# Bidirectional electro-optic conversion reaching 1% efficiency with thin-film
lithium niobate

Yuntao Xu  Department of Electrical Engineering, Yale University, New Haven,
CT 06511, USA  These authors contributed equally to this Letter.  Ayed Al
Sayem  Department of Electrical Engineering, Yale University, New Haven, CT
06511, USA  These authors contributed equally to this Letter.  Linran Fan
Department of Electrical Engineering, Yale University, New Haven, CT 06511,
USA  Current address: College of Optical Sciences, The University of Arizona,
Tucson, Arizona 85721, USA  Sihao Wang  Department of Electrical Engineering,
Yale University, New Haven, CT 06511, USA  Risheng Cheng  Department of
Electrical Engineering, Yale University, New Haven, CT 06511, USA  Chang-Ling
Zou  Department of Electrical Engineering, Yale University, New Haven, CT
06511, USA  Wei Fu  Department of Electrical Engineering, Yale University, New
Haven, CT 06511, USA  Likai Yang  Department of Electrical Engineering, Yale
University, New Haven, CT 06511, USA  Mingrui Xu  Department of Electrical
Engineering, Yale University, New Haven, CT 06511, USA  Hong X. Tang
Department of Electrical Engineering, Yale University, New Haven, CT 06511,
USA  Corresponding author<EMAIL_ADDRESS>
###### Abstract

Superconducting cavity electro-optics (EO) presents a promising route to
coherently convert microwave and optical photons and distribute quantum
entanglement between superconducting circuits over long-distance through an
optical network. High EO conversion efficiency demands transduction materials
with strong Pockels effect and excellent optical transparency. Thin-film
Lithium Niobate (TFLN) offers these desired characteristics however so far has
only delivered unidirectional conversion with efficiencies on the order of
10-5, largely impacted by its prominent photorefractive (PR) effect at
cryogenic temperatures. Here we show that, by mitigating the PR effect and
associated charge-screening effect, the device’s conversion efficiency can be
enhanced by orders of magnitude while maintaining stable cryogenic operation,
thus allowing a demonstration of conversion bidirectionality and accurate
quantification of on-chip efficiency. With the optimized monolithic integrated
superconducting EO device based on TFLN-on-sapphire substrate, an on-chip
conversion efficiency of 1.02% (internal efficiency, $15.2\%$) is realized.
Our demonstration indicates that with further device improvement, it is
feasible for TFLN to approach unitary internal conversion efficiency.

##  1 Introduction

With superconducting qubits recently emerging as one of the most promising
platforms for quantum computation [1, 2, 3, 4, 5, 6] and optical photons being
the most suitable quantum information carrier [7, 8], efficient bidirectional
conversion between microwave and optical photons at the quantum level is in
critical demand for interfacing distributed quantum computation and quantum
communication systems [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22,
23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37]. Through this
microwave-to-optical interconnection, a hybrid system where quantum
information is processed by superconducting circuits and distributed with
photonic circuits is one of the most promising schemes to build large-scale
quantum networks [38, 39, 40, 41, 42]. A variety of hybrid platforms have been
demonstrated to realize efficient microwave-to-optical conversion, including
spin ensembles [20, 21, 22, 23], electro-optomechanics (EOM) [24, 25, 26, 27,
28, 29, 30, 31, 32, 33], rare-earth-doped crystal [34, 35], ferromagnetic
magnons [36, 37], and etc. The highest conversion efficiency has been
demonstrated in EOM systems using 3D optical cavity and megahertz mechanical
membranes [28].

