# Direct writing of room temperature polariton condensate lattice by top-down
approach

Ravindra Kumar Yadav<EMAIL_ADDRESS>Department of Physics, The City
College of New York, 85 St. Nicholas Terrace, 85 St. Nicholas Terrace, New
York, 10031, USA.  Sitakanta Satapathy  Department of Physics, The City
College of New York, 85 St. Nicholas Terrace, 85 St. Nicholas Terrace, New
York, 10031, USA.  Prathmesh Deshmukh  Department of Physics, The City College
of New York, 85 St. Nicholas Terrace, 85 St. Nicholas Terrace, New York,
10031, USA.  Biswajit Datta  Department of Physics, The City College of New
York, 85 St. Nicholas Terrace, 85 St. Nicholas Terrace, New York, 10031, USA.
Addhyaya Sharma  Department of Physics, The City College of New York, 85 St.
Nicholas Terrace, 85 St. Nicholas Terrace, New York, 10031, USA.  Andrew
Olsson  Department of Chemistry, Indiana University, IN 47405, USA  Junsheng
Chen  Nano-Science Center and Department of Chemistry, University of
Copenhagen, Denmark.  Bo W. Laursen  Nano-Science Center and Department of
Chemistry, University of Copenhagen, Denmark.  Amar H. Flood  Department of
Chemistry, Indiana University, IN 47405, USA  Matthew Y. Sfeir  Photonics
Initiative, Advanced Science Research Center, City University of New York, New
York, 85 St. Nicholas Terrace, New York, 10031, USA.  Vinod M. Menon
<EMAIL_ADDRESS>Department of Physics, The City College of New York, 85
St. Nicholas Terrace, 85 St. Nicholas Terrace, New York, 10031, USA.

###### Abstract

Realizing lattices of exciton polariton condensates has been of much interest
owing to the potential of such systems to realize analog Hamiltonian
simulators and physical computing architectures. Prior work on polariton
condensate lattices has primarily been on GaAs-based systems, with the recent
advent of organic molecules and perovskite systems allowing room-temperature
operation. However, in most of these room temperature systems, the lattices
are defined using a bottom-up approach by patterning the bottom mirrors,
significantly limiting the types of lattices and refractive index contrast
that can be realized. Here, we report a direct write approach that uses a
Focused Ion Beam (FIB) to etch 2D lattice into a planar microcavity. Such
etching of the cavity allows for realizing high refractive index contrast
lattices. We realize the polariton condensate lattice using the highly
photostable host-guest Frenkel excitons of an organic dye small molecular
ionic lattice (SMILES)1, 2. The lattice structures are defined on a planar
microcavity embedded with SMILES using FIB, allowing the realization of
lattices with different geometries, including defect sites on demand. The band
structure of the lattice and the emergence of condensation are imaged using
momentum-resolved spectroscopy. The present approach allows us to study
periodic, quasi-periodic, and disordered polariton condensate lattices at room
temperature using a top-down approach without compromising on the quantum
yield of the organic excitonic material embedded in the cavity.

###### keywords:

Polariton, Molecular polaritons, Polariton Condensation, Polariton lattice,
Condensate lattice

The PhD Program in Physics, Graduate Center of the City University of New
York, 365 5th Ave, New York, 10016, USA. The PhD Program in Physics, Graduate
Center of the City University of New York, 365 5th Ave, New York, 10016, USA.

