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Optica Acta International Journal of Optics

Field Fluctuations in a Fabry-Pérot Cavity in Resonance with a Reservoir of Two-level Atoms: I. Adiabatic fluctuations

R. K. Colegrave, M. Sebawe Abdalla

Published Jun 1, 1983• 20 citations
Publisher

Abstract

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.

DOI
10.1080/716099648

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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 the chaotic dynamics of the interaction between an ensemble of two-level atoms in a high-Q Fabry-Perot cavity with a single mode of self-consistent field and with an external amplitude-modulated field. It is shown that in the case of an exact atom-field resonance and at the initial population of the atomic ground state, the Hamiltonian chaos in the system is always transient. The differences in the chaotic dynamics for the Fabry-Perot and ring cavity geometries are considered. The conditions for the experimental observation of the transient Hamiltonian chaos are discussed.
A method of calculation of multiple-time correlation functions of the resonance fluorescence light from a two-level atom driven by a realistic laser field with phase and amplitude fluctuations is developed. Both kinds of fluctuations are assumed to be Gaussian. The phase fluctuations are treated in the phase-diffusion model. The averaging over the amplitude fluctuations can be performed in a closed way when the relative mean-square amplitude fluctuation is small compared with the ratio of the amplitude correlation decay rate to the characteristic atomic relaxation rate. There is no restriction to Markovian amplitude fluctuations. Arbitrary values for the mean Rabi frequency are allowed. Results are presented for the intensity, the intensity correlation function, and the spectrum of the fluorescent light. It is shown that even in the case when the relative strength of the amplitude fluctuations is small, significant effects can occur due to the finite correlation length of the fluctuations. The results for fast amplitude correlation decay correspond to the situation without amplitude fluctuations. When the correlation time of the amplitude fluctuations becomes comparable with the atomic relaxation times, the Rabi oscillations of the intensity and the intensity correlation function are nearly washed out, and non-Lorentzian line shapes for the side peaks in the spectrum are observed. It is found that the ratio of the heights of the central peak to the side peak increases with increasing correlation time.
Significant fluctuations, above the shot-noise limit, have been observed in the intensity of fluorescent light scattered from atoms excited by an intense noisy laser, where a central role is played by the nonlinearity of the atom-field interaction. By considering the variance of the atomic populations, we show that ``noise spectroscopy'' is sensitive to the field statistics of the laser. We specifically consider the cases of resonance fluorescence (analogous in the weak-field limit to analysis by a Fabry-P\'erot interferometer), two-photon excitation, and double optical resonance for variable laser intensity and bandwidth. We show that large differences in the ``noise'' spectra can occur between lasers characterized by a phase-diffusion or a phase-jump model, although these models would give the same values for the mean atomic populations. We believe that observation of population fluctuations can become a useful method for characterizing laser noise.