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arXiv:1504.05066 · Physical Review A

Coherent effect of vacuum fluctuations on driven atoms

M. Donaire, Astrid Lambrecht

Published Jul 22, 2015• 3 citations
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Abstract

We study the coherent effect of the Casimir-Polder interaction on the oscillations of two-photon driven atoms. We find that, for oscillations between two degenerate states in $\mathrm{\ensuremath{\Lambda}}$ configuration, shifts on the Rabi frequency may be induced by nonadditive level shifts. For oscillations between two Rydberg states in ladder configuration, shifts on the Rabi frequency may be induced by the effective renormalization of the laser interaction.

DOI
10.1103/physreva.92.013838

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We study the coherent effect of the Casimir-Polder interaction on the oscillations of two-photon driven atoms. We find that, for oscillations between two degenerate states in \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ configuration, shifts on the Rabi frequency may be induced by nonadditive level shifts. For oscillations between two Rydberg states in ladder configuration, shifts on the Rabi frequency may be induced by the effective renormalization of the laser interaction.
We present an interaction scheme that exhibits a dynamical effect of virtual photons carried by a vacuum-field dressed two-level atom in the ultrastrong-coupling regime. We show that, with the aid of an external driving field, virtual photons provide a transition matrix element that enables the atom to evolve coherently and reversibly to an auxiliary level accompanied by the emission of a real photon. The process corresponds to a type of vacuum Rabi oscillation, and we show that the effective vacuum Rabi frequency is proportional to the amplitude of a single virtual photon in the ground state. Therefore, the interaction scheme could serve as a probe of ground-state structures in the ultrastrong-coupling regime.
When a two-level atom interacts resonantly with a coherent electromagnetic field, the polarizability of the atom can be modulated due to the Rabi oscillations between atomic levels. We show that in the quantum vacuum, such a time-dependent atomic polarizability can lead to a resonant generation of photon pairs, a phenomenon reminiscent of photon emission in the dynamical Casimir effect (DCE). Specifically, we employ a dressing transformation to obtain an effective Hamiltonian which uncovers a polarizability-dependent parametric interaction corresponding to DCE. We determine the photon emission rate and indicate features of DCE photon pairs distinguishable from regular fluorescence photons.
We derive a set of cavity-modified Maxwell-Bloch equations for a two-level atom in a cavity driven by a coherent field from the single-atom Fokker-Planck equation in the bad-cavity limit. These equations have the same form as the Maxwell-Bloch equations for a two-level atom in free space interacting with a coherent field. The presence of a cavity is reflected in three cavity-modified parameters: decay rate ${\ensuremath{\gamma}}_{\mathrm{eff}}$, Rabi frequency ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{eff}}$, and detuning ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{eff}}$. We show that the cavity-modified Maxwell-Bloch equations provide an easy way to study cavity-modified spontaneous emission, cavity-induced radiative energy level shifts, and vacuum Rabi splitting.
In the framework of the nonsecular perturbation theory based on the Bogoliubov averaging method, the coherent dynamics of multiphoton Raman transitions in a two-level spin system driven by an amplitude-modulated microwave field is studied. Closed-form expressions for the Rabi frequencies of these transitions are obtained beyond the rotating-wave approximation for the low-frequency driving component. It is shown that spin states dressed by the high-frequency component of the driving field are shifted due to the Bloch-Siegert-like effect caused by antiresonant interactions with the strong low-frequency driving. We predict that with increasing the order of the Raman transition, the Rabi frequency decreases and the contribution of the Bloch-Siegert shift to this frequency becomes dominant. It is found that the amplitude and phase of the Rabi oscillations strongly depend on the initial phase of the low-frequency field as well as on detuning from multiphoton resonance. The recent experimental data for the second- and third-order Raman transitions observed for the nitrogen-vacancy center in diamond (Z. Shu et al., arXiv:1804.10492) are well described in the frame of our approach. Our results may provide new possibilities for coherent control of quantum systems.