##  1 Introduction

Exciton-polaritons are hybrid quasiparticles that arise from the strong
coupling between excitons in semiconductors and cavity photons in
microcavities. These polaritons possess a small effective mass inherited from
the photonic component, as well as strong interactions stemming from the
excitonic part3, 4, 5, 6. The combination of small effective mass, interaction
effects, and bosonic nature enables the observation of intriguing phenomena
like Bose-Einstein-like condensation, superfluidity, and vortex formation3, 7,
8, 9, 10, 11. The realization of exciton-polariton condensate lattices has
emerged as an attractive platform for analog Hamiltonian simulators, such as
the classical XY Hamiltonian, and for physical computing architectures9, 12,
13, 14, 15. Previous studies on polariton condensate lattices have primarily
focused on GaAs-based systems16, 17, 18, 19, 20, with recent advancements in
organic molecules and perovskite systems allowing for room temperature
operation 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31. However, most of these
room temperature systems rely on a bottom-up approach, where the lattices are
defined by patterning the bottom mirrors32, 33, 34, 25. This is due to the
detrimental effect of top-down approaches on the condensates and, thereby
significantly limiting the types of lattices and the index contrast that can
be achieved. Here, we present a top down approach that utilizes Focused Ion
Beam (FIB) etching to pattern a planar microcavity. This etching technique
enables the realization of high-contrast lattices, as previously demonstrated
in GaAs systems16, 31, 35. Specifically, we report direct writing of a two-
dimensional exciton-polariton condensate lattice by patterning an array of
overlapping pillars etched into a planar microcavity. The patterned
microcavity structure shows condensation at room temperature along with the
bands arising from the lattice structure. To characterize the fabricated
lattice, we employ energy-resolved wavevector imaging of photoluminescence
(PL) and perform power-dependent PL measurements to study optical
nonlinearities.

##  2 Results and discussion

Figure 1: (a) Schematic for planar organic exciton-polariton cavity. (b) White
light angle-dependent reflectivity of the planar cavity region along with
coupled oscillator model fits to the observed dispersion. (c) Schematic for
patterned honeycomb organic exciton-polariton lattice . (d) Scanning electron
microscope image of a single micropillar, honeycomb unit cell, and lattice
patterned on the planar cavity using FIB.

Here, we fabricate an exciton-polariton microcavity on a glass substrate, as
shown in Fig. 1 a. The cavity consists of a 10.5-pair bottom distributed Bragg
reflector (DBR) consisting of alternating layers of a quarter wavelength thick
$SiO_{2}$ and $TiO_{2}$ deposited via radio-frequency sputtering. The center
wavelength of the bottom DBR was designed to be around 600 nm, and the
bandwidth was 200nm. We use the recently introduced an organic dye small
molecule ionic isolation lattice (SMILES) system as the excitonic material
owing to their enhanced photostability and high quantum yield 1, 36, 2.
Specifically, we use rhodamine 3B (R3B), a widely used laser dye (with bandgap
2.19 eV, 566 nm), composed as a SMILES material (See methods)(Supporting
Information(SI), Fig.S1). $30nm$ R3B-SMILES in PMMA matrix is deposited via
spin coating onto the bottom DBR as shown in Fig.1a. The cavity is completed
by depositing $~{}100nm$ thick silver film on top of the SMILES layer. This
results in the formation of a Tamm plasmon cavity mode with loaded Q of $200$
similar to our previous report2. Strong coupling between the Tamm mode and the
excitons of the SMILES results in the formation of polariton states whose
dispersion obtained via Fourier imaging is shown in Fig.1b along with fits
based on the coupled oscillator model. Anticrossing between the upper(UP) and
lower polariton(LP) branches is observed at finite in-plane momentum due to
the negative detuning ($40meV$) of the cavity with respect to the exciton in
SMILES. The estimated Rabi splitting based on the coupled oscillator model fit
is $100meV$. The strongly coupled cavity is patterned using FIB etching with
low ion current ($77pA$) and $30kV$ voltage to avoid heating caused by the
gallium ion beam. The microcavity is patterned into different structures, such
as a single pillar, honeycomb unit cell, and honeycomb lattice, as shown
schematically in Fig. 1c. The scanning electron microscope images of the
patterned structures are shown in Fig. 1d.

In the single pillar case, the refractive index contrast arising from the
etching of the pillar (diameter= $2.75\mu$m) results in lateral confinement
and emergence of discrete polariton states37, 38, 39, 40, 41, galbiati as
opposed to dispersive branches observed in planar cavities as shown in SI,
Fig.S2a. When the excitation power is increased above the condensation
threshold ($1.25p_{th}$) the emission is observed from the lowest energy state
as seen in SI, Fig.S2b.

