Kinetic Monte Carlo approach to nonequilibrium bosonic systems

We consider the use of a kinetic Monte Carlo approach for the description of nonequilibrium bosonic systems, taking nonresonantly excited exciton-polariton condensates and bosonic cascade lasers as examples. In the former case, the considered approach allows the study of the cross-over between incoherent and coherent regimes, which represents the formation of a quasicondensate that forms purely from the action of energy relaxation processes rather than interactions between the condensing particles themselves. In the latter case, we show theoretically that a bosonic cascade can develop an output coherent state.

Figure 1

Polariton energy relaxation mechanisms illustrated on the low-momentum polariton dispersion (blue/solid). The green/dashed curve illustrates the high-momentum exciton dispersion. (a) Polariton-phonon scattering. (b) Polariton-exciton scattering. (c) Polariton-polariton to polariton-exciton scattering. (d) Polariton pumping.

Figure 2

Polariton-phonon scattering rates from mode $k_1$ to $k_2$. (a) Polariton relaxation processes. The scattering to $k=0$ modes is larger than that of other modes due to the larger density of states at $k=0$ in a one-dimensional system. (b) Polariton excitation processes, requiring nonzero temperature.

Figure 3

(a) Time dependence of $\langle n\left(t\right)\rangle$ of the ground state below threshold. (b) Corresponding time dependence of $g_2\left(t\right)$. (c) Time dependence of $\langle n\left(t\right)\rangle$ for the ground state ($k=0$) above threshold. (d) Corresponding time dependence of $g_2\left(t\right)$. In each panel the light shaded region represents the statistical error, corresponding to one standard deviation.

Figure 4

(a–g) Momentum distribution of polaritons in the long-time (continuous-wave excitation) limit for increasing pumping intensity, represented by the maximum reservoir occupation number, $n_{\text{ex}}$. (h) Dependence of the second-order correlation function, $g_2$ (circles and left-hand scale), and the average occupation number, $\langle n\rangle$ (squares and right-hand scale), for the highest occupied state as a function of the reservoir occupation number. While there is a significant statistical error below threshold, the error bars narrow upon condensation.

Figure 5

Kinetic Monte Carlo simulation of a bosonic cascade laser with $M=10$ levels. (a) Power dependence of the level occupations. (b) Power dependence of the terahertz mode occupation. (c) Power dependence of the second-order correlation function of the terahertz mode. (d) Power dependence of the quantum efficiency of terahertz generation. In all panels the points show results from kinetic Monte Carlo simulation, while the solid curves in (a), (b), and (d) show the result of the solution of the classical Boltzmann equations (see Appendix pp3).