Without relying on intermediate excitations to assist the conversion process,
the cavity electro-optics (EO) system directly utilizes the Pockels
nonlinearity of the material to realize microwave-to-optical conversion [9,
10]. In the cavity EO systems, a high frequency microwave resonator is
directly coupled to optical resonators without introducing suspended
structures or external magnetic fields. With favorable tunability and high
optical power handling capability, cavity EO system enables a robust high-
efficiency microwave-to-optical frequency conversion as experimentally
demonstrated in [13] at 2K, and recently at the microwave ground state in a
dilution refrigerator [16, 15]. The highest EO conversion efficiency has been
achieved in Aluminium Nitride (AlN) material platform reaching $2\%$ on-chip
conversion efficiency.

The efficiency of cavity EO conversion critically relies on the strength of
Pockels nonlinearity and the optical transparency of the transduction
materials. Among the few Pockels materials other than AlN, thin-film Lithium
Niobate (TFLN) is the most promising candidate because of its excellent
optical properties [43] along with strong Pockels nonlinearity, which is
around thirty times stronger than AlN. Very recently, there have been two
successful demonstrations of cavity EO conversion based on TFLN platform [17,
18], both realizing impressive vacuum coupling rate ($g_{eo}$) compared to AlN
material platform. Nevertheless, the achieved conversion efficiency is on the
order of $10^{-5}$. This is largely impeded by the prominent photorefractive
(PR) effect which has been particularly challenging for cryogenic LN devices
and constrains the sustainable pump power at cryogenic temperatures. Also
because of the resonance shift induced by the PR effect at parametric pump
powers, only unidirectional microwave-to-optical conversion has been achieved.

In this article, we demonstrate a hybrid cavity EO converter based on TFLN
optical cavities and superconducting niobium nitride (NbN) resonator reaching
$1.02\%$ on-chip efficiency and $15.2\%$ internal efficiency. The PR effect
and charge-screening effects in TFLN are mitigated by a significant margin by
incorporating new microwave and optical resonator designs. High conversion
efficiency is achieved at elevated pump power levels while maintaining stable
device operation at cryogenic temperatures. The improved efficiency and
stability not only lead to a demonstration of the desired bidirectional
conversion process but also enable the measurement of the converter’s full
scattering matrix for accurate calibration of the system conversion
efficiency. Currently, our device is limited by the use of high-throughput,
albeit low-efficient grating couplers and the parasitic loss of microwave
resonator due to radio frequency (RF) packaging. With further device
improvement in light coupling and cryogenic packaging, we project that the
TFLN EO converter could approach unitary internal conversion efficiency and
provide a highly competitive transduction platform for future quantum network
applications.

##  2 TFLN EO converter Design

Figure 1:  (a) Schematic layout of the TFLN cavity EO converter, where two
strongly coupled microring resonators (red) are co-integrated with an
“Ouroboros” microwave resonator (yellow). DC electrodes are utilized for on-
chip tuning of the optical modes. (b) Circuit representation of the cavity EO
system. The capacitor plate of the lumped-element microwave resonator is
coupled to the $\chi^{(2)}$ optical cavity. (c) Three wave-mixing EO
conversion process. The optical doublet corresponds to the symmetric and anti-
symmetric supermodes of the coupled microrings. A strong pump (red) supported
in the anti-symmetric mode parametrically stimulates the bidirectional
conversion of signal photons in the symmetric mode (blue) and the microwave
mode (yellow) through difference/sum-frequency generation. (d) and (e) False-
color SEM images of the EO converter device. Insets show the electric field
profiles of interacting optical and microwave modes.

Figure 1(a) illustrates the schematic layout of our TFLN-superconductor hybrid
cavity EO converter, which consists of a pair of strongly coupled ring
resonators patterned from x-cut TFLN and a superconducting microwave resonator
of Niobium Nitride (NbN). The microwave resonator (“Ouroboros”[44])
capacitively couples to one of the double rings for EO conversion, while a
pair of DC electrodes is coupled to the other microring for electrical tuning
of the optical resonance modes. The circuit representation of the cavity EO
system is illustrated in Fig. 1(b), where the electric field of a lumped-
circuit LC resonator overlaps with the optical cavity field within an EO
($\chi^{(2)}$ non-linearity) media through Pockels effect. As a result of the
cavity enhanced EO interaction at the triply-resonant condition, the input
microwave field modulates the optical pump and produces an optical sideband in
the signal mode. Reversely, a microwave field output can be generated by the
optical frequency mixing in the LN cavity, and thus realizes the photon-photon
quantum frequency conversion [12, 13].