Figure 2:  Measured real space PL image of honeycomb lattice (a) below
condensation threshold and (b) above condensation threshold. (c) Measured
momentum space PL emission image of condensate lattice above condensation
threshold showing the condensation at the corners of the BZ. Energy resolved
momentum space PL (d) below condensation threshold along with tight binding
model fits to the observed dispersion and (e) above condensation
threshold.(f)Integrated PL intensity and full width at half maximum (FWHM) of
condensate lattice PL as a function of pulse energy.

Two-dimensional array of micropillars in a honeycomb lattice geometry with
micropillar diameter(d) $2.75\mu$m and lattice constant(a) $2.40\mu m$ is
realized using FIB following similar approach to the single pillar. The
polariton lattice is excited nonresonantly at $514$ nm wavelength using a flat
top beam with a spot size of approximately 25$\mu m$, generated by tightly
focusing 100 femtosecond pulsed laser with a repetition rate of $1KHz$ on the
back focal plane of a 50x microscope objective (numerical aperture=0.80).
Fig.2a and 2b illustrate the real-space PL of the lattice below and above the
condensation threshold (pulse energy=10nJ), respectively. A distinct
transition is observed from delocalized PL to localized PL, specifically at
the lattice sites. Fig.2c displays the momentum resolved image of the PL from
the lattice after condensation, demonstrating the localization of polariton PL
at the six Dirac points of the first Brillouin Zone(BZ). Fig.2d shows the
experimentally observed band structure of the honeycomb lattice in Energy
resolved momentum space PL with the momentum slice taken along $k_{x}$=0
(dashed line in Fig.2c) below the condensation threshold. Modified
bandstructure along other in-plane momentum directions are shown in SI
Fig.S3a-c.Above the threshold, we observe the collapse of PL to the lowest
energy bands as shown in Fig.2e. Pump power dependence of emission intensity
and linewidth is shown in Fig.2f. Clear threshold and nonlinear increase in
output intensity is observed along with the decrease in the linewidth
indicative of the onset of polariton condensation similar to what was reported
previously in non-patterned SMILES system2.

Figure 3:  Real space PL image of polariton condensate lattice with
micropillar diameter d=$2.75\mu m$, and lattice constant (a) $a=2.0\mu m$, (b)
$a=2.4\mu m$, (c) $a=2.75\mu m$,(d) $a=2.4\mu m$ with missing lattice sites
defect,(e) $a=2.4\mu m$ with missing hole,(f) $a=2.4\mu m$ with "CCNY" logo as
an example of arbitrary defects that can be realized through design.

Finally, we investigate polariton condensation in 2D honeycomb lattices with
varying degree of coupling between the lattice sites and on the presence of
defects. Fig.3a-c, show the real space image of condensation in lattices with
varying degree of coupling between lattice sites with lattice constant varying
from $a=2.0\mu m$ to $2.75\mu m$. We observe the transition from delocalized
to localized condensate formation by increasing the inter-pillar distance
(reduced intersite coupling). For the highly coupled case (Fig.3a), the
condensate is delocalized over the entire structure in contrast to the weakly
coupled case (Fig.3c), where the condensates are localized at the pillar
sites. The versatility of our top-down approach is shown in Fig.3 d-f, where
lattices with a missing pillar (Fig.3d), missing hole (Fig.3e) and arbitrary
defect pattern showing the abbreviation of City College of New York (CCNY)
(Fig.3f) are realized. We also studied the role of lattice defects in the
condensate formation. Shown in Fig.4 a-c is the real space image of the PL
from the lattice for increasing pump power. Below the condensation threshold,
the PL is distributed throughout the lattice. The onset of condensation is
observed first at the defect site (Fig.4b), followed eventually by
condensation emerging across the entire lattice. The threshold for
condensation at the lattice site is lower than what was observed previously in
defect-free lattices, indicating enhanced scattering to the defect site.

