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arXiv:quant-ph/0505047 · Journal of Optics B Quantum and Semiclassical Optics

A two-level atom coupled to a controllable squeezed vacuum field reservoir

Jun-Hong An, Shun-Jin Wang, Hong-Gang Luo, Cheng-Long Jia

Published Oct 16, 2004• 4 citations
arXivHTMLPDF

Abstract

The dissipative and decoherence properties of a two-level atom interacting with a squeezed vacuum field reservoir are investigated based on the nonautonomous master equation of the atomic density matrix in the framework of algebraic dynamics. The nonautonomous master equation is converted into a Schrödinger-like equation and its dynamical symmetry is found based on the left and right representations of the relevant algebra. The time-dependent solutions and the steady solutions are obtained analytically. The asymptotic behaviour of the solutions is examined and the approach to the equilibrium state is proved. Based on the analytic solution the response of the system to the squeezed vacuum field reservoir is studied numerically.

DOI
10.1088/1464-4266/6/12/005

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The dissipative and decoherence properties of a two-level atom interacting with a squeezed vacuum field reservoir are investigated based on the nonautonomous master equation of the atomic density matrix in the framework of algebraic dynamics. The nonautonomous master equation is converted into a Schrödinger-like equation and its dynamical symmetry is found based on the left and right representations of the relevant algebra. The time-dependent solutions and the steady solutions are obtained analytically. The asymptotic behaviour of the solutions is examined and the approach to the equilibrium state is proved. Based on the analytic solution the response of the system to the squeezed vacuum field reservoir is studied numerically.
The dissipative and decoherence properties of the two-level atom interacting with the squeezed vacuum field reservoir are investigated based on the nonautonomous master equation of the atomic density matrix in the framework of algebraic dynamics. The nonautonomous master equation is converted into a Schr\\"{o}dinger-like equations and its dynamical symmetry is found based on the left and right representations of the relevant algebra. The time-dependent solution and the steady solution are obtained analytically. The asymptotic behavior of the solution is examined and the approach to the equilibrium state is proved. Based on the analytic solution the response of the system to the squeezed vacuum field reservoir is studied numerically.
The dissipative and decoherence properties as well as the asymptotic behaviour of the single mode electromagnetic field interacting with the time-dependent squeezed vacuum field reservoir are investigated in detail by using the algebraic dynamical method. With the help of the left and right representations of the relevant hw (4) algebra, the dynamical symmetry of the nonautonomous master equation of the system is found to be su (1,1). The unique equilibrium steady solution is found to be the squeezed state and any initial state of the system is proven to approach the unique squeezed state asymptotically. Thus the squeezed vacuum field reservoir is found to play the role of a squeezing mold of the cavity field.
In this paper, the quantum properties of a two-level atom interaction with squeezed vacuum reservoir is throughly analyzed. With the aid of the interaction Hamiltonian and the master equation, we obtain the time evolution of the expectation values of the atomic operators. Employing the steady-state solution of these equations, we calculate the power spectrum and the second-order correlation function for the interaction of two-level atom with squeezed vacuum reservoir. It is found that the half width of the power spectrum of the light increases with the squeeze parameter, r . Furthermore, in the absence of decay constant and interaction time, it enhances the probability for the atom to be in the upper level.
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.
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.