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The Journal of Chemical Physics

Signatures of non-Markovian relaxation in two-level atoms due to environmental perturbations

Gautam Vemuri, Marvin D. Kemple

Published Feb 8, 2000• 3 citations
Publisher

Abstract

The effect of environmental perturbations on a system of two-level atoms is to alter the coupling between the atoms and their surroundings, which manifests itself as a change in the relaxation rates of the atoms. One of the ways in which environmental fluctuations can affect an atom is to modulate its transition frequency in a stochastic manner. We study the response of such two-level atoms to irradiation by a monochromatic laser, and report the results of numerical experiments on the spectrum of scattered light. It is observed that this spectrum is a sensitive indicator of the parameters that describe the stochastic modulation. In addition, the spectra exhibit substantially different features depending on whether the stochastic process follows a diffusion or a jump mechanism. The numerical results are based on a Monte Carlo procedure, which can be applied to stochastic processes in a wide variety of biological, chemical, and physical processes.

DOI
10.1063/1.480837

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The effect of environmental perturbations on a system of two-level atoms is to alter the coupling between the atoms and their surroundings, which manifests itself as a change in the relaxation rates of the atoms. One of the ways in which environmental fluctuations can affect an atom is to modulate its transition frequency in a stochastic manner. We study the response of such two-level atoms to irradiation by a monochromatic laser, and report the results of numerical experiments on the spectrum of scattered light. It is observed that this spectrum is a sensitive indicator of the parameters that describe the stochastic modulation. In addition, the spectra exhibit substantially different features depending on whether the stochastic process follows a diffusion or a jump mechanism. The numerical results are based on a Monte Carlo procedure, which can be applied to stochastic processes in a wide variety of biological, chemical, and physical processes.
We investigate nonlinear wave mixing in two-level atoms wherein, using a dressed state formalism, it is shown that the signal arises as a consequence of quantum interference between relevant probability amplitudes for photon emission. We then report a theoretical study of the modifications that are induced in the four-wave mixing signals when the transition frequency of the atoms is stochastically modulated. Such modulations, which arise from perturbations in the immediate environment of the atoms, are shown to cause significant alterations in the nonlinear response of the atoms. We also describe how one can, via an investigation of the four-wave mixing signal, differentiate between Markov and non-Markov fluctuations in the transition frequency of the two-level system. The calculations rely on a recently developed Monte Carlo procedure that can be used to obtain exact solutions to a wide variety of spectroscopic problems, with minimal restrictions on atom, field, and noise parameters.
The coupling between a chromophore and its surroundings can, in the event of environmental perturbations, result in a stochastic modulation of the chromophore’s transition frequency, which in turn can cause fluctuations in the population of the excited state. We demonstrate that by using these fluctuations in population inversion as the spectroscopic variable, one can extract information on whether the random modulation of the chromophore follows a diffusion process or a jump process. The population fluctuations also discriminate between Markov and non-Markov fluctuations of the atomic frequency. In addition, we show that this observable allows, in certain regimes, to unambiguously determine whether the population fluctuations are due to atomic frequency noise, or due to noise in the irradiating laser field. Finally, through a dressed state analysis, we demonstrate that the response of a randomly modulated atom is similar to that of an unmodulated atom driven by a noisy field that has amplitude fluctuations in only one quadrature.
The fluorescence radiation, emitted by a two-level atom in a perturber bath, is considered. The atom is driven by a single-mode laser with a Lorentzian profile, which is brought about by a fluctuating phase. The stochastics of this phase is taken to be the Markovian random-jump process. The authors derive explicit expressions for the atomic density matrix, the temporal photon correlations and the fluorescence spectrum. The results greatly resemble the results for a non-Gaussian diffusive phase, but deviate slightly from the corresponding expressions in the Wiener-Levy limit of the diffusion process.
The nature of light scattered from a two-level atom, where the transition frequency between the two levels is a stochastic quantity, pumped by a strong monochromatic field is investigated. The optical Bloch equations, modified to include the stochastic nature of the atomic frequency, are solved using Monte Carlo techniques to include arbitrary strengths and bandwidths of the frequency noise. We find in the spectrum of scattered light a shift of the Rabi sidebands due to the stochastic nature of the transition frequency. We also find the height of the Rabi sideband first decreases and then increases with increasing strength of the noise. The intensity-intensity correlation function for the emitted fluorescence is observed to be sensitive to the time scale of the noise. The calculated line shapes for weak driving fields can be fitted to a superposition of Gaussian and Lorentzian lines.
The relaxation process and resonance fluorescence of a two-level atom strongly driven by stochastically fluctuating laser light is studied. A laser with small intensity fluctuations about a constant mean value and a diffusing phase is assumed. Depending on the relative time scales of the intensity fluctuations and the atomic response to these fluctuations, the time decay of the atomic population is found to be non-exponential. The broadening of the sidebands in the triplet spectrum of resonance fluorescence is shown to be non-Lorentzian.
By means of quantum stochastic calculus we construct a model for an atom with two degenerate levels which is stimulated by a circularly polarized laser and we compute its fluorescence spectrum. Let us stress that, once the model for the unitary atom–field dynamics has been given, then the spectrum is computed without further approximations. If only the absorption/emission term is included in the interaction, we reobtain the Mollow spectrum in the case of a monochromatic laser and the Kimble–Mandel spectrum in the case of a ‘phase diffusion model’ for a non-monochromatic laser. However, our model can also describe another type of light scattering, a ‘direct scattering’ due to the response of the atom as a whole, which we expect to be small but which interferes with the scattering due to the absorption/emission channel. When both the scattering channels are introduced we obtain a modification of the Mollow–Kimble–Mandel spectrum, which shares its main features with the usual case, but which presents some asymmetries even in the case of no detuning.