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Physical Review A

Dynamical Lamb effect versus dynamical Casimir effect

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

Published Oct 4, 2001• 41 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.64.053807

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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 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 excitation of the atom, even if photons were initially absent in the cavity. We study a new mechanism of atom excitation and photon creation inside the cavity which we call the dynamical Lamb effect, and which has no relation to the dynamical Casimier effect. Several aspects of this mechanism are studied, including physical interpretation, amplification of the amplitude in the case of long-time periodic variation of the cavity parameters, and possible physical realization. Although the consideration is based mainly on a simple model of an atom interacting with a single mode of quantized electromagnetic field, and the results are qualitatively valid for more realistic models.
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.
A natural atom placed into a cavity with time-dependent parameters can be parametrically excited due to interaction with the quantized photon mode. One of the channels for this process is the dynamical Lamb effect, induced by a nonadiabatic modulation of the atomic-level Lamb shift. However, in experiments with natural atoms it is quite difficult to isolate this effect from other mechanisms of atom excitation. We point out that a transmission line cavity coupled with a superconducting qubit (an artificial macroscopic atom) provides a unique platform for observation of the dynamical Lamb effect. A key idea is to exploit a dynamically tunable qubit-resonator coupling, which was implemented quite recently. By varying the coupling nonadiabatically, it is possible to parametrically excite a qubit through a nonadiabatic modulation of the Lamb shift, even if the cavity was initially empty. The dynamics of such a coupled system is studied within the Rabi model with a time-dependent coupling constant and beyond the rotating-wave approximation. An efficient method to increase the effect through the periodic and nonadiabatic switching of the qubit-resonator coupling energy is proposed.
We study analytically and numerically the dynamics of the quantum non-stationary system composed of a two-level atom interacting with a single mode cavity field whose frequency is rapidly modulated in time (with a small amplitude). We identify modulation laws resulting in qualitatively different dynamical regimes and we present analytical solutions in some simple cases. In particular, we analyse minutely the influence of the field–atom coupling on the photon generation from vacuum via the dynamical Casimir effect.
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.