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Physical Review Letters

Reversal of Radiation Reaction Force and Instability of the Ground State of an Atom Located above the Surface of an Active Medium

Vl. V. Kocharovsky, Vl. V. Kocharovsky, Alexey A. Belyanin

Published Apr 29, 1996• 11 citations
Publisher

Abstract

It is shown that spontaneous emission of an excited atom is suppressed, and electromagnetic instability of the ground state is possible, if an atom is located in the vicinity of an active medium which amplifies the propagating radiation. The effect is due to a modified and phase-shifted near field of an oscillating atomic dipole, which prevails over the usual radiation reaction field related to the wave zone. The necessary conditions for the reversal of the total electromagnetic back reaction are found, and possible experimental realizations are discussed.

DOI
10.1103/physrevlett.76.3285

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It is shown that spontaneous emission of an excited atom is suppressed, and electromagnetic instability of the ground state is possible, if an atom is located in the vicinity of an active medium which amplifies the propagating radiation. The effect is due to a modified and phase-shifted near field of an oscillating atomic dipole, which prevails over the usual radiation reaction field related to the wave zone. The necessary conditions for the reversal of the total electromagnetic back reaction are found, and possible experimental realizations are discussed.
. Each transition dipole in a single atom has a radiation reaction field which acts on itself and on the other transition dipoles of the atom. The self interaction on a given transition gives rise to spontaneous emission and radiative decay on that transition. Here we emphasize that the mutual radiative interaction of different transition dipoles can sometimes have important consequences. The mutual radiative interaction can substantially alter radiative decay rates and inhibit the radiative decay of certain expectation values. The hydrogen atom and the harmonic oscillator are cited as examples and a possible experimental test of mutual radiation reaction involving a single electron in a Penning trap is discussed. Introduction Modern quantum mechanics began with Heisenberg's picture of a bound charge as a “virtual orchestra” of transition dipoles oscillating at different frequencies. It is known from modern quantum theory that each of these dipoles generates a radiation reaction field which, acting on the dipole itself, gives rise to spontaneous emission and radiative relaxation (Milonni, 1976). In this paper we consider the mutual interaction of different transition dipoles within a single “atom”. We begin by considering some simple cases of mutual radiation reaction in classical electrodynamics and proceed to the quantum theory of mutual radiation reaction (MRR), citing the hydrogen atom and the charged harmonic oscillator as examples. We point out that the equations describing MRR are not at all new, but can be traced to the earliest treatments of the interaction of atoms with the quantized electromagnetic field.
Spontaneous emission may be regarded as a result of the radiation-reaction fields emitted by an atom acting back on the atom itself. It is commonly (and often implicitly) assumed that the frequencies of different transitions in the atom are sufficiently different that the field radiated by one dipole is not in near resonance with any other transition. The “secular assumption” is then made that the field couples back only on the same dipole that originally sent it. In this work we study spontaneous emission without making the secular approximation.
The novel effect of self-excitation of an atomic beam propagating above a metal surface is predicted and a theory is developed. Its underlying mechanism is positive feedback provided by the reflective surface for the atomic polarization. Under certain conditions the atomic beam flying in the near field of the metal surface acts as an active device that supports sustained atomic dipole oscillations, which generate, in their turn, an electromagnetic field. This phenomenon does not exploit stimulated emission and therefore does not require population inversion in atoms. An experiment with Rydberg atoms in which this effect should be most pronounced is proposed and the necessary estimates are given.
The theory of absorption and emission of electromagnetic radiation by an oscillator consisting of the atomic nucleus and one electrically charged particle is deduced using classical electrodynamics. In the steady state of an atom, emission and absorption of electromagnetic radiation are equal, so the atom is stable. In order to include reactive effects of electromagnetic radiation in the motion equations, the Newton equation is modified by adding the radiative reaction force. This paper is an introduction to the derivation of the basic assumptions of quantum mechanics.
Fluorescent emission by an atom near a phase conjugator (PC) based on four-wave mixing is studied from first principles. The Maxwell-Heisenberg equations are solved for the radiation field, and with an asymptotic expansion an expression is derived for the field in the far zone. The total emitted power that can be measured by a detector in this region is evaluated, and it is found that this power acquires three distinct contributions. First, there are photons that are emitted by the atom directly towards the detector, and without any interaction with the medium. Second, there are photons that first travel towards the surface of the PC, and they have a certain probability of being reflected in the specular direction and towards the detector. The third kind of radiation consists of phase-conjugated photons, which are emitted independently of the previous ones. It is shown that the first two processes are a result of simple atomic spontaneous decay, but that the emission of a phase-conjugated fluorescent photon involves a three-photon process. The latter process has a probability proportional to the population of the atomic ground state. It is pointed out that an atom in its ground state polarizes the nonlinear medium of the PC, which subsequently can emit spontaneously two photons. An absorption-emission-absorption process by the atom then produces a fluorescent photon, together with a spontaneous excitation of the atom.