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Physical Review A

Stimulated recombination: A stochastic approach

Alessandro Lami, N. K. Rahman

Published Aug 1, 1985• 2 citations
Publisher

Abstract

Stimulated recombination is examined as a stochastic process. The master equation, its stationary solution, and the fluctuation around the stationary solution are obtained. The existence of multiple solutions and its implication are discussed.
DOI
10.1103/physreva.32.901

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We arrive at transition probabilities for a laserlike system by neglecting wave properties of matter and radiation, and treating the problem, in an analogy to chemical systems, entirely in a number representation. Thus, for example, stimulated emission is idealized as a collision between a photon and an excited atom and the transition rate is proportional to the amount of each species present in the cavity. In all, transition probabilities for stimulated emission, absorption of radiation, cavity loss, atomic deexcitation (other than stimulated emission), and pumping of atoms are included in the model. The resulting stochastic master equation analogous to that employed for the discussion of fluctuations in chemical systems is then used to obtain the deterministic behavior of atoms and field. This agrees with that of the quantum mechanical laser model of Casagrande and Lugiato; thus the rate parameters of the stochastic model may be related to the parameters of their model. Returning to the master equation, we project out the atomic variable and use adiabatic elimination to arrive at a closed, single-variable equation for P(n), the probability of having n photons in the cavity. The stationary solution of this equation is obtained and graphs of (n) and log[(n2)/(n)2] versus the pumping parameter show close agreement with the microscopic results of the Casa-grande-Lugiato model. A similar discussion of the fluctuations can also be given for a laser with saturable absorption. It shows a first-order phase transition. A comparison with the microscopic results of Lugiato et al. is outlined. Again a remarkable agreement of the stochastic approach via the master equation and the microscopic theory is obtained.
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The problem of stimulated recombination at a resonance is investigated by a time-dependent, non-perturbative approach. The number of pairs recombined by a laser pulse is computed as a function of the intensity, of the pulse duration, and of the initial electron-energy distribution (as well as of the parameters which characterize the atomic resonance and its field-induced coupling to the final bound state). The role of spontaneous emission (or other paths) from the recombined state (if it is excited) is also discussed. Numerical results are given including an example of recombination to the ground state in the Sr atom.