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Optica Acta International Journal of Optics

Periodic Fluctuations in a Fabry-Perot Cavity in Resonance with a Reservoir of Two-level Atoms

R. K. Colegrave, A. Vahabpour-Roudsari

Published Apr 1, 1985• 18 citations
Publisher

Abstract

The Maxwell equations for the field in a cavity are modified to include the effect of irradiation by a reservoir of two-level atoms. A canonical treatment of the time-dependent field modes leads to predictions of the changes in the electric and magnetic field intensities, and in the photon statistics, for sufficiently small times. Coherent states evolve to squeezed states. The frequency converter and possible resonance phenomena are discussed.

DOI
10.1080/713821744

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The Maxwell equations for the field in a cavity are modified to include the effect of irradiation by a reservoir of two-level atoms. A canonical treatment of the time-dependent field modes leads to predictions of the changes in the electric and magnetic field intensities, and in the photon statistics, for sufficiently small times. Coherent states evolve to squeezed states. The frequency converter and possible resonance phenomena are discussed.
A canonical approach using variable mass parameters presented in an earlier paper is applied to the case of an electromagnetic field of slowly varying intensity in a cavity in the presence of a reservoir of resonant two-level atoms. The effect is to replace any cavity frequency y s by a reduced variable frequency z s (t). Calculations have been carried out for the changes in the atomic transition amplitudes that are produced by an externally imposed adiabatic change in the field intensity, or by a small low-frequency periodic fluctuation in the photon population which could be due to the Rabi flopping of the atoms.
Two kinds of periodic fluctuation in the intensity of the field in a Fabry-Pérot cavity are considered: (a) a strong pulsation with periodically vanishing intensity, identifiable with the interaction of a low-density atomic reservoir and (b) a pulsation of adjustable strength and non-vanishing intensity whose frequency is approximately twice that of a natural mode. Self-consistent values are found in each case for the resonance frequency and for the on-resonance Rabi frequency. Case (b) may be identified with a pump-signal-idler system in which the signal and idler frequencies are approximately equal, and these modes can be damped out if the pulsation is sufficiently strong.
We consider effects of a broadband squeezed reservoir on the second-order intensity correlation, and on squeezing properties in the resonance fluorescence of a bichromatically driven two-level atom in a cavity of moderate Q. Phase-dependent squeezed reservoir effects change the photon statistics, and lead to an amplification of the degree of squeezing. Squeezed reservoir effects in the second-order correlation function ${g}^{(2)}(\ensuremath{\tau})$ are determined by two-photon emission processes which can be enhanced or suppressed in dependence on the squeezing phase.
There is increasing interest in the photon statistics and spectroscopic properties of the radiation from atoms confined in an optical cavity. Effects such as the cavity enhancement and inhibition of spontaneous emission, which were first observed using microwave cavities, have recently been measured at optical frequencies.1 Recent measurements of squeezing and the dynamic effects of single-quantum-level splittings also demonstrate the possibilities for quantum-statistical studies of coupled atom-cavity systems at optical frequencies.2 We study a single two-level atom confined inside an optical cavity which is driven by coherent light in resonance with both cavity and atom. For weak driving field intensities we have calculated the spectrum of the light transmitted by the cavity and fluorescence out the sides of the cavity.
Interesting new aspects of atomic behavior in the presence of strong driving fields appear when the driven atom resides not in free space, but in a region (such as an optical cavity) that displays a frequency-dependent photon-mode density. Under such conditions, it is found that a strong driving field can modify the spontaneous decay properties of an atom, and thereby give rise to interesting new features in the spectrum of strong-field resonance fluorescence. It is also found that a high level of dressed-state polarization can be maintained in a sample of resonantly or nonresonantly driven atoms by appropriate tuning of an enclosing cavity. Furthermore, for appropriate laser and cavity tunings, it is found that the atomic states become highly squeezed. In the course of analyzing these effects, a set of modified Bloch equations is derived that explicitly accounts for the finite response time associated with a frequency-dependent photon-mode density.