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Soviet Journal of Quantum Electronics

New effects of spontaneous relaxation of quantum systems in a strong laser field

É. G. Pestov

Published Feb 28, 1986• 0 citations
Publisher

Abstract

It is shown that the laser field influences spontaneous relaxation of quantum systems and alters the relaxation scheme. New quantum kinetic equations are obtained for the density matrix of quantum systems and it follows from these equations that an additional frequency shift appears in the dispersion function of a quantum system. This shift is over an order of magnitude larger than the familiar Bloch-Siegert shift and the absorption line profile of a quantum system is found to be an asymmetric function of the laser field frequency.

DOI
10.1070/qe1986v016n02abeh005726

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It is shown that the laser field influences spontaneous relaxation of quantum systems and alters the relaxation scheme. New quantum kinetic equations are obtained for the density matrix of quantum systems and it follows from these equations that an additional frequency shift appears in the dispersion function of a quantum system. This shift is over an order of magnitude larger than the familiar Bloch-Siegert shift and the absorption line profile of a quantum system is found to be an asymmetric function of the laser field frequency.
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We study the field correlation functions and the natural laser spectrum for a slow-inversion laser with the thresholdless intensity fluctuations. In such a laser, the spontaneous-emission-driven relaxation oscillations are responsible for some unique features: The field correlation function oscillates with the frequency of relaxation oscillations ${\ensuremath{\omega}}_{r}$ and the laser line changes its profile. We show that appreciably above threshold the laser spectrum consists of three lines. In addition to the main line at the frequency of the lasing mode ${\ensuremath{\omega}}_{c}$ appear two lines at frequencies ${\ensuremath{\omega}}_{c}+{\ensuremath{\omega}}_{r}$ and ${\ensuremath{\omega}}_{c}\ensuremath{-}{\ensuremath{\omega}}_{r}$. The spontaneous emission noise in such lasers gives rise to nonlinear stochastic effects: Quantum noise affects the oscillation frequency ${\ensuremath{\omega}}_{r}$ and the decay rates of the field correlation function.
We develop the theory of propagation of laser wave in a gas of two-level atoms (with an optical transition frequency ω0\omega^{}_0ω0​) under the condition of inhomogeneous Doppler broadening, considering the self-consistent solution of the Maxwell-Bloch equations in the mean-field approximation and for one-atomic density matrix. The nonlinear effects in the atomic density nnn, caused by the free motion of atoms, are found. These effects distort the lineshape (shift, asymmetry, broadening), but are not associated with atom-atom interaction. Moreover, in the case nk0−3<1nk^{-3}_0<1nk0−3​<1 (where k0=ω0/ck^{}_0=\omega^{}_0/ck0​=ω0​/c) and temperatures T≳300T\gtrsim 300T≳300~K, these quasi-collective effects exceed the well-known influence of the dipole-dipole interatomic interaction (e.g., Lorentz-Lorenz shift) by more than one order of magnitude. It was also found that for some area of parameters, the frequency interval appears, within which the non-trivial self-consistent solution of the Maxwell-Bloch equations is absent at all. Thus, the physical picture of collective effects in a gas medium should be substantially revised.
We describe strong-field effects in a class of collisional energy-transfer processes occurring among atoms in a gas irradiated by a laser beam. The time evolution of the atomic system is evaluated by solving a system of differential equations, and by using the Magnus-Light expansion of the scattering matrix. Results from the two methods are then compared. The resulting spectrum is shifted in frequency towards the antistatic side, and the line shape becomes less asymmetric. All these theoretical predictions are based on the assumption that the motion of the atoms during the collision can be described by classical mechanics, with no appreciable change of the kinetic energy of the atoms.
The resonant response of a multilevel atomic system to strong coherent radiation is analyzed using an extension of the methods of time-independent scattering theory, adapted to the density-matrix formalism in order to include thermal bath effects. General steady-state expressions are derived for self-attenuation and resonance scattering rates in strong saturating fields, as functions of the coupling strengths, relaxation parameters, and frequency detunings. Formal expressions are given for radiative-damping and collision-broadening relaxation parameters, relating the latter to scattering amplitudes. Modifications of collision-broadening parameters by the presence of very strong fields are discussed. The Bloch equations are derived by transformation to the time domain, under specified conditions.