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Annual Meeting Optical Society of America

Visible spontaneous emission by atoms in an optical resonator

Daniel J. Heinzen, James Childs, Michael S. Feld

Published Jan 1, 1987• 0 citations
Publisher

Abstract

Recently, we observed enhancement and inhibition of visible spontaneous emission by atoms in a confocal resonator.1 In these experiments, the partial emission rate of the atom into the resonator modes is modified by a factor of 1/(1 − R), where R is the mirror reflectivity. The change in the total spontaneous emission rate is proportional to the solid angle ΔΩ subtended by the mirrors; the change was small (+1.6%, −0.5%) because ΔΩ ≈ 0.04 sr was small. Currently we are conducting experiments in which atoms are placed in a concentric resonator of large solid angle ΔΩ ≈ 3.6 sr and finesse of ~10. We estimate that a 30% decrease and 300% increase should be observable in the total spontaneous emission rate, when the resonator is tuned off or on-resonance, respectively. Results of this new experiment are presented. In addition to studying spontaneous processes, one can also consider the stimulated emission which occurs when a cavity field builds up which contains more than one photon. We have formulated a model which describes both the spontaneous and stimulated emission by the atom into the cavity and clarifies the relationship between enhanced spontaneous emission and stimulated emission.

DOI
10.1364/oam.1987.mi5

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Annual Meeting Optical Society of America•Jan 1, 1989•0 citations
Recently, we observed enhancement and inhibition of visible spontaneous emission by atoms in a confocal resonator.1 In these experiments, the partial emission rate of the atom into the resonator modes is modified by a factor of 1/(1 − R), where R is the mirror reflectivity. The change in the total spontaneous emission rate is proportional to the solid angle ΔΩ subtended by the mirrors; the change was small (+1.6%, −0.5%) because ΔΩ ≈ 0.04 sr was small. Currently we are conducting experiments in which atoms are placed in a concentric resonator of large solid angle ΔΩ ≈ 3.6 sr and finesse of ~10. We estimate that a 30% decrease and 300% increase should be observable in the total spontaneous emission rate, when the resonator is tuned off or on-resonance, respectively. Results of this new experiment are presented. In addition to studying spontaneous processes, one can also consider the stimulated emission which occurs when a cavity field builds up which contains more than one photon. We have formulated a model which describes both the spontaneous and stimulated emission by the atom into the cavity and clarifies the relationship between enhanced spontaneous emission and stimulated emission.
We report the alteration of visible spontaneous emission by atoms coupled to the degenerate modes of a confocal resonator. The partial emission rate into the resonator modes is enhanced by a factor of 19 when the resonator is tuned to the atomic transition frequency and inhibited by a factor of 42 when it is detuned. This results in a fractional increase of 1.6% and decrease of 0.5%, respectively, in the total spontaneous emission rate, which we verify by monitoring changes in the intensity of light emitted out the sides of the resonator as it is tuned.
We revisit the problem of spontaneous emission by a two-level system in a cavity, concentrating in particular on those aspects associated with the finite propagation time of light between the atom and the cavity boundaries. We find that spontaneous emission always occurs first at the free space rate and there is then an abrupt change in these dynamics when light reflected by the cavity mirrors returns to the atom, leading to interference effects that result either in an enhancement or a reduction of this rate or in a periodic exchange of excitation between the atom and the cavity field. From this point of view, reversible spontaneous emission in terms of single-mode ``vacuum Rabi oscillations'' can be interpreted as resulting from the interference between the multimode partial waves reflected at the cavity mirrors and the instantaneously radiated light. \textcopyright{} 1996 The American Physical Society.
It is well known that spontaneous emission is not an intrinsic atomic property, but rather results from the coupling of the atom to the vacuum modes of the electromagnetic field. As such, it can be modified by tailoring the electromagnetic environment into which the atom can radiate. This was already realized by Purcell, who noted that the spontaneous emission rate can be enhanced if the atom placed inside a cavity is resonant with one of the cavity is resonant with one of the cavity modes, and by Kleppner, who discussed the opposite case of inhibited spontaneous emission. It has also been recognized that spontaneous emission need not be an irreversible process. Indeed, a system consisting of a single atom coupled to a single mode of the electromagnetic field undergoes a periodic exchange of excitation between the atom and the field. This periodic exchange remains dominant as long as the strength of the coupling between the atom and a cavity mode is itself dominant. 23 refs., 6 figs.
This chapter presents a tutorial review of spontaneous emission in optical resonators. Approximating correlation functions as delta functions means that the reservoir is assumed to lose its memory in a short time, compared to the time scale over which the dynamics of the small system occurs, the Markov approximation. In a generic cavity quantum electrodynamics experiment, an atom is coupled to one, or possibly a few, cavity mode(s). These modes are in turn coupled to the external world via mirror losses and diffraction. In addition, the atom might also be coupled to a continuum of vacuum modes, in the case where the cavity is open-sided. A simple physical interpretation of the spontaneous emission spectrum can be obtained if one adopts the point of view that the atom-cavity mode small system represents a single quantum system, and by analyzing its eigenenergy spectrum.
Introduction Ever since 1916/17 when Einstein argued [45] [46] that spontaneous emission must occur if matter and radiation are to achieve thermal equilibrium, physicists have believed that spontaneous emission is an inherent quantum mechanical property of atoms and that excited atoms inevitably radiate. This view, however, overlooks the fact that spontaneous emission is a consequence of the coupling of quantized energy states of atoms with the quantized radiation field, and is a manifestation of quantum noise or of emission ‘stimulated’ by ‘vacuum fluctuations’. An infinity of vacuum states is available to the photon radiated by an excited atom placed in free space, leading to the effective irreversibility of such emissions. If these vacuum states are modified, as for example by placing an excited atom between closely spaced mirrors or in a small cavity (essentially the Casimir effect), spontaneous emission can be greatly inhibited or enhanced or even made reversible. Recent advances in atomic and optical techniques have made it possible to control and manipulate spontaneous emission. A whole new branch of quantum optics called ‘cavity QED’ has developed since 1987 utilizing these dramatic changes in spontaneous emission rates in cavities to construct new kinds of microscopic masers or micromasers that operate with a single atom and a few photons or with photons emitted in pairs in a two-photon transition.
The properties of a phase conjugate mirror (PCM) interacting radiatively with other objects are investigated. The spontaneous emission rate of a two-level atom (TLA) is attributed to the dipole emission of the upper energy level into vacuum field modes incident on the front face of the PCM, the emission into vacuum modes transmitted from the rear port of the PCM, enhanced by a factor 1 + R (R = reflectivity), and the emission of a photon while the atom is in the lower level, accompanied by annihilation of two pump photons, weighted by a factor of R per emitted photon. These processes lead to an enhancement factor of 1 + R for the spontaneous decay rate and a steady state upper level occupation probability R/(2R + 2), both in agreement with solution of the Heisenberg equations of TLA operators.1 The momentum transfer is zero, and the steady state emission rate is A12R(R + 2)/(2R + 2) photons/s atom. The stimulated emission and absorption constants are enhanced in a similar way. Contrary to the case of a conventional mirror, the Lippman fringes are present only for coherent radiation states.