Second-Order Temporal Coherence of Polariton Lasers Based on an Atomically Thin Crystal in a Microcavity

Bosonic condensation and lasing of exciton polaritons in microcavities is a fascinating solid-state phenomenon. It provides a versatile platform to study out-of-equilibrium many-body physics and has recently appeared at the forefront of quantum technologies. Here, we study the photon statistics via the second-order temporal correlation function of polariton lasing emerging from an optical microcavity with an embedded atomically thin ${\mathrm{MoSe}}_2$ crystal. Furthermore, we investigate the macroscopic polariton phase transition for varying excitation powers and temperatures. The lower-polariton exhibits photon bunching below the threshold, implying a dominant thermal distribution of the emission, while above the threshold, the second-order correlation transits towards unity, which evidences the formation of a coherent state. Our findings are in agreement with a microscopic numerical model, which explicitly includes scattering with phonons on the quantum level.

Figure 1

Sample structure and polariton lasing. (a) Sketch of the sample structure. The optical cavity is composed of two DBRs. The ${\mathrm{MoSe}}_2$ monolayer is transferred by dry-stamping technique and is capped by a thin layer of hBN. (b) Left: angle-resolved PL map. The energy of the pulsed excitation laser is set at 1.675 eV. Right: angle-resolved white light reflectivity. The fit depicts the dispersion relation of polaritons, extracted from the angle-resolved spectral data. The fitted dispersion relations of upper (UP) and lower polaritons (LP) are shown as solid lines. The dotted and dashed lines represent dispersions of bare excitons and microcavity photons, respectively. (c) Emission spectra of LP at around ${\mathrm{K}}_{//}=0\mathrm{\mu }{\mathrm{m}}^{-1}$. The pump power ranges from 2 to 40 mW. The dashed line denotes the spectral position of the LP peak under a 2 mW pump. (d) The integrated intensity of the LP emission versus pump power. The input-output results feature a kink at pump power of 10 mW, which is assigned to the threshold of lasing. The error bars are obtained from the standard deviation of the background noise. (e) Extracted LP linewidth and peak energy as a function of pump power. The peak energy (linewidth) is marked as blue (orange) dots. At 10 mW, a remarkable reduction in linewidth appears, and it is a fingerprint of the phase transition. The energy and linewidth error bars correspond to the 95% confidence interval of the peak fitting. (f) Angle-resolved PL map above the threshold at 20 mW.

Figure 2

Second-order correlation function of polariton emission. (a),(b) The second-order correlation function below [above] the polariton lasing threshold, $0.6{\mathrm{P}}_{\mathrm{th}}$ $[3.5{\mathrm{P}}_{\mathrm{th}}]$. The value of $\overline{g^{(2)}}(0)$ is $1.020\pm 0.005$ $[1.004\pm 0.003]$, respectively. The temperature is 3.2 K. ${\mathrm{P}}_{\mathrm{th}}=10\mathrm{mW}$. (c) The second-order correlation function at zero delay $\overline{g^{(2)}}(0)$ (circles) and intensity of uncorrelated peaks (squares) as a function of pump power. The magnitude of $\overline{g^{(2)}}(0)$ experiences a reduction towards unity at threshold power. (d) $\overline{g^{(2)}}(0)$ as a function of pump power at temperatures of 6.0, 10.0. and 20.0 K (from bottom to top panels).

Figure 3

Simulation results for the second-order correlation function. (a) Exemplary second-order correlation function $g^{(2)}(\tau )$ as a function of delay time $\tau$ at a temperature of 3.2 K. The pump power is $\mathrm{P}/{\mathrm{P}}_{\mathrm{th}}=0.6$, 2, 6. (b) Averaged second-order correlation function at zero delay $\overline{g^{(2)}}(0)$ for different pump powers. It is calculated by averaging the original $g^{(2)}(\tau )$ data [as shown in panel (a)] over an integration period of 2 ps.