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Journal of Experimental and Theoretical Physics Letters

Excitation of an atom in a nonstationary cavity

Yu. E. Lozovik, Nikolay B. Narozhny, Alexander M. Fedotov

Published Sep 1, 2000• 3 citations
Publisher

Abstract

The effect of excitation of an atom in an initially photon-free nonstationary cavity is predicted. Two excitation mechanisms are considered, both different from the trivial absorption of photons created due to the nonstationary Casimir effect. The first one is based on the fact that the photon states appear simultaneously with atomic excitation if the characteristic time of cavity nonstationarity is of the same order as the atomic transition time. The second one is associated with the “shake-up” effect caused by the modulation of the atomic ground-state Lamb shift upon a fast change in the cavity parameters. The presence of an atom in the nonstationary cavity affects the photon creation process. In particular, it changes the average number of generated photons and removes the constraint (inherent in the nonstationary Casimir effect) that only an even number of photons can be created. In addition, a new mechanism of photon generation associated with the shake-up effect appears.

DOI
10.1134/1.1324017

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Journal of the Optical Society of America B•May 21, 2019•2 citations
The effect of excitation of an atom in an initially photon-free nonstationary cavity is predicted. Two excitation mechanisms are considered, both different from the trivial absorption of photons created due to the nonstationary Casimir effect. The first one is based on the fact that the photon states appear simultaneously with atomic excitation if the characteristic time of cavity nonstationarity is of the same order as the atomic transition time. The second one is associated with the “shake-up” effect caused by the modulation of the atomic ground-state Lamb shift upon a fast change in the cavity parameters. The presence of an atom in the nonstationary cavity affects the photon creation process. In particular, it changes the average number of generated photons and removes the constraint (inherent in the nonstationary Casimir effect) that only an even number of photons can be created. In addition, a new mechanism of photon generation associated with the shake-up effect appears.
We consider an atom interacting with a quantized electromagnetic field inside a cavity with variable parameters. The atom in the ground state located in the initially empty cavity can be excited by variation of cavity parameters. We have discovered two mechanisms of atomic excitation. The first arises due to the interaction of the atom with the non-stationary electromagnetic field created by modulation of cavity parameters. If the characteristic time of variation of cavity parameters is of the order of the atomic transition time, the processes of photon creation and atomic excitation are going on simultaneously and hence excitation of the atom cannot be reduced to trivial absorption of the photons produced by the dynamical Casimir effect. The second mechanism is "shaking" of the atom due to fast modulation of its ground state Lamb shift which takes place as a result of fast variation of cavity arameters. The last mechanism has no connection with the vacuum dynamical Casimir effect. Moreover, it opens a new channel of photon creation in the non-stationary cavity. Nevertheless, the process of photon creation is altered by the presence of the atom in the cavity, even if one disregards the existence of the new channel. In particular, it removes the restriction for creation of only even number of photons and also changes the expectation value for the number of created photons. Our consideration is based on a simple model of a two-level atom interacting with a single mode of the cavity field. Qualitatively our results are valid for a real atom in a physical cavity.
An atom interacting with a quantized electromagnetic field in a cavity with time-dependent parameters is considered. Variation of the cavity parameters results in nonstationary dynamics of the field which leads, in turn, to excitation of the atom, even if photons were initially absent in the cavity. We distinguish three mechanisms of such excitation: excitation due to absorption of real photons created by the dynamical Casimir effect, excitation due to absorption of virtual photons during the transient process, and excitation due to nonadiabatic parametric modulation of the atomic Lamb shift. The last mechanism has no relation to the dynamical Casimir effect and thus should be considered as a new vacuum QED effect. Normally all these three mechanisms give a contribution to the amplitude of the atom excitation and are accompanied by the creation of photons. Therefore the presence of an atom in the cavity alters the average number of created photons in comparison with the case of an empty non-stationary cavity. Our consideration is based mainly on a simple model of a two-level atom interacting with a single mode of quantized electromagnetic field. However, our results are qualitatively valid for more realistic models.
We study theoretically the nonstationary circuit QED system in which the artificial atom transition frequency, or the atom-cavity coupling, have a small periodic time modulation, prescribed externally. The system formed by the atom coupled to a single cavity mode is described by the Rabi Hamiltonian. We show that, in the dispersive regime, when the modulation periodicity is tuned to the 'resonances', the system dynamics presents the dynamical Casimir effect, resonant Jaynes-Cummings or resonant Anti-Jaynes-Cummings behaviors, and it can be described by the corresponding effective Hamiltonians. In the resonant atom-cavity regime and under the resonant modulation, the dynamics is similar to the one occurring for a stationary two-level atom in a vibrating cavity, and an entangled state with two photons can be created from vacuum. Moreover, we consider the situation in which the atom-cavity coupling, the atomic frequency, or both have a small non-periodic time modulation, and show that photons can be created from vacuum in the dispersive regime. Therefore, an analog of the dynamical Casimir effect can 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.
We study a simple version of the dynamical Casimir effect in a single electromagnetic cavity mode containing a Kerr medium. We obtain an approximate expression for the time evolution operator valid for short times and/or low average photon number. We have found that the generation of photons from quantum vacuum is strongly affected by the presence of the Kerr medium. In the time domain it shows strong oscillations, whose frequency increases with the intensity of the nonlinear medium, sharing physical features with the case of two two-level atoms in a cavity with oscillating walls. Using a semiclassical approach, we show that Kerr nonlinearity produces a faster decrease in the photon production rate than that reported in previous studies working on quasi-resonant nonstationary cavities. We also found that the initial vacuum state can evolve in a cat sate. We expect that these results could be relevant for any study involving the dynamical Casimir effect that is willing to incorporate Kerr nonlinearities.
We develop a microscopic toy model for cavity dynamical Casimir effect (DCE), namely, the photon generation from vacuum due to a nonstationary dielectric slab in a fixed single-mode cavity. We represent the slab by N ≫ 1 noninteracting two-level atoms coupled to the field via the standard dipole interaction. We show that the DCE is contained implicitly in the light–matter interaction Hamiltonian when its parameters are assumed externally prescribed functions of time. We also predict several new phenomena, such as saturation of the photon growth due to effective Kerr nonlinearity, generation of pairs of atomic excitations instead of photons (‘inverse DCE’) and coherent annihilation of pair of system excitations due to the atomic modulation (‘anti-DCE’). These results are extended to the circuit QED architecture where similar effects can be implemented with a single qubit, providing an alternative way to generate novel cavity and atom–field entangled states.
We study a simple version of the dynamical Casimir effect in a single electromagnetic cavity mode containing a Kerr medium and a two-level atom. We obtain approximate expressions for the time-evolution operator valid at short times and/or low average photon number. We have found an interplay between the effect of the nonlinear Kerr medium, which is to decrease the growth of photon generation from the vacuum state, and that of the two-level atom, which is to increase the photon generation. We explore an ample range of Hamiltonian parameters going from the resonant to the dispersive regimes.