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arXiv:physics/0105087

Effect of Thermal Fluctuations in the Resonance Fluorescence of a Three-Level System

Couto, H., L. A. Amarante Ribeiro

Published May 24, 2001• 0 citations
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Abstract

The effect of thermal fluctuations in the resonance fluorescence of a three-level system is studied. The damped three-level system is driven by two strong incident classical fields near resonances frequencies. The simulation of a thermal bath is obtained with a large system of harmonic oscillators that represent the normal modes of the thermal radiation field. The time evolution of the fluorescent light intensities are obtained solving by a iterative method the Heisenberg equations of motion in the integral form. The results show that the time development of the intensity of the fluorescence light is strongly affected by the interaction of the system with the thermal bath.

DOI
10.48550/arxiv.physics/0105087

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Physical Review A•Sep 1, 1983•20 citations
The effect of thermal fluctuations in the resonance fluorescence of a three-level system is studied. The damped three-level system is driven by two strong incident classical fields near resonances frequencies. The simulation of a thermal bath is obtained with a large system of harmonic oscillators that represent the normal modes of the thermal radiation field. The time evolution of the fluorescent light intensities are obtained solving by a iterative method the Heisenberg equations of motion in the integral form. The results show that the time development of the intensity of the fluorescence light is strongly affected by the interaction of the system with the thermal bath.
In this work we study the effect of thermal fluctuations in the resonance fluorescence of a two-level system. The damped two-level system is driven by a strong incident classical field near resonance frequency. To simulate the thermal bath we introduce a large system of harmonic oscillators that represent the normal modes of the thermal radiation field. To obtain the time development of the fluorescent light intensity we solve the Heisenberg equations of motion transformed in a system of coupled integral equations by an iterative method. The results show that the presence of the bath modifies dramatically the time development of the fluorescence light intensity when compared with the case T=0 K.
The damped two-level system, driven by a strong incident classical field near resonance frequency is subjected to the effect of thermal fluctuations. To simulate the thermal bath we introduce a large system of harmonic oscillators that represents the normal modes of the thermal radiation field. From the Heisenberg equations of motion we calculate the power spectrum of the scattered field and the intensity correlation function. The results show that the presence of the bath dramatically modifies the light scattered by the two-level system when compared with the case without a thermal bath.
The problem of resonant interaction between an electromagnetic radiation field and a vibronic system, such as a molecule or a localized electronphonon system, is considered. The vibronic coupling is assumed to result from displaced and distorted potential energy surfaces for the vibrational motion in the electronic quantum states involved in the resonant interaction with the radiation field. Furthermore, the vibrational energy relaxation is taken into account without assumptions about Markovian-type relaxation. In order to study correlation properties of higher than second order in the electric field strength of the light emitted a method of calculation of the expectation value of an arbitrary product combination of effective time evolution operators of the vibronic system is developed. The calculations are performed by utilizing Feynman's disentangling and operator ordering techniques and yield closed solutions in the low-temperature limit. The theory is used for studying the intensity and the normally ordered intensity correlation function of the resonance fluorescence light from a two-atom molecule excited by a relatively weak laser field, which undergoes phase fluctuations. It is shown that the vibronic coupling can give rise to an anticorrelation effect which is substantially stronger than in the case of resonance fluorescence from an atom. For the case of small vibrational damping a general formula which directly connects the asymptotic long-time behaviour of the normalized intensity correlation function with the vibrational relaxation in the molecule is deduced. It should be convenient for the determination of very small vibrational decay rates.
A non-Markovian microscopic theory for the spontaneous emission spectrum of a two-level atom driven by a strong laser field and undergoing dephasing via the interaction with a thermal bath is developed. The present theory is valid for an arbitrary correlation time scale of the bath relative to the linewidth and interpolates from the Markovian to the static limits. Model calculations using the stochastic line-shape function of Kubo show how the characteristic triplet spectrum is modified by the interaction with the bath. The present results generalize our previous studies of resonance Raman scattering in a three-level system in a strong radiation field.
We consider light scattering from a multilevel system (e.g., a molecule) interacting with several heat baths. The Liouville space approach is employed and weak incident radiation intensity is assumed, whereas the light scattering process is described in the lowest appropriate order in the interaction between the molecule and the incident and emitted photons. The interaction with other radiation field modes as well as with the thermal baths is treated more fully, such as to account for the correct damping terms and their temperature dependence. The formalism is suited for light scattering from an impurity molecule in both gas and dense phases. The thermal baths induce relaxation within the manifold of excited states as well as transitions to nonradiative channels. Damping due to such transitions (as well as radiative damping) corresponds to interactions with zero temperature baths. The physical interpretation of such a bath depends on the nature of the particular damping process. Thermal relaxation within the excited manifold is induced by interaction with the environment represented by a bath of temperature T. Part of this interaction which is diagonal in the molecular space corresponds to the so-called ’’quasielastic collisions’’ and induces modulations of the molecular energy levels and broadening of the relaxed emission. The remainder, nondiagonal part induces actual transitions between the excited molecular energy levels. The formalism yields in a single calculation expressions for the cross section for both the coherent (Raman) scattering process and the relaxed luminescence and enables us to discuss the effects of different factors such as temperature and quenching processes on the relative yields for these processes. The formalism also allows for interference between different levels of the excited manifold due to coupling of several levels to the same bath, and makes it possible to study the effect of thermal relaxation on these interference phenomena.
A method of calculation of multiple-time correlation functions of the resonance fluorescence light from a two-level atom driven by a realistic laser field with phase and amplitude fluctuations is developed. Both kinds of fluctuations are assumed to be Gaussian. The phase fluctuations are treated in the phase-diffusion model. The averaging over the amplitude fluctuations can be performed in a closed way when the relative mean-square amplitude fluctuation is small compared with the ratio of the amplitude correlation decay rate to the characteristic atomic relaxation rate. There is no restriction to Markovian amplitude fluctuations. Arbitrary values for the mean Rabi frequency are allowed. Results are presented for the intensity, the intensity correlation function, and the spectrum of the fluorescent light. It is shown that even in the case when the relative strength of the amplitude fluctuations is small, significant effects can occur due to the finite correlation length of the fluctuations. The results for fast amplitude correlation decay correspond to the situation without amplitude fluctuations. When the correlation time of the amplitude fluctuations becomes comparable with the atomic relaxation times, the Rabi oscillations of the intensity and the intensity correlation function are nearly washed out, and non-Lorentzian line shapes for the side peaks in the spectrum are observed. It is found that the ratio of the heights of the central peak to the side peak increases with increasing correlation time.