023.  _Over 60,000 Tracks are Now Uploaded to Spotify Every Day. That’s Nearly One per Second._ Retrieved January, 2023 from https://www.musicbusinessworldwide.com/over-60000-tracks-are-now-uploaded-to-spotify-daily-thats-nearly-one-per-second/
  * Li et al. (2023a) Chen Li, Yixiao Ge, Jiayong Mao, Dian Li, and Ying Shan. 2023a.  TagGPT: Large Language Models are Zero-shot Multimodal Taggers.  _arXiv preprint arXiv:2304.03022_.
  * Li et al. (2023b) Jiacheng Li, Ming Wang, Jin Li, Jinmiao Fu, Xin Shen, Jingbo Shang, and Julian McAuley. 2023b.  Text Is All You Need: Learning Language Representations for Sequential Recommendation. In _KDD_.
  * Li et al. (2023c) Jinming Li, Wentao Zhang, Tian Wang, Guanglei Xiong, Alan Lu, and Gerard Medioni. 2023c.  GPT4Rec: A generative framework for personalized recommendation and user interests interpretation.  _arXiv preprint arXiv:2304.03879_.
  * Lin et al. (2024) Jianghao Lin, Rong Shan, Chenxu Zhu, Kounianhua Du, Bo Chen, Shigang Quan, Ruiming Tang, Yong Yu, and Weinan Zhang. 2024.  Rella: Retrieval-enhanced large language models for lifelong sequential behavior comprehension in recommendation.  _TheWebConf_.
  * Liu et al. (2023b) Junling Liu, Chao Liu, Renjie Lv, Kang Zhou, and Yan Zhang. 2023b.  Is chatgpt a good recommender? a preliminary study.  _arXiv preprint arXiv:2304.10149_.
  * Liu et al. (2023a) Qijiong Liu, Nuo Chen, Tetsuya Sakai, and Xiao-Ming Wu. 2023a.  A First Look at LLM-Powered Generative News Recommendation.  _arXiv preprint arXiv:2305.06566_.
  * Mahajan et al. (2023) Khushhall Chandra Mahajan, Amey Porobo Dharwadker, Romil Shah, Simeng Qu, Gaurav Bang, and Brad Schumitsch. 2023.  PIE: Personalized Interest Exploration for Large-Scale Recommender Systems. In _Companion Proceedings of the ACM Web Conference 2023_. 508–512.
  * Mansoury et al. (2020) Masoud Mansoury, Himan Abdollahpouri, Mykola Pechenizkiy, Bamshad Mobasher, and Robin Burke. 2020.  Feedback loop and bias amplification in recommender systems. In _CIKM_.
  * Shaw et al. (2018) Peter Shaw, Jakob Uszkoreit, and Ashish Vaswani. 2018.  Self-attention with relative position representations.  _arXiv preprint arXiv:1803.02155_ (2018).
  * Song et al. (2022) Yu Song, Shuai Sun, Jianxun Lian, Hong Huang, Yu Li, Hai Jin, and Xing Xie. 2022.  Show me the whole world: Towards entire item space exploration for interactive personalized recommendations. In _WSDM_.
  * Su et al. (2024) Yi Su, Xiangyu Wang, Elaine Ya Le, Liang Liu, Yuening Li, Haokai Lu, Benjamin Lipshitz, Sriraj Badam, Lukasz Heldt, Shuchao Bi, et al. 2024\.  Long-Term Value of Exploration: Measurements, Findings and Algorithms. In _WSDM_.
  * Touvron et al. (2023) Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al. 2023\.  Llama 2: Open foundation and fine-tuned chat models.  _arXiv preprint arXiv:2307.09288_.
  * Wang et al. (2024) Jianling Wang, Haokai Lu, James Caverlee, Ed Chi, and Minmin Chen. 2024.  Large Language Models as Data Augmenters for Cold-Start Item Recommendation.  _arXiv preprint arXiv:2402.11724_ (2024).
  * Wu et al. (2024) Haolun Wu, Yansen Zhang, Chen Ma, Fuyuan Lyu, Bowei He, Bhaskar Mitra, and Xue Liu. 2024.  Result Diversification in Search and Recommendation: A Survey.  _TKDE_ (2024).
  * Xi et al. (2023) Yunjia Xi, Weiwen Liu, Jianghao Lin, Jieming Zhu, Bo Chen, Ruiming Tang, Weinan Zhang, Rui Zhang, and Yong Yu. 2023.  Towards Open-World Recommendation with Knowledge Augmentation from Large Language Models.  _arXiv preprint arXiv:2306.10933_.
  * Yang et al. (2020) Ji Yang, Xinyang Yi, Derek Zhiyuan Cheng, Lichan Hong, Yang Li, Simon Xiaoming Wang, Taibai Xu, and Ed H Chi. 2020.  Mixed negative sampling for learning two-tower neural networks in recommendations. In _Companion Proceedings of the Web Conference 2020_.
  * Yu et al. (2022) Yang Yu, Fangzhao Wu, Chuhan Wu, Jingwei Yi, and Qi Liu. 2022.  Tiny-newsrec: Effective and efficient plm-based news recommendation. In _EMNLP_.