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arXiv:1112.0523 · Physical Review A

Approximate analytical results on the cavity dynamical Casimir effect in the presence of a two-level atom

Alexandre V. Dodonov, V. V. Dodonov

Published Jan 17, 2012• 35 citations
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Abstract

We analytically study the photon generation from vacuum due to the dynamical Casimir effect in a cavity with a two-level atom, initially prepared in an arbitrary pure state. Performing small unitary transformations, we obtain closed analytical expressions for the probability amplitudes and other important quantities in the resonant and dispersive regimes.

DOI
10.1103/physreva.85.015805

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We analytically study the photon generation from vacuum due to the dynamical Casimir effect in a cavity with a two-level atom, initially prepared in an arbitrary pure state. Performing small unitary transformations, we obtain closed analytical expressions for the probability amplitudes and other important quantities in the resonant and dispersive regimes.
We consider the scenario in which a damped three-level atom in a ladder or V\mathsf{V}V configuration is coupled to a single cavity mode whose vacuum state is amplified by dint of the dynamical Casimir effect. We obtain approximate analytical expressions and exact numerical results for the time-dependent probabilities, demonstrating that the presence of the third level modifies the photon statistics and its population can serve as witness of photon generation from a vacuum.
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We study analytically and numerically the dynamical Casimir effect in a cavity containing two stationary two-level atoms that interact with the resonance field mode via the Tavis-Cummings Hamiltonian. We determine the modulation frequencies for which the field and atomic excitations are generated and study the corresponding dynamical behaviors in the absence of damping. It is shown that the two-atom setup allows for monitoring of photon generation without interrupting the growth, and different entangled states can be generated during the process.
We study theoretically the non-stationary circuit QED system in which the artificial atom transition frequency has a small periodic modulation in time, prescribed externally. We show that, in the dispersive regime, when the modulation periodicity meets the `resonances', the dynamics may be described by the dynamical Casimir effect, Jaynes-Cummings or Anti-Jaynes-Cummings effective Hamiltonians. In the resonant atom-cavity regime, under the modulation `resonance' the dynamics resembles the behavior of the dynamical Casimir effect in a vibrating cavity containing a resonant two-level atom, and entangled states with two photons can be created from vacuum. Thus, an analog of the dynamical Casimir effect may be simulated in circuit QED, and several photons, as well as entangled states, can be generated from vacuum due to the anti-rotating term in the Rabi Hamiltonian.