This triply-resonant enhanced EO conversion scheme, as illustrated in Fig.
1(c) in frequency domain [13], is described by an interaction Hamiltonian

$H_{\mathrm{I}}=\hbar g_{eo}(ab^{\dagger}c+a^{\dagger}bc^{\dagger}).$ (1)

Here, $a$, $b$ and $c$ denote annihilation operators for the optical pump,
signal and microwave modes, respectively. $g_{eo}$ denotes the vacuum EO
interaction strength, which in turn is determined by the mode volume, triple-
mode overlap and the Pockels coefficient. The optical frequency doublet (Fig.
1(c)) corresponds to the symmetric and anti-symmetric supermodes of the
photonic molecule [45] induced by the strong mutual coupling between the
fundamental transverse electric (TE) modes of the double-microring resonators
[12, 16, 17, 18, 15]. To leverage the highest EO coefficient $r_{33}\sim
30\,\mathrm{pm/V}$ [46] in x-cut TFLN, we utilize the microwave mode with in-
plane electrical field. The corresponding microwave and optical mode profiles
are shown in the insets of Figs. 1(d) and (e).

To initiate quantum frequency conversion, the lower-frequency supermode in the
photonic molecule, i.e. the anti-symmetric optical mode $a$, is loaded with a
strong pump to produce a photon-number enhanced electro-optical linear
conversion. The advantage of the cavity enhanced coherent conversion is
quantified by the cooperativity $C=4n_{p}g_{eo}^{2}/\kappa_{b}\kappa_{c}$,
where $n_{p}$ is the intracavity pump photon number and $\kappa_{b}$,
$\kappa_{c}$ are the total energy loss rates for modes $b$ and $c$,
receptively. By fine-tuning of the DC bias, the frequency splitting of the
optical doublet can be tuned to match the microwave resonance frequency, and
fulfill the triply-resonant condition ($\omega_{a}+\omega_{c}=\omega_{b}$).
Under this ideal condition, the on-chip peak conversion efficiency is given
by,

$\eta=\frac{\kappa_{b,ex}}{\kappa_{b}}\frac{\kappa_{c,ex}}{\kappa_{c}}\frac{4C}{(1+C)^{2}}.$
(2)

Here, $\kappa_{b,ex}$ ($\kappa_{c,ex}$) is the external loss rates for mode
$b$ ($c$), and $\eta_{\mathrm{int}}=4C/(1+C)^{2}$ is the internal conversion
efficiency. Optimal conversion is achieved when $C=1$, and the corresponding
on-chip efficiency is eventually limited by the extraction ratio
$\kappa_{b,ex}\kappa_{c,ex}/\kappa_{b}\kappa_{c}$.

##  3 PR effect mitigation at cryogenic temperature

As indicated by Eq. 2, the EO conversion efficiency $\eta$ is proportional to
pump photon number. One of the major obstacles hindering high conversion
efficiency on TFLN platform is the strong PR effect and associated charge-
screening effect, which limit achievable intracavity pump power [17, 18]. The
PR effect in LN is a combination of cascaded processes that first builds up a
space-charge field in presence of light illumination and subsequently
modulates the refractive index of the material [46]. With the PR effect,
highly dynamic resonance shift prevents strong pump light from launching into
a stable resonance. Especially at cryogenic temperature, the relaxation time
of the PR effect is found to be extremely long, leading to an accumulated
space-charge field that modulate the resonance frequency [47]. Additionally,
the space-charge field induced by the PR effect can screen and even cancel the
external DC bias voltage, therefore disturb the alignment of resonances [48].
An illustration of this charge-screening effect is shown in Fig. 2, where DC
bias is applied to a LN double-microring resonator to tune the supermode
splitting. After the laser scans across the optical resonances for several
times, the DC tuning becomes ineffective and the supermode splitting $\Delta
f$ restores to its zero-bias value. The PR effect and its associated charge-
screening effect not only limit the intracavity pump power, but also hinder
future quantum applications that require long-time stable operation.

