Efficient stochastic simulation of rate equations and photon statistics of nanolasers

Abstract

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“Amplified Spontaneous Emission” in Micro- and Nanolasers

“…A modification of the REs introduces a new element in the class of discrete models, allowing for the observation of photon bursts [104]. Its central point lies in the introduction, in a rate equation description, of correlations among emitters, recently predicted and observed in different contexts, as we now outline.…”

“…Based on this bulk of evidence, ref. [104] makes the hypothesis that a phenomenological asymmetry between the relaxation rates of spontaneous and stimulated emission, in a RE model with Pauli blocking [112], may qualitatively provide an acceptable description of correlations at the semiclassical level. The resulting modified REs predict the appearance of photon bursts in the presence of subradiant coupling.…”

“…The resulting modified REs predict the appearance of photon bursts in the presence of subradiant coupling. Without entering into a discussion on the underlying assumptions, it is worth noting the strong novelty which [104] brings to the class of differential models, as it is the only one capable of predicting any form of bursts with Langevin noise. Since below and near threshold the latter is quite small (proportional to the photon number), it is in general not surprising that bursts should be excluded from the dynamical predictions obtained from the integration of stochastic differential equations for nanolasers.…”

“…Since below and near threshold the latter is quite small (proportional to the photon number), it is in general not surprising that bursts should be excluded from the dynamical predictions obtained from the integration of stochastic differential equations for nanolasers. Thus, it is worth trying to gain some topological understanding of the reasons why photon bunching should appear in [104]. This point will be examined in Section 7, after the topological investigation (Section 6) of the phase space properties of the radiation-matter interaction and of its relation with the photon bursts numerically predicted by fully Stochastic, discrete models (Sections 5.2 and 5.3).…”

“…A parallel approach, preceded by a discretization of the Rate Equations implemented in stochastic terms [101], directly implements the physical processes as a sequence of probabilistic events, either computed at fixed steps [83], or by (probabilistically) computing the time at which an event takes place [104] (using a Gillespie-like algorithm [118] also used in [116]). The two approaches are equivalent [118] provided that conditions on additivity are fulfilled [83], with the Gillespie-like strategy leading to much shorter computing times [104,116].…”