Figure 4:  Real space PL image of defect lattice with missing hole at (a)
$p=0.5p_{th}$ collected for longer integration time ($30sec$) to show
background lattice below condensation threshold, (b) $p=p_{th}$ collected with
integration time $1sec$ and (c) $p=1.25p_{th}$ collected with integration time
$1sec$. Preferential condensation at the lattice defect site is observed.

.

##  3 Conclusion

In summary, we report the realization of room temperature polariton condensate
lattice using a top-down fabrication approach involving FIB etching on the
host-guest-based organic SMILES material microcavity. Experimental results
demonstrate the confinement of polaritons resulting in discrete states and
condensation to the ground state energy in the energy-and momentum resolved
spectroscopy of single micropillars. Through the patterning of a honeycomb
lattice on the SMILES microcavity, we have successfully realized a polariton
condensate lattice consisting of coupled micropillars. By changing the lattice
constant, we demonstrate the transition from delocalized to localized
condensate. Furthermore, we study the effect of deterministically placed
defects in the condensate lattice, revealing that condensates prefer high
refractive index sites for localization and also reduce the condensation
threshold pump power. Our top-down approach provides a versatile platform for
studying arbitrary polariton condensate lattices and polaritonic circuits at
room temperature over large area.

##  4 Methods

###  4.1 SMILES Microcavity

To prepare the SMILES solution, we followed a previously reported recipe1, 2.
The SMILES-based microcavity is fabricated on a quartz substrate with a
$500nm$ thick distributed Bragg reflector (DBR) centered at $620nm$. The DBR,
composed of 10.5 pairs of $SiO_{2}$/$TiO_{2}$, was cleaned using $O_{2}$
plasma for $5$ minutes. A $30nm$ thick SMILES film is then deposited on the
cleaned DBR using a spin coating technique with a two-step process. In the
first step, the film is spun for $20$ seconds at a speed of $1000$ rpm,
followed by a second step of spinning for $80$ seconds at $3000$ rpm. The
deposited SMILES film is placed in a constant pressure vacuum at $25$ ℃.
Finally, a $100$ nm thick silver layer is deposited on top of the SMILES film
using an e-beam evaporator, completing the fabrication of the microcavity.

###  4.2 Experimental techniques

We employed real space PL and Fourier space PL imaging to map the condensate
emission characteristics and the band structure of the lattice. For our
measurements, we utilized two lasers. To investigate the band structures, we
used a 488 nm laser with a repetition rate of 76 MHz to excite the patterned
structure on the silver sides of the microcavity. For the excitation of the
larger area in the lattice, we created a large laser spot ($~{}25\mu m$) by
focusing the laser on the back focal plane of the objective lens. The band
structure of the lattice is measured using far-field imaging techniques, where
the back focal plane of the objective lens is imaged in front of a charged
coupled device(CCD) camera. Energy-resolved angle-dependent PL was measured by
selecting a specific in-plane momentum using a narrow slit in front of the CCD
camera and dispersing the PL using a $300$ grooves per line grating. In
addition, we employed a pulsed $514$nm laser with a pulse width of $280$ fs
and a repetition rate of $1kHz$ for the condensation experiments. The
Brillouin zone and band structure were measured using the Fourier imaging
technique.

###  4.3 Coupled oscillator model

Upper and lower polariton branches in reflectivity of the strongly coupled
cavity are fit using coupled oscillator model defined by following Hamiltonian
matrix:

$H=\begin{bmatrix}E_{x}(k)-\iota\gamma_{x}/2&g&\\\
g&E_{c}(k)-\iota\gamma_{c}/2&\\\ \end{bmatrix}$ (1)

Where $g$ is the coupling strength between exciton and single cavity mode.
$E_{x}(k)$ and $E_{c}(k)$ are the energy of exciton and cavity mode,
respectively.$\gamma_{x}$ and $\gamma_{c}$ are full width at half
maximum(FWHM) of exciton and cavity mode resonance, respectively.