Figure 2:  (a) Laser-scan spectra of the optical resonances under charge-
screening effect. After illumination the supermode frequency splitting $\Delta
f$ remains unchanged despite of varying DC bias. (b) Laser-scan spectra of
optical resonances after PR effect mitigation. The DC tuning effect is
maintained after illumination, with no apparent charge-screening being
observed. (c) The supermode splitting $\Delta f$ as a function of DC bias with
and without PR mitigation. (d) The resonance frequency shift under light
illumination with and without PR mitigation.

We found the PR effect and the charge-screening effect are highly related to
the fabrication process. While the underlying mechanism remains to be
investigated, we identified that the commonly used intermediate layer of
silicon dioxide ($\mathrm{SiO_{2}}$) layer deposited on TFLN aggravates these
photo-induced charge effects. The details of these findings and the room
temperature PR effect characterizations can be found in Ref. [49]. The
effectiveness of this PR effect mitigation approach is also manifested at
cryogenic temperature, where the optical cavities without $\mathrm{SiO_{2}}$
cladding experience significantly reduced PR and charge-screening effect. With
this mitigation approach, the DC tuning can be maintained during illumination
(Fig. 2(b)), making it feasible to fine tune the optical frequency difference
to match the microwave resonance frequency (Fig. 2(c)). As the frequency
difference between two supermodes is stable during operation, no further
feedback on DC bias is required, which greatly simplifies the measurement. The
absolute resonance shift induce by the PR effect is also reduced by a
significant margin, as shown in Fig. 2(d). As a result, triple-resonance
condition can be easily obtained for boosted intracavity intensities after
compensating the weak PR-induced drift by a slow PID feedback on drive laser
wavelength.

##  4 Device fabrication and cryogenic characterization

Here we briefly outline the device fabrication process, which starts with
$600\text{\,}\mathrm{nm}$-thick TFLN bonded on a sapphire substrate (supplied
by NANOLN). Figures 1(d) and (e) show the false-color scanning electron
microscope (SEM) images of the fabricated EO converter. All structures are
patterned with electron beam lithography (EBL) using Hydrogen silsesquioxane
(HSQ) resist. Low-loss ridge waveguides and microrings are defined by etching
$350\text{\,}\mathrm{nm}$ into TFLN by $\mathrm{Ar^{+}}$ milling. The
microring resonators have a radius of $80\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ and a top width of $1.6\text{\,}\mathrm{\SIUnitSymbolMicro m}$. As shown
in Fig. 1(e), the majority of remaining $250\text{\,}\mathrm{nm}$ TFLN slab is
removed in a second $\mathrm{Ar^{+}}$ milling step in order to minimize the
total coverage of TFLN, leaving only a $3.5\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ wide pedestal to support the microring resonators. This is a crucial step
to suppress the microwave loss induced by the strong piezo-electricity of LN.
After patterning the optical structures, superconducting NbN is deposited on
the sapphire substrate using atomic layer deposition (ALD), followed by a
fluorine-based etching to define the microwave resonator and tuning
electrodes. The microwave resonator layout is adjusted to avoid directly
crossing over the uncladded optical structures.

