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Stochastic process in quantum optics

Bruce W. Shore

Published Jan 1, 1985• 0 citations
OpenAlex

Abstract

The case of a two-state atom immersed in nearly monochromatic, nearly resonant radiation is considered. The radiation has a finite bandwidth. Collisional effects are also included. Time evolution equations of quantum excitation are presented. Examples of the stochastic processes are provided by showing the fluctuation of the coefficients of these equations. (WRF)

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The case of a two-state atom immersed in nearly monochromatic, nearly resonant radiation is considered. The radiation has a finite bandwidth. Collisional effects are also included. Time evolution equations of quantum excitation are presented. Examples of the stochastic processes are provided by showing the fluctuation of the coefficients of these equations. (WRF)
The theory of optical Bloch equations with stochastic coefficients is discussed in detail. It is shown that Bloch equations with stochastic fields lead to multiplicative stochastic processes for which exact solutions can be obtained. The steady state and the transient regimes of the phase-diffusion model of the laser bandwidth are treated, and exact solutions of Bloch equations are obtained. The case of fluctuation due to collisions is also discussed. A simple stochastic model of radiation-induced collisions is presented. For each stochastic model of incoherences formulas for the longitudinal and transverse lifetimes are derived exactly. It is shown that the finite bandwidths of light or the collision incoherences do not, in general, have a simple additive effect in atomic equations of motion.
The authors incorporate in the theory of collisional redistribution of resonance radiation the effect of a finite bandwidth of the intense incident radiation. The phase of the radiation is treated as a process with independent increments, which contains the phase-diffusion model as a special case. These phase fluctuations give rise to effective decay operators affecting the evolution of the density matrix and the regression of the correlation function. For a two-level atom suffering binary collisions the combined effect of collisions and phase fluctuations on the fluorescence spectrum is evaluated in several limiting cases of practical interest.
We develop the quantum theory of the propagation of nonclassical radiation in a nearly resonant medium. The medium is taken to have two levels, which are coupled by the radiation field. Heisenberg equations of motion are developed and compared with stochastic equations in a positive P representation. Initial conditions for absorbers and amplifiers are calculated, so that, for example, superfluorescence or self-induced transparency can be treated. The theoretical methods introduced here allow nonclassical statistics of the radiation field to be calculated such as photon antibunching or squeezing. Both radiative and collisional damping are included.
The problem of resonance fluorescence from a two-level atom that is driven near resonance by a laser beam of finite bandwidth is tackled via the Heisenberg equations of motion, by a simple generalization of our previous treatment. It is found that the two-time intensity correlation function is again factorizable into a product of the mean light intensities at the two times, each of which is slightly modified under broad-band excitation from its value under monochromatic excitation. The spectrum of the fluorescence is affected rather more drastically, and, in general, becomes asymmetric under broad-band excitation.
A complete and detailed treatment of a three-level atom interacting with two near-resonant monochromatic fields is presented. It is assumed that the only damping mechanism is radiative damping, and that the atoms all have the same resonance frequencies, as is the case in an atomic beam. Detailed analytic solutions as well as numerical examples are determined from quantum-electrodynamic equations of motion. In addition, approximation techniques are presented which allow one to get accurate quantitative predictions for strong applied fields from simple rate-equation-like arguments. Absorption and emission spectra are determined, as are the transient and steady-state response of the atom. Two of the more interesting predictions are an emission spectrum containing up to seven components and a prediction of steady-state populations larger than 0.5 in the second excited state.
The interaction of simple, two- and three-level atomic systems with monochromatic and nonmonochromatic laser radiation near resonance transitions is discussed based on the Schroedinger equation with radiation decay and no collisional relaxation, outside the framework of the usual perturbation theory. The mathematical schemes employed include the resonance approximation, exact methods, the quasi-energy method, the adiabatic approximation, etc. A large number of physical phenomena, such as oscillating and inverted populations, self-induced resonances, processes of first order in the weak field, Raman scattering, coherent population transfer, etc. are considered. The review is intended for a broad readership.