###  4.4 Tight binding model for bandstructure

Tight binding approximation is used to fit the bandstructure of the honeycomb
polariton lattice. The tight binding model for honeycomb polariton lattice is
given by the following expression16, 42, 38:

$E(k)=\pm t_{n}\sqrt{3+F(k)}-t_{nn}F(k)$ (2)

where F(k) is expressed as:

$F(k)=2\cos{\sqrt{3}k_{y}a}+4\cos{\frac{\sqrt{3}}{2}k_{y}a}.\cos{\frac{3}{2}k_{x}a}$
(3)

where $t_{n}$ and $t_{nn}$ are coupling to the first and second nearest
neighbor and used as free parameters in the fitting. Extracted value of
$t_{nn}$/ $t_{n}$ is $\approx 0.10$, which is in good agreement with the
previously reported pattern structure through etching16.

##  5 Supporting Information

Absorption and photoluminescence of SMILES, Polariton condensation in single
micropillar, Bandstructure of honeycomb polariton lattice.

##  6 Acknowledgments

V.M.M. and R.K.Y. were supported by the U.S. Air Force Office of Scientific
Research$-$MURI Grant FA9550$-$22$-$1$-$0317\. S.S., and P.D., acknowledge
support from the US National Science Foundation (NSF$-$ QTAQS program
OMA$-$1936351\. M.Y.S. work was supported by the U.S. Department of Energy,
Office of Science, Office of Basic Energy Sciences under Award No.
DE$-$SC0022036. A.H.O. and A.H.F. acknowledge support from the U.S. National
Science Foundation (DMR-2118423).

## Declarations

Financial Declaration: The authors declare the following competing financial
interest(s): A.H.F. and B.W.L. are cofounders in Halophore, Inc. R.K.Y., S.S.,
P.D., V.M.M., B.W.L., and A.H.F. have filed a provisional patent application.

## Data Availability

All data will be provided by the corresponding authors upon reasonable
request.

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Supporting Information

##  Appendix A Absorption and photoluminescence of SMILES

Fig.1 shows absorption and photoluminescence of thin SMILES film on glass.
Absorption spectra are measured using a UV-Vis spectrometer, and the PL of the
thin film was collected by exciting SMILEs material using a 514nm laser,
repetition rate 76 MHz.

Figure 1:  Absorbance and normalized PL intensity of SMILES film on glass

##  Appendix B Polarition condensation in single micropillar

We demonstrate the polariton condensation in a single micropillar using
energy-resolved momentum space PL. Fig.S2a and b show a single micropillar’s
energy-resolved momentum space PL below and above the condensation threshold.

Figure 2: Momentum space energy resolved photoluminescence from micropillar
with diameter,$d=2.75\mu$m under (a) linear regime at $p<p_{th}$ and non-
linear regime at (b) $p$=$1.25p_{th}$

##  Appendix C  Bandstructure of honeycomb polariton lattice

PL from the honeycomb lattice is captured using energy-resolved momentum space
imaging, employing a non-resonant pulsed laser, 514nm with a repetition rate
of $~{}76MHz$ and a spot size of 25$\mu m$. In the low excitation limit, the
incoherent relaxation of polaritons leads to the population of all energy
bands. The first Brillouin zone (BZ) of the lattice is measured using FIM at
Dirac energy, as depicted in Fig.3a. Dirac points are observed as bright spots
at the six corners of the measured first BZ. Energy bands of the honeycomb
polariton lattice are measured along line 1 and line 2 (black lines in
Fig.3a). Fig.3b displays the energy bands along line 1, exhibiting Dirac
points at $k_{x}/k_{0}=0,\pm(2\pi/3a)$, accompanied by other higher-order
energy bands. The measured bandstructure along line 2, beyond the Dirac point,
displays energy bands with a resolved energy gap, as illustrated in Fig.3c.

Figure 3:  (a) Measured BZ of the honeycomb lattice at the Dirac energy.
Experimentally measured band structure along with tight binding model fits to
the observed dispersion along (b) line 1 at $k_{y}=4\pi/(3\sqrt{3}a)$ and (c)
line 2 at $k_{y}=0$ in (a).