Prior to cryogenic packaging, the as-fabricated device dies are characterized
separately in microwave and optical domains. A pair of grating couplers
designed for TE polarized light is used to couple light in and out the device.
The average intrinsic quality (Q) factor of the fundamental TE modes of the
microring resonator is measured to be $\sim 9\times 10^{5}$. For the microwave
readout, we utilize a coaxial cable terminated with a hoop antenna [22, 15].
While the optical transmission can be measured on die-level at room and
cryogenic temperatures showing no apparent change in performances, die-level
microwave Q testing is more involved because it has to be accomplished at
cryogenic temperatures. The superconducting resonator is first characterized
in a RF tight, compact cooper box package to suppress the undesired microwave
modes from coupling to the on-chip resonator. Under this condition, the device
exhibits an intrinsic Q of $9.7\times 10^{3}$ at $2.6\text{\,}\mathrm{K}$ when
tested at die-level, with the microwave reflection spectrum shown in Fig. 3
(trace A). The microwave Q measured here is most likely already limited by the
dielectric and piezoelectric coupling induced loss by the residual TFLN traces
supporting optical waveguides. In addition to the microwave loss induced by LN
itself, the microwave Q is significantly impacted by the device packaging. For
example, the wire bonds used for dc-tuning contribute directly to the
microwave loss. As indicated by trace B shown in Fig. 3, when measured with
wire bonds in the same closed box at $2.6\text{\,}\mathrm{K}$, the device
displays a reduced intrinsic Q of $5.4\times 10^{3}$.

Figure 3:  Microwave reflection spectrum of the device (A) in a closed copper
box (B) in a closed copper box with wire bonds (C) packaged with fiber-array
for conversion measurement. The inset shows the fitted intrinsic microwave
quality factors.

In the final EO conversion package, additional microwave loss also arises from
the cryogenic optical interfaces required to accommodate the fiber array. The
fiber array is manipulated by a set of attocubes for precision alignment,
preventing the use of a fully closed copper box. A copper box with open lid is
utilized instead, similar to the configuration previously used in AlN
microwave-to-optics experiment [31] where we did not observe significant Q
change before and after packaging. However, this is not the case for the TFLN
converter studied here. As shown in Fig. 3 (trace C), the device exhibits a
further degradation of microwave quality factor, and the extracted intrinsic Q
drops to $1.3\times 10^{3}$. We conjecture that the excess microwave loss is
mainly induced by the stronger piezoelectric coupling of LN (than AlN) to
spurious modes supported by the RF packaging. To mitigate this loss, it is
critical to further reduce the TFLN trace volume that does not participate in
the EO conversion, and utilize a RF packaging that can effectively suppress
spurious modes.

##  5 bidirectional microwave-to-optics conversion

Figure 4:  (a) Schematic of measurement setup. For CW measurement, the RF
signal generated by a vector network analyzer (VNA) is sent to the device
either as the microwave input or as the optical input through an optical
single-sideband modulator (SSBM). The output from the device is then sent back
to the VNA. For pulsed measurements, the pump is gated by an acoustic-optic
modulator (AOM) driven by an arbitrary wave generator (AWG), which also
triggers VNA. The pump is locked on resonance using a
proportional–integral–derivative (PID) controller. FPC: fiber polarization
controller. PD: photodetector. LNA: low-noise amplifier. HVS: high voltage
source. (b) Measured microwave reflection $S_{\mathrm{ee}}$, optical-to-
microwave conversion $S_{\mathrm{eo}}$, microwave-to-optical conversion
$S_{\mathrm{oe}}$ and optical reflection $S_{\mathrm{oo}}$. The peak pump
power is $-12.0\text{\,}\mathrm{dBm}$ in the waveguide and all matrix
coefficients are normalized to the output power of VNA.

