Rate equation description of quantum noise in nanolasers with few emitters

Abstract

Rate equations for micro- and nanocavity lasers are formulated which take account of the finite number of emitters, Purcell effects as well as stochastic effects of spontaneous emission quantum noise. Analytical results are derived for the intensity noise and intensity correlation properties, g(2), using a Langevin approach and are compared with simulations using a stochastic approach avoiding the mean-field approximation of the rate equations. Good agreement between the two approaches is found even for large values of the spontaneous emission beta-factor, i.e., for threshold-less lasers, as long as more than about ten emitters contribute to lasing. A large value of the beta-factor improves the noise properties.

Efficient stochastic simulation of rate equations and photon statistics of nanolasers

“…In this work we will show that another stochastic approach, often used in the fields of chemistry and biochemistry [19][20][21][22], can be used to describe the laser dynamics, and can decrease the computation times by several orders of magnitude compared to previous approaches [16][17][18]. Additionally, certain numerical assumptions made in [18] can be avoided with the new method, leading to a robust and versatile stochastic approach with numerous applications. Here we use it to consider the intra-cavity photon probability density functions as a lasing system transitions from thermal to coherent emission, and we will investigate the prospects of introducing effectively altered rates of emission in the rate equations as a way to qualitatively describe the effects of collective inter-emitter correlations.…”

“…One major area of interest in regards to nanolasers is the photon noise and photon statistics: With a relatively small number of intra-cavity photons and a large fraction of the spontaneously emitted photons ending up in the cavity mode(s), the associated quantum noise becomes increasingly important [11][12][13][14][15]. Recently, stochastic methods have been used to simulate nanoscale lasers with large values of the spontaneous emission β-factor [16][17][18], and it was found that the noise and statistics of nanolasers can be captured surprisingly well by including only shot noise; that is, the noise associated with the discreteness of the photons and emitters in the cavity.…”

Active Nanophotonics

“…The idea was to tightly confine light in the form of localized plasmons into deep subwavelength dimensions overlapping with a gain material to achieve stimulated emission and plasmon oscillations amplification or lasing. Enhanced coherent plasmon oscillations, in this case, would be a source of giant near fields (hotspots) and coherent light at the nanometer scale [149], even beyond the diffraction limit. In contrast to all-dielectric semiconductor microlasers, the quanta of the resonator in the spaser is a plasmon, instead of a photon, but it can also generate 22 coherent light emission, which has been realized in a series of subsequent experiments [61], [78], [238], [239].…”

“…The remaining part of the total Purcell factor tot m () FF  corresponds to the change of energy decay rate to all other modes. Thus, in order to make the laser threshold smaller, one has to increase  by enhancement of the mode Purcell factor m F as much as possible, simultaneously reducing tot m () FF  .Rate equations.Taking into account all the processes of pumping, energy transfer, radiation and dissipation, the dynamics of the coupled gain-resonator system can be described (weak-coupling regime) by so-called rate equations[149]-[151]:…”

Mutual coupling and synchronization of optically coupled quantum-dot micropillar lasers at ultra-low light levels

“…The model used in this paper is based on semi-classical stochastic rate equations [43] taking into account the electron scattering mechanisms into the QDs as derived in our previous works [37,44,45]. The description of micro-and nanolasers with semi-classical equations was recently shown to be valid down to a surprisingly low number of emitters on the order of 10 [46]. Our chosen theoretical framework should therefore be suited to accurately describe the dynamical properties of the micropillar lasers considered here.…”