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Journal of Physics B Atomic Molecular and Optical Physics

Spontaneous emission in a Fabry–Perot cavity: frequency modulation and collective effects

Maciej Janowicz, Arkadiusz Orłowski, Jan Mostowski

Published Mar 10, 2008• 3 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/41/6/065501

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Cavity-modified spontaneous emission: From Rabi oscillations to exponential decay

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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.

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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 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 resonant quantum dynamics of an excited two-level emitter is investigated via classical modulation of its transition frequency while simultaneously the radiator interacts with a broadband electromagnetic field reservoir. The frequency of modulation is selected to be of the order of the bare-state spontaneous decay rate. In this way, one can induce quantum interference effects, and consequently, quantum coherences among multiple decaying transition pathways. Depending on the modulation depth and its absolute phase, both the spontaneous emission and the frequency shift may be conveniently modified and controlled.
We discuss the frequency dependence of the spontaneous-emission rate (power) in a Fabry-Perot microcavity containing a Lorentz dielectric, with emphasis on modifications of the spectrum under the circumstances of the strong medium-cavity coupling. With the standard-cavity tuning, the total spontaneous-emission power spectrum consists of a multiwave version of the familiar low-frequency vacuum Rabi split peak and a broad structure on the high-frequency side coming from the enhanced spontaneous emission into the continuum of the obliquely propagating waves. This form of the spectrum derives from the properties of the (single-wave) radiation-intensity spectrum of the molecule. Depending on the observation direction, the radiation-intensity spectrum exhibits either a double-peak structure characteristic of the vacuum Rabi splitting, as observed in light transmisssion and reflection experiments, or a single-peak structure describing the enhanced spontaneous emission at the corresponding cavity resonant frequency.
In the paper, we theoretically discuss the use of dynamic cavity environment to realize controlling of the evolution of spontaneous emission from an excited two-level atom. It is found that cyclical changes in cavity environment leads to the interaction betwcen the electromagnetic modes, resulting in the redistribution of the electromagnetic modes density; both the frequency of energy exchange and the energy dissipation rate between atom and environment are affected. When the frequency of environment change is relatively accordant with the process of energy exchange between the atom and environment, the decay rate is obviously inhibited and a stable coherence evolution can be obtained. Thus the evolution of coherent states can be modulated by using dynamic environment changes.
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.