The schematic setup for EO conversion measurement is presented in Fig. 4(a).
The device is loaded in a closed-cycle refrigerator (Cryomech) cooled down to
$1.9\text{\,}\mathrm{K}$ base temperature. A tunable telecom laser (Santec
710) amplified by erbium-doped fiber amplifier (EDFA) is tuned to the anti-
symmetric mode (lower frequency supermode) frequency as a parametric pump. In
order to compensate for the residual PR-induced slow resonance frequency
drift, 1% of the transmitted light from the device is sampled to provide
wavelength feedback to the laser through its build-in piezo. RF signal from a
vector network analyzer (VNA) is either directly sent to the device as the
microwave signal input or used to generate the optical signal input through
optical single-sideband modulation [13]. The microwave output from the
converter is analyzed after a low-noise amplifier at room temperature. The
optical output is collected and down-converted through heterodyne with the
pump laser by a high-speed photodetector and then sent to the VNA. For
measurement in high power regime, we reduce the thermal load to the device by
gating the pump light to $1\text{\,}\mathrm{ms}$ pulses, using a high
extinction acoustic-optic modulator (AOM) driven by an arbitrary waveform
generator at 10% duty cycle with a repetition of $10\text{\,}\mathrm{ms}$. In
the pulsed mode, each point of the VNA sweep is triggered by the AWG to
synchronize with the pump pulse.

Figure 5:  The on-chip conversion efficiency (blue) and cooperativity (red) as
a function of on-chip peak pump power. The discontinuity in the CW and pulsed
pump data is due to the use of different pairs of optical modes during the
measurements. The maximum efficiency is recorded with a peak pump power of
$13.0\text{\,}\mathrm{dBm}$, reaching an on-chip efficiency of $1.02\%$,
internal efficiency of $15.2\%$ and cooperativity of $0.041$. The dashed lines
are the linear predictions obtained from the data measured with a pulsed pump.
The measured intrinsic microwave Q under different optical pump power is
presented in the upper panel.

With a DC bias of $220\text{\,}\mathrm{V}$, the optical mode splitting is
tuned (at a rate of $\sim$
$0.6\text{\,}\mathrm{p}\mathrm{m}\mathrm{/}\mathrm{V}$) to match with the
microwave resonance frequency. Fig. 4 shows the full spectra of scattering
matrix elements employed for calibrating the conversion efficiency: optical
refection $S_{\mathrm{oo}}$, microwave refection $S_{\mathrm{ee}}$, microwave-
to-optical conversion $S_{\mathrm{oe}}$ and optical-to-microwave conversion
$S_{\mathrm{eo}}$. The bidirectional nature of the EO conversion is thus fully
established. The Lorentzian fit of the $S_{\mathrm{oe}}$ and $S_{\mathrm{eo}}$
spectral yield a $3\text{\,}\mathrm{dB}$ bandwidth matching the microwave
linewidth. The peak conversion efficiency is obtained by calibrating out the
off-chip gain and loss factor of each input and output signal path[26]:

$\eta=\frac{S_{\mathrm{eo,p}}S_{\mathrm{oe,p}}}{S_{\mathrm{oo,bg}}S_{\mathrm{ee,bg}}},$
(3)

where $S_{\mathrm{eo,p}}$ and $S_{\mathrm{eo,p}}$ are the peaks of conversion
spectra, $S_{\mathrm{oo,bg}}$ and $S_{\mathrm{oo,bg}}$ are the backgrounds of
reflection spectra, respectively.

We gradually increase the on-chip pump power from $-12.0\text{\,}\mathrm{dBm}$
to boost the on-chip conversion efficiency which is obtained from the above-
mentioned calibration method. Considering the loss and coupling
characteristics of microwave and optical cavities, we could also extract the
internal conversion efficiency $\eta_{\mathrm{int}}$ and thus cooperativity
$C$ from Eqn. 2 under different pump power, as shown in Fig. 5. We switch to
10% duty cycle pulsed mode from $-2.0\text{\,}\mathrm{dBm}$ on-chip power to
reduce the thermal load on the fridge. After extended exposure during CW
measurement, the pair of optical modes we used are no longer accessible due to
the accumulated charge. Therefore, we switch to another pair of optical modes
in the pulsed measurement, leading to a discontinuity in the data trace. The
detailed device characteristic is presented in the supplementary material.

