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Journal of the Physical Society of Japan

Second Order Optical Process of A Randomly Modulated Multi-Level Atom

Yoshitaka Tanimura, Hiroshi Takano, Ryogo Kubo

Published Dec 15, 1986• 8 citations
Publisher

Abstract

A stochastic model of a multi-level atom interacting with its environment randomly in its excited states is considered. Assuming a two state-jump model for the random intermediate-state interaction, analytical expressions of emission spectra of three- and four-level atoms in the second order optical process are obtained. In each case, the expression is shown to be separated into three types of terms. Two types of terms correspond to the pure Raman spectrum and the luminescence, respectively, while the other type of term bears a mixed character contributing to broadening of the Raman line when the random modulation is slow and merging into the luminescence when the modulation is fast. This characteristic behavior is discussed with the use of the analytical expressions.

DOI
10.1143/jpsj.55.4550

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A general theory of transient light scattering is developed on the basis of our stochastic theory of intermediate state interaction. The transient behaviors of various components of the second order optical process under a pulsed irradiation are discussed and model calculations of the time-resolved emission spectra are performed. It is clarified that in the fast modulation limit the Raman component has a time constant determined by the phase memory time of the intermediate state while the time constant of the luminescence component is given by the radiative damping rate. The transient behaviors of the scattered light intensity are also discussed.
A general theory of the intermediate state interaction in the second order optical process is developed by extending the stochastic theory of line shape. We introduce the stochastic models of the intermediate state interaction and discuss the general features of the secondary emission spectrum, focusing particular attention on how the correlation between the incident and the scattered photons are affected by the intermediate state interaction. It is clarified how the spectral features or the relative weights among the various components of the second order optical process are determined by a few physical parameters; the radiative damping rate and the modulation amplitude and rate. Further we discuss the relationships between the first and the second order optical processes.
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We have studied the stimulated Raman spectra arising from the interaction of a three-level atom with two strong electromagnetic fields whose initially populated modes ω a and ω b are in resonance with the two atomic transition frequencies. The Green's function formalism has been used in the limit of high photon densities to calculate the excitation spectra near the frequencies ω = ± ω ab = ± (ω a - ω b ). Expressions are derived for the relative intensities, which describe, apart from the usual Raman peak at the frequency ω = ω ab , four pairs of lorentzian lines peaked at the frequencies ω - ω ab = ± Ω a /√2, ± Ω b /√2, ± Ω and ± 2Ω, respectively, and having spectra widths of the order of 3γ0/4. The parameter Ω is defined as Ω2 = (Ω a 2 + Ω b 2)/2, where Ω a and Ω b are the Rabi frequencies of the two laser fields and γ0 is the spontaneous emission probability. Numerical calculations for selected values of the Rabi frequencies are graphically presented and discussed. Conditions have been established for which Raman gain processes are anticipated to take place.
A general formulation is given for the second order optical process of a three-level system in contact with a heat bath consisting of harmonic oscillators with a proper frequency spectrum producing a Markoffian random perturbation. Elimination of the bath using the influence functional method of Feynman and Vernon yields a continuous fraction expression and the result affords a basis to clarify the relation between the stochastic and dynamical approaches to treat the partial destruction of the quantum coherence of the optical process. As an example, a three-level system with intermediate-state interaction is treated in some detail.