Bose condensation of upper-branch exciton-polaritons in a transferrable microcavity

TL;DR

This work demonstrates nonequilibrium Bose–Einstein condensation of the upper polariton branch in a transferable WS$_2$ monolayer microcavity, combining angle-resolved spectroscopy and coherence measurements with a two-tier theoretical model. Condensation arises under conditions where the UP is more excitonic than the LP, the UP receives greater nonresonant pumping (with $P^{UP}/P^{LP}\gtrsim 2.5$), and the UP→LP conversion time $\tau_{\text{conv}}$ exceeds the UP lifetime. The UP gas is quasi-thermal at moderate density (with $T\approx 89\ \mathrm{K}$ and $|\mu/k_B T|=0.168$) and exhibits extended temporal coherence up to $\delta t\approx 138\ \mathrm{fs}$, while a higher-density regime shows non-thermal features, consistent with nonequilibrium dynamics captured by the Boltzmann framework. The study provides design principles for manipulating condensation competition between UP and LP branches and informs potential polaritonic laser applications in two-dimensional materials.

Abstract

Exciton-polaritons are composite bosonic quasiparticles arising from the strong coupling of excitonic transitions and optical modes. Exciton-polaritons have triggered wide exploration in the past decades not only due to their rich quantum phenomena such as superfluidity, superconductivity and quantized vortices but also due to their potential applications for unconventional coherent light sources and all-optical control elements. Here, we report the observation of Bose-Einstein condensation of the upper polariton branch in a transferrable WS$_2$ monolayer microcavity. Near the condensation threshold, we observe a nonlinear increase in upper polariton intensity. This sharp increase in intensity is accompanied by a decrease of the linewidth and an increase of the upper polariton temporal coherence, all of which are hallmarks of Bose-Einstein condensation. By simulating the quantum Boltzmann equation, we show that the upper polariton condensation only occurs for a particular range of particle density. We can attribute the creation of Bose condensation of the upper polariton to the following requirements: 1) the upper polariton is more excitonic than the lower one; 2) there is relatively more pumping in the upper branch; and 3) the conversion time from the upper to the lower polariton branch is long compared to the lifetime of the upper polaritons.

Figures (8)

• Figure 1: Sample structure and optical properties of WS$_2$ monolayer microcavity polaritons.a, Schematic of the microcavity structure. The bottom DBR is composed of 12 pairs of SiO$_2$/SiN$_x$ grown by PECVD. The top DBR was mechanically separated from the substrate and transferred on top of the WS$_2$ monolayer. b, Optical microscope image of the full microcavity. The dotted red line indicates the WS$_2$ monolayer position. c, Angle-resolved PL measurements (left) compared with the simulated absorption image (middle) of the WS$_2$ monolayer microcavity, showing the same lower (LPB) and upper (UPB) polariton branches. The red lines are fitted to the LPB and UPB dispersion and the blue dotted lines are fitted to the cavity and the ex$_A$ mode with the coupled harmonic oscillator model, giving the Rabi splitting ($\Omega$) of 30 meV and cavity-exciton energy detuning ($\Delta$) of -11 meV, respectively. The strong coupling is illustrated by the PL spectrum (right), showing two dominant peaks assigned as the upper and lower polaritons, denoted with the red dotted lines.
• Figure 2: Power-dependent measurements at 10 K.a, Angle-resolved PL measured at 0.25P$\textsubscript{th}$ (left panel) and 1.1P$\textsubscript{th}$ (right panel), where P$\textsubscript{th}$ = 110 $\mu$W is the threshold power of the condensation. Below the threshold, the emission is broadly distributed in momentum and energy in UPB and LPB. Above the threshold, the emission comes almost exclusively from the k$_\parallel$ = 0 lowest energy state from the UPB. b, Occupancy of the k$_\parallel$ = 0 ground state (blue circles), linewidth (red circles) and energy blueshift (green circles) versus the pump power for the upper polariton branch. At low pump power, the ground state occupancy increases linearly with the excitation and then increases exponentially after the threshold before becoming linear again. c, Upper polariton occupation expressed in a semi-logarithmic scale for various pump powers. The power values from low to high are 0.05, 0.2, 0.9, 1.1, 1.3, 1.5, and 1.8 times the threshold values. The solid curves are best fits obtained from the solution of the Boltzmann equation. The fitted temperature (T) is 89 K and the reduced chemical potential $(\mid \mu/k\textsubscript{B}T\mid)$ is 0.168 for the excitation power 1.1P$\textsubscript{th}$, indicating the polariton gas is in the degenerate regime. For exciton power larger than 1.1P$\textsubscript{th}$, the experimental occupation becomes non-thermal, while our model predicts thermal equilibrium. Possible reasons for this are discussed in the main text.
• Figure 3: Temporal coherence for upper polaritons.a, b, Typical interference patterns pumped below and c, d, above the threshold with two different time delays, $\Delta$t = 0 ps (left column) and $\Delta$t = 0.1 ps (right column), respectively. e, f, Visibility as a function of the time delay for the corresponding pump powers. The experimental data were fitted with a Gaussian function. The coherence time is increased from $\delta$t = 55 fs to $\delta$t = 138 fs when the excitation power increases from 0.6Pth up to 2Pth.
• Figure 4: Time-resolved photoluminescence spectra and the underlying mechanism for the upper polariton condensate.a, c, Time-resolved photoluminescence images for the pumping power at 0.8P$\textsubscript{th}$ and 1.2P$\textsubscript{th}$ measured by a streak camera, respectively. The time-integrated spectra (yellow) were fitted by two Lorenz peaks and were assigned to the upper (red) and lower (blue) polaritons. b, d, Experimental measurements (black) and simulated results (red), based on dynamic equations mentioned in the main text and methods) of the time-resolved upper and lower polariton photoluminescence spectra for different pumping power (b: $0.8P_\text{th}$, d: $1.2P_\text{th}$). e, The occupation of the lower and upper polaritons obtained from the quantum Boltzmann simulations for the case of $\frac{P^\mathrm{UP}}{P^\mathrm{LP}} = 2.5$. For this pumping ratio, the upper polariton undergoes condensation at a lower threshold power than the lower one. f, The transition from UP to LP condensation at higher power with the same ratio of pumping $\frac{P^\mathrm{UP}}{P^\mathrm{LP}} = 2.5$.
• Figure S1: Schematic illustration of the top DBR transfer process. The DBRs were prepared and deposited onto the substrates. Then a monolayer was transferred onto the bottom DBR. A sharp tool (like a diamond scriber) was used to scratch the surface of DBR at moderate pressure, and thereafter the segment of the top DBR was separated from the substrate. We used the polypropylene-carbonate (PPC) film to pick up the DBR flakes at room temperature. After that, we stacked the DBR flake onto the monolayer and released the DBR flake and PPC at 90$^\circ C$. Finally, the PPC was removed in chloroform to leave the DBR flake in the sample.