The maximum on-chip conversion efficiency of $1.02\%$ (internal efficiency of
$15.2\%$) is extracted with a peak pump power adjusted to
$13.0\text{\,}\mathrm{dBm}$ in the waveguides. The corresponding cooperativity
reach a value of $0.041$, which is significantly higher than the recent
reported values [17]. We note that the cooperativity no longer increases
linearly with peak pump power in high power regime. This is attributed to the
quality factor degradation of the superconducting resonator, as shown in the
upper panel of Fig. 5. Similar microwave loss has also been observed in
previous studies [17, 18]. The source of the additional microwave loss could
be a combination of light absorption of the superconductor, thermo-optic
heating, and undesired coupling from cryogenic packaging. From a linear
fitting (dashed lines in Fig. 5(a) of the conversion efficiency in the low
power regime, the vacuum coupling rate can be estimated to be
$g_{eo}=2\pi\times 750\mathrm{Hz}$, which is within the same order of
magnitude compared to simulated value ($2\pi\times 1.5\mathrm{kHz}$, see
supplementary material).

##  6 Discussion, prospect and conclusion

According to Eqn. 2, the conversion performance of our current devices is
mostly limited by the microwave Q affected by device packaging for cryogenic
operation. The microwave Q, when measured on die-level, shows significantly
higher value ($\sim 10^{4}$) compared to prior works [18, 17]. However, in the
final packaged conversion device, the measured intrinsic quality factor
remains low compared to similar resonators patterned on other type of
substrates, such as AlN [13, 15]. With improved cryogenic packaging to
suppress parasitic losses, if the intrinsic Q of $\sim 10^{4}$ can be
recovered, unitary internal conversion efficiency ($C=1$) can be obtained at
the current pump power level. Also, the on-chip efficiency could be further
improved by engineering the external loss rate of optical and microwave modes.
Our current devices use grating couplers which introduce a insertion loss as
high as $12.0\text{\,}\mathrm{dB}$ per facet due to weak index contrast
between LN and sapphire substrate. By ultilizing side-coupled inverted tapers,
the insertion loss could be reduced to $3.4\text{\,}\mathrm{dB}$ per facet
[15, 50], which will also dramatically reduce the thermal-optic heating and
light absorption induced by scattered light. Finally, we note that the
microwave resonator is not at its ground state (thermal photon occupancy
$\bar{n}_{\mathrm{th}}\sim 5$) in this work. Future characterization of ground
state conversion will be done in a dilution refrigerator at milikelvin
temperature [15]. Using blue-detuned pump pulses and photon-counting setup,
non-classical correlation and entanglement between microwave and optical
photon can be demonstrated [51, 52].

In conclusion, we demonstrate that it is possible to mitigate the most
detrimental PR effect and charge-screening effects in TFLN and achieve
conversion efficiency up to $1.02\%$ maintaining stable device operation at
cryogenic temperatures. Such stable operation at cryogenic temperature not
only allows us to reach high conversion efficiency but also is fundamentally
critical for quantum applications such as generation of entangled microwave
and optical photon pairs, conversion of non-classical photon states from the
microwave to optical domain along with entanglement transfer [53]. Our device
performance can be further improved by proper cryogenic packaging and light
coupling. With such improvements, we anticipate to maintain high conversion
efficiency with sufficiently low pump power for ground state operation at
millikelvin temperature.

Funding. This work is funded by ARO under grant number W911NF-18-1-0020. HXT
acknowledges partial supports from NSF (EFMA-1640959), ARO (W911NF-19-2-0115)
and the Packard Foundation. Funding for substrate materials used in this
research was provided by DOE/BES grant under award number DE-SC0019406.

Acknowledgements. The authors thanks Michael Rooks, Yong Sun, Sean Rinehart
and Kelly Woods for support in the cleanroom and assistance in device
fabrication.

Disclosures. The authors declare no conflicts of interest.

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