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Physica Scripta

How ‘cold’ can a Markovian dissipative cavity QED system be?

Alexandre V. Dodonov

Published Aug 18, 2010• 7 citations
Publisher

Abstract

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.

DOI
10.1088/0031-8949/82/03/038102

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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 Rabi Hamiltonian describes the interaction between a two-level atom and a single mode of the quantized electromagnetic field. When the system is subject to the Markovian atomic dephasing reservoir, the anti-rotating term leads to the photon generation from vacuum. In the presence of Markovian damping reservoirs, the asymptotic mean photon number is higher than the thermal photon number expected in the absence of the anti-rotating term. We obtain approximate analytical expressions in the asymptotic regime for the photon creation rate in the pure dephasing case and the mean photon number and the atomic population inversion in the general case. Our analytical results are valid in the small mean photon number limit and they were tested by numerical analyses.
We study numerically the dynamics of the Rabi Hamiltonian, which describes the interaction of a single cavity mode and a two-level atom without the rotating wave approximation. We analyze this system subjected to damping and dephasing reservoirs, included via the usual Lindblad superoperators in the master equation. We show that the combination of the antirotating term and the atomic dephasing leads to linear asymptotic photon generation from the vacuum. We reveal the origins of the phenomenon and estimate its importance in realistic situations.
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 study the Fano effect in dissipative cavity quantum electrodynamics (QED), which originates from the interference between the emitter's direct radiation and that mediated by a cavity mode. Starting from a two-level system coupled to a structured reservoir, we show that a quantum master equation previously derived within the Born-Markov approximation can be rederived by introducing a single auxiliary mode through the pseudomode approach. We identify the corresponding spectral function of the system--environment interaction and show that it consists of a constant contribution and a non-Lorentzian contribution, whose interplay gives rise to a spectral profile of the Fano form. The constant contribution represents a Markovian background and is essential for obtaining a Lindblad master equation. Furthermore, by applying Fano diagonalization to an atom--cavity system coupled to common and independent reservoirs, we independently derive the same spectral function and clarify its physical origin. Our results provide a unified description of the Fano effect in single-mode cavity QED systems and reveal its non-Markovian origin encoded in the spectral function of the structured reservoir.