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arXiv:quant-ph/0412134 · Physical Review A

Quantum electrodynamics of accelerated atoms in free space and in cavities

Alexey A. Belyanin, Vitaly V. Kocharovsky, Federico Capasso, Edward S. Fry, Muhammad Suhail Zubairy, Marlan O. Scully

Published Aug 15, 2006• 59 citations
arXivHTMLPDF

Abstract

We consider a gedanken experiment with a beam of atoms in their ground state that are accelerated through a single-mode cavity. We show that taking into account of the ``counterrotating'' terms in the interaction Hamiltonian leads to the excitation of an atom with simultaneous emission of a photon into a field mode. In free space, when the atom-field interaction is turning on/off adiabatically, the only nonadiabatic effect that causes the excitation is the time-dependent Doppler shift. The resulting ratio of emission and absorption probabilities is exponentially small and is described by the Unruh factor. In the opposite case of rapid turn on of the interaction on the cavity boundaries the above ratio is much greater and radiation is produced with an intensity which can exceed the intensity of radiation in free space by many orders of magnitude. In both cases real photons are produced. The cavity field at steady state has a thermal density matrix. However, under some conditions laser gain is possible. We present a detailed discussion of how the acceleration of atoms affects the generated cavity field in different situations. We identify a common physical mechanism behind the Unruh effect and similar QED radiation processes.

DOI
10.1103/physreva.74.023807

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We consider a gedanken experiment with a beam of atoms in their ground state that are accelerated through a single-mode cavity. We show that taking into account of the ``counterrotating'' terms in the interaction Hamiltonian leads to the excitation of an atom with simultaneous emission of a photon into a field mode. In free space, when the atom-field interaction is turning on/off adiabatically, the only nonadiabatic effect that causes the excitation is the time-dependent Doppler shift. The resulting ratio of emission and absorption probabilities is exponentially small and is described by the Unruh factor. In the opposite case of rapid turn on of the interaction on the cavity boundaries the above ratio is much greater and radiation is produced with an intensity which can exceed the intensity of radiation in free space by many orders of magnitude. In both cases real photons are produced. The cavity field at steady state has a thermal density matrix. However, under some conditions laser gain is possible. We present a detailed discussion of how the acceleration of atoms affects the generated cavity field in different situations. We identify a common physical mechanism behind the Unruh effect and similar QED radiation processes.
When ground-state atoms are accelerated through a high Q microwave cavity, radiation is produced with an intensity which can exceed the intensity of Unruh acceleration radiation in free space by many orders of magnitude. The reason is a strong nonadiabatic effect at cavity boundaries and its interplay with the standard Unruh effect. The cavity field at steady state is still described by a thermal density matrix under most conditions. However, under some conditions gain is possible, and when the atoms are injected in a regular fashion, squeezed radiation can be produced.
Rapid advances in quantum technology have made possible the control of quantum states of elementary material quantum systems, such as atoms or molecules, and of the electromagnetic radiation field resulting from spontaneous photon emission of their unstable excited states to such a level of precision that subtle quantum electrodynamical phenomena have become observable experimentally. Recent developments in the area of quantum information processing demonstrate that characteristic quantum electrodynamical effects can even be exploited for practical purposes provided the relevant electromagnetic field modes are controlled by appropriate cavities. A central problem in this context is the realization of an ideal transfer of quantum information between a state of a material quantum system and a quantum state of the electromagnetic radiation field which contains a small number or even a single photon only. Despite much recent work in cavity quantum electrodynamics, which has explored this problem successfully in cases in which the number of accessible electromagnetic field modes is strongly restricted by a cavity, currently still much less is known about ideal quantum state transfer between matter and few-photon quantum states of the electromagnetic field in the extreme opposite case of free space. In this contribution we review recent work which explores characteristic quantum electrodynamical phenomena governing the interaction of a material quantum system with the electromagnetic field in extreme many-mode cases which are close to cavity-free situations. For this purpose the simplest possible quantum electrodynamical situation, namely the interaction of a single material two-level system with the wave packet of a single optical photon, is investigated in free space and in situations in which a large cavity modifies the mode structure of the electromagnetic field modes. It is demonstrated that perfect excitation of an atom by a properly shaped single-photon wave packet is possible even in free space. In particular, it is demonstrated that perfect excitation of an atom can be achieved by a single optical photon which is prepared initially in an appropriate superposition of plane-wave modes, provided this photon is focused subsequently onto the absorbing atom by a parabolic cavity.
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.
The contribution of vacuum fluctuations and the radiation reaction to the energy-level shifts of a hydrogen atom, moving with uniform acceleration and interacting with the electromagnetic field, is considered. It is found that the reaction field contribution is not affected by the acceleration, whereas the vacuum fluctuations' contribution depends on the acceleration. The differences with previous results for an accelerated two-level atom interacting with a scalar field are discussed in detail; in particular, it is shown that the effect of electromagnetic vacuum fluctuations on atomic level shifts, contrarily to the scalar field case, is not totally equivalent to that of a thermal field. It is argued that this lack of equivalence should be observable.
Abstract We investigate a two-level atom interacting with a massless real scalar field inside an infinitely long cylindrical cavity, and calculate separately the contributions of vacuum fluctuations and radiation reaction to the mean atomic energy-change rate when the atom moves along the cavity axis. Using the formalism suggested by Dalibard, Dupont-Roc, and Cohen-Tannoudji, we analyze both inertial and uniformly accelerated motion, and discuss the behavior in the low-acceleration and high-acceleration regimes. For the inertial atom, we further introduce a finite cavity quality factor Q to phenomenologically account for cavity dissipation, which regularizes the resonant singularity of the ideal lossless cavity and yields finite resonant peaks. For a uniformly accelerated excited-state atom in the low-acceleration regime, the energy-change rate remains finite at the nominal resonance points, but exhibits pronounced oscillatory enhancement near resonance. In certain parameter regions, the cavity result can exceed both the corresponding inertial result in the same cavity and the uniformly accelerated result in free space, revealing the combined effect of acceleration-induced broadening and the discrete transverse mode structure of the cylindrical boundary. In the high-acceleration regime, a ground-state atom may undergo spontaneous excitation, while the cavity resonance structure is strongly suppressed and the energy-change rate gradually approaches the corresponding free-space value. These results show that the cylindrical geometry can significantly reshape the radiative response of accelerated atoms, enhancing acceleration-induced effects at low acceleration while washing out cavity-induced resonances at high acceleration.
We review recent experimental advances in the field of efficient coupling of single atoms and light in free space. Furthermore, a comparison of efficient free space coupling and strong coupling in cavity quantum electrodynamics (QED) is given. Free space coupling does not allow for observing oscillatory exchange between the light field and the atom which is the characteristic feature of strong coupling in cavity QED. Like cavity QED, free space QED does, however, offer full switching of the light field, a 180° phase shift conditional on the presence of a single atom as well as 100% absorption probability of a single photon by a single atom. Furthermore, free space cavity QED comprises the interaction with a continuum of modes.