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Physical Review A

Power spectra and variance of laser-noise-induced population fluctuations in two-level atoms

Helmut Ritsch, P. Zoller, J. Cooper

Published Mar 1, 1990• 44 citations
Publisher

Abstract

Variances and power spectra of the resonance fluorescence intensity induced by laser noise in two-level systems are studied theoretically. The effects of amplitude and phase noise fluctuations of a single-mode laser are investigated. Correlations of amplitude and phase fluctuations, as is relevant for excitation with diode lasers, are shown to lead to pronounced asymmetries in variance spectra.

DOI
10.1103/physreva.41.2653

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Variances and power spectra of the resonance fluorescence intensity induced by laser noise in two-level systems are studied theoretically. The effects of amplitude and phase noise fluctuations of a single-mode laser are investigated. Correlations of amplitude and phase fluctuations, as is relevant for excitation with diode lasers, are shown to lead to pronounced asymmetries in variance spectra.
We have measured the variance in fluorescence intensity and the spectrum of those fluctuations for two-level atoms in a phase-diffusing laser field. We compare our results with recent theoretical predictions that have been extended to include the effects of Doppler broadening and spatial variation of the laser intensity. Our study includes the effects of laser power, bandwidth, and shape (Lorentzian and non-Lorentzian) of the laser spectrum. At lower laser intensities, our measured variances versus detuning are in quantitative agreement with the theoretical predictions. At intensities above saturation, the variance is sensitive to inhomogeneities in the distribution of laser intensity in the interaction region, and only qualitative agreement is achieved. Asymmetries in the variance versus detuning resulting from correlated amplitude and phase noise have been observed. Spectra of the phase-noise-induced fluorescence-intensity fluctuations are shown to contain contributions from transients excited by the phase noise and are more sensitive to artifacts in the noise modulation process than the intensity spectrum of the laser field itself.
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.
The nonlinear dynamics of a sample of two-level systems exposed to noisy laser light is investigated. As stochastic models we treat the chaotic field and the real Gaussian field. Based on the method of marginal characteristic functions, we deduce analytical solutions for the mean values and variances of the atomic populations in terms of matrix continued fractions. We find significantly enhanced on-resonance fluctuations for a real Gaussian field compared to a chaotic field of the same bandwidth and intensity. Furthermore, in contrast to phase-noise models, the fluctuations in the fluorescence intensity do not decrease to zero in the limit of slow fluctuations.
The dynamical behavior of an atom interacting with a coherent and a chaotic field is investigated. Langevin equations describing the time dependent behavior of the dipole moment and population inversion are numerically integrated using Monte-Carlo techniques. The model can account for a finite correlation time for the chaotic component. Results on fluctuations in the fluorescence intensity from an ensemble of two-level atoms and the power spectra of these intensity fluctuations are presented. The effect of detuning the pump field from the resonant frequency of the two-level atoms on the fluctuations in fluorescence is studied. The effect of field fluctuations on the macroscopic polarization produced by the atoms is also reported. The fluctuation behavior of the atomic fluorescence is found to be very sensitive to the correlation time of the stochastic component.