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Physica Scripta

Errors in zero-excitation state preparation due to anti-rotating terms in two-atom Markovian cavity QED

Alexandre V. Dodonov

Published Oct 12, 2010• 1 citation
Publisher

Abstract

We consider the two-atom cavity quantum electrodynamics system subject to standard Markovian damping and dephasing mechanisms, and study the asymptotic system state achieved via relaxation in the presence of anti-rotating terms in the Hamiltonian. Using the two-photon approximation, we investigate the behavior of the errors in the zero-excitation state preparation as a function of system parameters, showing that the errors vary typically in the range 0.01–1%.

DOI
10.1088/0031-8949/82/05/055401

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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.
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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.
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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.