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Physical Review A

Spontaneous emission in a Fabry-Pérot cavity: The effects of atomic motion

Martin Wilkens, Z. Bial ynicka-Birula, Pierre Meystre

Published Jan 1, 1992• 41 citations
Publisher

Abstract

We show that the spontaneous emission of a moving atom inside a cavity is modified by two different mechanisms. The first one is a Doppler-induced detuning of the cavity line that leads to observable changes in the spontaneous emission rate for atomic velocities in excess of a characteristic velocity ${\mathit{v}}_{\mathrm{cav}}$=c/Q, Q being the quality factor of the cavity. In addition, spatial mode effects can lead to a temporal modulation of the exponential decay rate. This modulation is observable for velocities that do not exceed another characteristic velocity ${\mathit{v}}_{\mathrm{mod}}$ which is typically several orders of magnitude smaller than ${\mathit{v}}_{\mathrm{cav}}$.

DOI
10.1103/physreva.45.477

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The earliest studies on the subject of spontaneous emission from an excited atom via interaction with the vacuum modes of the radiation field go back to the early days of quantum mechanics. In view of the fundamental nature of the vacuum fluctuations, it was long thought that spontaneous emission could not be controlled. However, in 1946 Purcell noted that the spontaneous emission rate of the atom inside a resonant cavity can be substantially enhanced (or suppressed) over its free-space value. This is due to the dramatic change of the density of modes of the vacuum field in a cavity. The enhancement and suppression of spontaneous emission in resonant and off-resonant cavities were observed experimentally in the 1980s. It was also realized in the 1950s and 1960s that coherent driving fields can dramatically change the characteristics of the spontaneous emission. The Autler-Townes doublet and Mollow three-peak spectrum are the examples of such behavior. A dramatic narrowing of the spectral peaks were discovered in driven multilevel atomic systems in the early 1990s. The role of atomic coherence in quenching spontaneous emission fluctuations in the context of laser physics was studied in the 1980s, via the correlated spontaneous emission laser (CEL). In this case atomic coherence results in the correlation of two spontaneous emission noise events so that the spontaneous emission quantum noise is eliminated in the relative linewidth. Later, it was “discovered” that the spontaneous emission can be suppressed through quantum interference between decay channels. Properly stated, this was rediscovered since it was first discovered and explained by Lamb in the 1940s. If the dipoles of two transitions from one upper level to two lower levels are parallel, the spontaneous emission in an ordinary vacuum can be cancelled. In a nonuniform vacuum, e.g., a cavity, the quenching of spontaneous emission can be achieved, even for the orthogonal dipoles.

•Mar 25, 2017•1 citation
We show that the spontaneous emission of a moving atom inside a cavity is modified by two different mechanisms. The first one is a Doppler-induced detuning of the cavity line that leads to observable changes in the spontaneous emission rate for atomic velocities in excess of a characteristic velocity vcav{\mathit{v}}_{\mathrm{cav}}vcav​=c/Q, Q being the quality factor of the cavity. In addition, spatial mode effects can lead to a temporal modulation of the exponential decay rate. This modulation is observable for velocities that do not exceed another characteristic velocity vmod{\mathit{v}}_{\mathrm{mod}}vmod​ which is typically several orders of magnitude smaller than vcav{\mathit{v}}_{\mathrm{cav}}vcav​.
The spontaneous emission of radiation from two two-level atoms in a Fabry–Perot cavity is considered. The transition frequency of the atoms is assumed to be modulated. It is shown that the frequency modulation leads to radical change of the spontaneous emission dynamics, including the decoherence properties of the entangled atomic states. Two ingredients are necessary in order to achieve this. Firstly, the modulation should be able to periodically detune the atoms from the resonance with the cavity. Secondly, the dynamics of spontaneous emission is efficiently modified if a resonant condition between the modulation frequency and modulation depth is fulfilled. Thus, frequency modulation can be used to dynamically control the collective effects in spontaneous emission in cavities.
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.
The spontaneous emission of an excited atom in a lossy cavity with nonorthogonal eigenmodes is analyzed. The quantum Langevin formalism is used to describe the dynamics of the spontaneous decay. The analysis shows that the spontaneous decay is modified by the Q value and the effective mode volume factor of each cavity eigenmode. The effective mode volume is generalized for cavities with nonorthogonal modes, which can be a very significant modification in the microcavity regime. It is shown that the spontaneous decay is not enhanced by the excess noise factor as claimed by other analyses.
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.
The earliest studies on the subject of spontaneous emission from an excited atom via interaction with the vacuum modes of the radiation field go back to the early days of quantum mechanics. In view of the fundamental nature of the vacuum fluctuations, it was long thought that spontaneous emission could not be controlled. However, in 1946 Purcell noted that the spontaneous emission rate of the atom inside a resonant cavity can be substantially enhanced (or suppressed) over its free-space value. This is due to the dramatic change of the density of modes of the vacuum field in a cavity. The enhancement and suppression of spontaneous emission in resonant and off-resonant cavities were observed experimentally in the 1980s. It was also realized in the 1950s and 1960s that coherent driving fields can dramatically change the characteristics of the spontaneous emission. The Autler-Townes doublet and Mollow three-peak spectrum are the examples of such behavior. A dramatic narrowing of the spectral peaks were discovered in driven multilevel atomic systems in the early 1990s. The role of atomic coherence in quenching spontaneous emission fluctuations in the context of laser physics was studied in the 1980s, via the correlated spontaneous emission laser (CEL). In this case atomic coherence results in the correlation of two spontaneous emission noise events so that the spontaneous emission quantum noise is eliminated in the relative linewidth. Later, it was “discovered” that the spontaneous emission can be suppressed through quantum interference between decay channels. Properly stated, this was rediscovered since it was first discovered and explained by Lamb in the 1940s. If the dipoles of two transitions from one upper level to two lower levels are parallel, the spontaneous emission in an ordinary vacuum can be cancelled. In a nonuniform vacuum, e.g., a cavity, the quenching of spontaneous emission can be achieved, even for the orthogonal dipoles.