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Physical Review A

Stimulated recombination in open systems

J. L. Muoz-Cobo, G. Verdú, P. Jiménez, J. Pea

Published Sep 1, 1986• 2 citations
Publisher

Abstract

In this comment we study the problem of the stimulated recombination in an open system from a stochastic point of view. We set up the bivariate master equation for the number of photons and ions inside the system. Then we perform a systematic expansion, with the system volume as an expansion parameter, and we obtain the fluctuations of the number of photons and ions around its macroscopic values in the linear noise approximation; the stationary solution is also investigated.

DOI
10.1103/physreva.34.2524

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In this comment we study the problem of the stimulated recombination in an open system from a stochastic point of view. We set up the bivariate master equation for the number of photons and ions inside the system. Then we perform a systematic expansion, with the system volume as an expansion parameter, and we obtain the fluctuations of the number of photons and ions around its macroscopic values in the linear noise approximation; the stationary solution is also investigated.
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.
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.
We consider one source of decoherence for a single trapped ion due to intensity and phase fluctuations in the exciting laser pulses. For simplicity we assume that the stochastic processes involved are white noise processes, which enables us to give a simple master equation description of this source of decoherence. This master equation is averaged over the noise, and is sufficient to describe the results of experiments that probe the oscillations in the electronic populations as energy is exchanged between the internal and electronic motion. Our results are in good qualitative agreement with recent experiments and predict that the decoherence rate will depend on vibrational quantum number in different ways depending on which vibrational excitation sideband is used.
The random nature of spontaneous emission leads to unavoidable fluctuations in a laser's output. This is often included through random Langevin forces in laser rate equations, but this approach falls short for nanolasers. In this paper, we show that the laser quantum noise can be quantitatively computed for a very broad class of lasers by starting from simple and intuitive rate equations and merely assuming that the number of photons and excited electrons only takes discrete values. While the approach has seen previous success, we here derive it rigorously from an open quantum system master equation, whereas it was previously introduced only on phenomenological grounds. We further show that in the many-photon limit, the model simplifies to Langevin equations. We perform an extensive comparison of different approaches for computing quantum noise in lasers, identifying the best approach for different system sizes, ranging from nanolasers to macroscopic lasers, and different levels of excitation, i.e., cavity photon number. In particular, we show that below the laser threshold, stochastic fluctuations in the numerical solution to the Langevin equations can drive populations to unphysical negative values, requiring the introduction of population bounds, which in turn skew the noise statistics, leading to inaccuracies. The Laser Markov Chain model, on the other hand, is accurate for all pump values and laser sizes when collective emitter effects are excluded.