Stochastic pumping of a polariton fluid

We investigate the response of a polariton laser driven slightly off-resonantly using light fields differing from the routinely studied coherent pump sources. The response to driving light fields with thermal and displaced thermal statistics with varying correlation times shows significant differences in the transmitted intensity, its noise, and the position of the nonlinear threshold. We predict that adding more photons on average may actually reduce the transmission through the polariton system.

Figure 1

Comparison of the two pumping schemes. Shown on the top are the thermal (black line) and coherent (red line) pump photon number $n_{\mathrm{pump}}$ time streams for the same mean photon number ${\langle n\rangle }_{\mathrm{pump}}=79$. Shown on the bottom is the time series of the polariton occupation number $n_{\mathrm{pol}}$. For the coherent pump beam, the system may be in the on state (upper red line) or the off state (lower red line) depending on the initial polariton number. For the thermal pump (black line), the system state switches irregularly between the on and off states.

Figure 2

Mean polariton occupation number for pumping with thermal light fields with different ${\tau }_c$. The solid red line denotes the corresponding curve for coherent pumping.

Figure 3

Mean polariton occupation for pumping with several displaced thermal states in the slow fluctuation limit ${\gamma }_c{\tau }_c=15.8$. Red lines show the bistability curves under coherent pumping for comparison. The nonlinear rise becomes steeper with increased coherent offset. For large coherent offsets, additional thermal pumping may actually reduce the occupation number.

Figure 4

Wigner quasiprobability distributions of a coherent state with $\langle n\rangle =100$ (top), a thermal state with $\langle n\rangle =20$ (middle), and the combined displaced thermal state with $\langle n\rangle =120$ (bottom). Note that the displaced thermal state yields significant probabilities for lower field quadratures than the pure coherent state, although it has a larger mean photon number.

Figure 5

Equal-time second-order correlation function $g^{\left(2\right)}\left(0\right)$ of $n_{\mathrm{pol}}$ for pumping with several displaced thermal states. The red line denotes the photon number statistics of a purely coherent pump beam for comparison. Dashed lines mark the range of the bistable region for coherent pumping.