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Physical Review A

General properties of quantum systems interacting with a field mode in a low- Q cavity

A. B. Klimov, José Luis Romero, C. Saavedra

Published Nov 8, 2001• 9 citations
Publisher

Abstract

We consider the interaction of an arbitrary quantum system with a single field cavity mode without the Rotating-Wave Approximation (RWA). The cavity mode is damped by coupling to a reservoir at zero temperature. We show that the system evolution is governed by an effective Linblad-type master equation with nonzero temperature terms leading to a nonzero stationary state, even without an external driven field. The system evolution under the RWA is also considered. Two particular cases of atom-field and field-field interaction are discussed.

DOI
10.1103/physreva.64.063802

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We consider the interaction of an arbitrary quantum system with a single field cavity mode without the Rotating-Wave Approximation (RWA). The cavity mode is damped by coupling to a reservoir at zero temperature. We show that the system evolution is governed by an effective Linblad-type master equation with nonzero temperature terms leading to a nonzero stationary state, even without an external driven field. The system evolution under the RWA is also considered. Two particular cases of atom-field and field-field interaction are discussed.
We present the complete analytical solution of the cavity QED of a two-level atom and a field mode at zero temperature. It includes both dissipation of the field due to a finite Q value of the cavity and incoherent decay mechanisms for the atom. This analytical solution is provided by a powerful method for treating general master equations that appear in quantum optics. As distinct from the usual approaches we first deal with that part of the master equation which describes the dissipative coupling of the field and the atom to their reservoirs. Rather than using number-state or dressed-state bases we expand the density operator into the eigenstates of the nonunitary parts of the master equation which model the dissipative part of the dynamics. The set of these eigenstates is the damping basis. With the aid of this expansion we find the eigenvalues and eigenstates of the total Liouville operator. The evolution of an arbitrary initial state is then known. We employ these results to give an exact solution of the dynamics of the photon field in realistic experiments with one-atom masers at very low temperatures. It includes detuning, cavity leakage effects, spontaneous decay mechanisms for the atoms, a Fizeau-type velocity distribution for the atomic beam, and a statistical parameter for the probability of the excitation of incoming atoms, covering the limits of Poissonian pumping and of regular pumping. On the same grounds one can treat the one-atom laser, consisting of a single atom which stays in permanent interaction with the field mode and which is continuously pumped by external heat baths.
We consider the cavity quantum electrodynamics (QED) system described by the Rabi Hamiltonian, composed of a two-level atom and a single cavity field mode, subject to Markovian damping and dephasing mechanisms. It is shown that without the rotating wave approximation the asymptotic mean photon number and the atomic excitation probability are above the thermal values due to the anti-resonant term in the Rabi Hamiltonian, and are always greater than zero. These quantities are evaluated approximately for two different master equations and compared to exact numerical results, showing good agreement. We discuss the origin of this phenomenon and show that it also persists for an empty dissipative cavity if one uses a quite general form of the Markovian master equation.
The interaction of a two-level atom with a single mode of the radiation field is examined. The cavity mode is damped by coupling to a reservoir in a squeezed state, and the atom is also driven by an external laser field. A master equation for the atomic density operator in the bad-cavity limit is derived. The effect of the squeezing in the stationary population inversion and in the resonance spectrum of the light emitted by the atom into the background modes is studied. The results are compared with the numerical solution of the full master equation for the atom-plus-cavity mode-density operator.
The aim of this study is to investigate dynamical properties of a two-mode f-deformed cavity- field ‎coupled to an effective two-level atom with and without the rotating wave approximation. The first ‎section discusses the theoretical model of the interaction between a two-mode cavity-field and an ‎effective two-level atom within the framework of an f-DJCM without the rotating wave ‎approximation. After that, we obtain the reduced density matrix of the cavity-field with and without ‎the rotating-wave approximation. Then, we have investigated the effect of the counter-rotating ‎terms on temporal evolution of various non-classical properties of the cavity-field, i.e., photon-‎counting statistics, the cross correlation between the modes of the field, and the quantum ‎fluctuations of the quadrature components. Particularly, we compare the numerical result for three ‎different values of the deformation parameter q (q=1, q=1.1, q=0.9) with and without applying the rotating ‎wave approximation. By using of the numerical method, we concluded that even under the ‎condition in which the RWA is considered to be valid, there are the significant effects of virtual-‎photon field on the photon-counting statistics, the cross correlation between the modes of the ‎field, and the quantum fluctuations of the quadrature components‎.
The aim of this paper is to investigate dynamical properties of a harmonic oscillator coupled to a non-equilibrium bath without the rotating wave approximation. At first, we investigate the theory of this model and obtain the Heisenberg equations of motion for the oscillator and bath annihilation operators in the absence and in the presence of a rotating wave approximation. Then, we obtain the fluctuation and fluctuation-dissipation relations in the absence and in the presence of a rotating wave approximation for the non-equilibrium bath annihilation operator, respectively. After that, we study the decay of system modes using the Wigner-Weisskopf approximation. Finally, we calculate the time-dependent spectrum of a cavity field mode coupled to a non-equilibrium reservoir. We show that even under the condition in which the RWA is considered to be valid (weak interaction), there are significant effects of virtual-photon field on the diffusion coefficient, the energy density, line width and the shift frequency.