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Optics and Spectroscopy

Markovian master equation for a two-level atom in a strong field and/or a tailored reservoir

A. Kowalewska-Kudłaszyk, R. Tanaś

Published Sep 1, 2001• 2 citations
Publisher

Abstract

The master equation for a two-level atom driven by a strong classical field and damped into a tailored reservoir with nonflat density of modes is derived under the Born-Markov approximation. To derive the master equation, the dressing transformation on the atomic operators is performed first, and, next, the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The effects of a strong field and/or structured reservoir are seen as nonstandard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs. The master equation leads to the generalized optical Bloch equations that can easily be solved for the steady state and, together with the quantum regression theorem, allow for analytical expressions for the fluorescence, as well as absorption spectra.

DOI
10.1134/1.1405230

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The master equation for a two-level atom driven by a strong classical field and damped into a tailored reservoir with nonflat density of modes is derived under the Born-Markov approximation. To derive the master equation, the dressing transformation on the atomic operators is performed first, and, next, the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The effects of a strong field and/or structured reservoir are seen as nonstandard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs. The master equation leads to the generalized optical Bloch equations that can easily be solved for the steady state and, together with the quantum regression theorem, allow for analytical expressions for the fluorescence, as well as absorption spectra.
The generalized master equation for a two-level atom driven by a strong classical field and damped into a ‘tailored’ reservoir with a non-flat density of modes is derived under the Born-Markov approximation. To derive the master equation the dressing transformation on the atomic operators is performed first and next the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The modifications introduced by a strong field and/or by the reservoir with the non-flat density of modes lead to non-standard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs. The optical Bloch equations based on this generalized master equation are obtained and solved for the steady state. The solutions are discussed from the point of view of both bare and dressed atoms. Analytical formulas for the fluorescence and probe absorption spectra are obtained and illustrated graphically.
The generalized master equation for a two-level atom driven by a strong classical e eld and damped into a 'tailored' reservoir with a non-e at density of modes is derived under the Born-Markov approximation. To derive the master equation the dressing transformation on the atomic operators is performed e rst and next the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The modie cations introduced by a strong e eld and/or by the reservoir with the non-e at density of modes lead to non-standard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs. The optical Bloch equations based on this generalized master equation are obtained and solved for the steady state. The solutions are discussed from the point of view of both bare and dressed atoms. Analytical formulas for the e uorescence and probe absorption spectra are obtained and illustrated graphically.
A two level atom driven by a strong resonant field and coupled to a structured reservoir is studied. The generalized master equation describing the evolution of the atom is derived under the Born-Markov approximation. To derive the master equation the dressing transformation on the atomic operators is performed first and next the dressed operators are coupled to the reservoir and the corresponding damping rates are calculated. The modifications introduced by a strong field and/or by the reservoir with non-flat density of modes lead to non-standard terms in the master equation, some of which are reminiscent of terms known for squeezed vacuum reservoirs although the reservoir is not a squeezed vacuum. The optical Bloch equations based on this generalized master equation are obtained and solved for the steady state. The resonance fluorescence spectra of the atom are shortly discussed.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
If a broadband squeezed vacuum is treated as a reservoir with respect to a two-level atom, the non-zero phase-dependent reservoir correlation functions characterizing the squeezed vacuum introduce `squeezing terms' to the master equation. These terms are responsible, for example, for the well known narrowing of the spectral lines in the resonance fluorescence spectrum of the atom. For a squeezed vacuum reservoir with finite bandwidth it is possible to derive the master equation that is consistent with the Born-Markov approximation by a two-step procedure which consists in dressing the atom first and next coupling it to the finite-bandwidth reservoir. The master equation is valid whenever the bandwidth of the reservoir is much broader than the atomic linewidth but not necessarily broader than the Rabi frequency. This procedure can be applied not only for the squeezed vacuum reservoir but also for the ordinary vacuum with the structure of the mode density that is not flat, e.g., modelled by a Lorentzian function as in a cavity. The master equation for this case, in the operator form, shows some similarities to the master equation for the squeezed vacuum reservoir due to the presence of the `squeezing-like terms'. The similarities and differences of the two master equations are discussed in this paper.
The master equation for a two-level atom interacting with a strong coherent field and damped into a reservoir formed by a finite bandwidth squeezed vacuum is derived. The master equation extends the Yeoman and Barnett approach to a non-zero detuning of the driving field from the atomic resonance and allows to discuss the role of squeezing bandwidth and the detuning in the level shifts, widths and intensities of spectral lines. The approach is valid for arbitrary values of the Rabi frequency and detuning but for the squeezing bandwidths larger than the natural linewidth in order to satisfy the Markov approximation.