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The Journal of Chemical Physics

Resonant absorption in stationary and nonstationary fields

V. Sethu Raman, Gerald J. Small

Published Apr 15, 1976• 2 citations
Publisher

Abstract

Response of a two-level atom, relaxing owing to strong thermalizing collisions, in a weak near-resonant pulsed radiation field is examined using the second order perturbation solution of the optical Bloch equations. Dependence of the rate of absorption on the collisional relaxation time of the atom, the correlation time, pulse width, and the degree of detuning of the incident field are discussed.

DOI
10.1063/1.432626

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Physical Review A•Oct 1, 1978•211 citations
Response of a two-level atom, relaxing owing to strong thermalizing collisions, in a weak near-resonant pulsed radiation field is examined using the second order perturbation solution of the optical Bloch equations. Dependence of the rate of absorption on the collisional relaxation time of the atom, the correlation time, pulse width, and the degree of detuning of the incident field are discussed.
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.
An analysis is made of the spectrum of absorption of a weak probe electromagnetic by two-level atoms in a strong resonant laser field, undergoing collision with buffer gas atoms. The analysis is made using an approach that allows for the direct influence of a strong electromagnetic on the dynamics of an elastic collision between an active atom and a buffer gas atom. Rate equations are analyzed for a combined atom–strong electromagnetic field system (an atom dressed by the field) allowing for spontaneous and optical collisional transitions, and also for the interaction with the probe field. In the steady-state case, an expression is derived for the electric susceptibility of the medium at the small-signal frequency. This expression contains the rates of the optical collisional transitions that depend nontrivially on the parameters of the strong electromagnetic field. The phenomenological characteristics of optical collisional transitions generally used are only valid at low intensities and for small frequency detunings of the strong electromagnetic field, i.e., in the impact limit.
The author derives an expression for the spectrum of the radiation scattered by an atom that suffers binary collisions in the weak-field limit. The frequency of the incident radiation is in near-resonance with a multiplet transition. The authors accounts for strong atom-perturber correlations that are induced when the incident or the detected frequency is in the far wing of an absorption line. For an isolated transition between two degenerate atomic levels the model picture of quasistatic absorption followed by adiabatic reorientation of the excited state predicts a redistributed fluorescence line with a polarisation that is determined by geometrical factors.
The method of multiple scales is used to derive a solution of the damped optical Bloch equations of a two-level atomic system due to a strong pulsed field. The time dependence of the oscillations of the atomic inversion influenced by detuning and power broadening is found. The population inversion consists, in general, of three terms: a quasisteady term, quasisteady term that decays with time, and an oscillatory term that also decays with time. In the limit of constant fields, the solution of Torrey for damped systems and that of Rabi for undamped systems are recovered. For an adiabatic switching of the field, the solution for undamped systems reduces to that of Crisp in the adiabatic following limit. An equation describing the field envelope is derived for an arbitrary amount of detuning. At exact resonance, this equation reduces to a pendulum equation, in agreement with previous analyses.
Algebraic methods are developed for deriving steady-state solutions of the Bloch equations for a system of NNN atomic (molecular) levels resonantly coupled to strong coherent radiation fields in the rotating-wave approximation, and undergoing thermal (radiative and collisional) homogeneous relaxation. These methods are applied to a "ladder" model, in which the excitation and relaxation occur by one-level steps, with one field mode in resonance with each step. Explicit solution (in terms of coupling strengths, relaxation rates, and frequency detunings) is given for the three-level system, and some observations are made on systems of four or more levels. The process of solution of the N2{N}^{2}N2-dimensional set of Bloch equations involves matrices of dimension $N\ensuremath{-}1$ or less.
A quantum statistical theory of resonant optical phenomena is developed for the case when the fluctuations of the laser, used for exciting transitions, are important. The general equations describing the dynamics of a relaxing two-level atom (TLA) are solved exactly for different types of mean values and the two-time amplitude and intensity correlations. The phase-diffusion model is adopted for laser fluctuations. The exact results are used to analyze the effect of laser fluctuations on a number of optical effects-optical free-induction decay, adiabatic following, the spectrum of the scattered light from a relaxing TLA, the energy-absorption spectrum from a weak field, Hanle resonances, etc. In each case, the laser fluctuations are found to affect in an important way the characteristics of the above optical-resonance phenomena. For example, the spectrum of scattered radiation from a TLA has the usual three-peak structure for fields at resonance and with strengths $\ensuremath{\alpha}$ above the threshold and for $\ensuremath{\alpha}\ensuremath{\gg}{\ensuremath{\gamma}}_{c}$; however, now the peak heights (widths) are in the ratio 3x3x3x (23x\frac{2}{3x}3x2​), $x=\frac{[{\ensuremath{\gamma}}_{c}+\frac{({T}_{1}^{\ensuremath{-}1}+{T}_{2}^{\ensuremath{-}1})}{3}]}{[2{\ensuremath{\gamma}}_{c}+{T}_{2}^{\ensuremath{-}1}]}$, where ${\ensuremath{\gamma}}_{c}^{\ensuremath{-}1}$ is the correlation time for laser phase fluctuations. For ${\ensuremath{\gamma}}_{c}\ensuremath{\gg}\ensuremath{\alpha}$, one gets a single-peak spectrum. The laser field is treated as a second-quantized field with excitation in either a coherent state or a Fock state. The results, obtained by straightforward perturbation theory, but valid for arbitrary values of the relaxation parameters, detuning, and the laser correlation time, are also presented.