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Physical Review Letters

Observation of population fluctuations in two-level atoms driven by a phase diffusing field

Michael H. Anderson, Rob D. Jones, J. Cooper, Stuart James Smith, Daniel S. Elliott, Helmut Ritsch, P. Zoller

Published Mar 19, 1990• 50 citations
Publisher

Abstract

We have measured the variance in fluorescence intensity as a phase diffusing laser is scanned through resonance with a beam of two-level atoms. For laser intensities below saturation, our results are in quantitative agreement with recent theoretical predictions provided Doppler effects are treated. Above saturation, the agreement is somewhat less quantitative primarily due to the sensitivity of the predictions to the laser intensity profile and the experimental uncertainty in measuring it.

DOI
10.1103/physrevlett.64.1346

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We have measured the variance in fluorescence intensity as a phase diffusing laser is scanned through resonance with a beam of two-level atoms. For laser intensities below saturation, our results are in quantitative agreement with recent theoretical predictions provided Doppler effects are treated. Above saturation, the agreement is somewhat less quantitative primarily due to the sensitivity of the predictions to the laser intensity profile and the experimental uncertainty in measuring it.
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 behaviour of a two-level atom saturated by a resonant fluctuating laser beam is studied. A classical description of the light wave is used, corresponding to a laser well above threshold. Two different approximations are introduced for treating the effects of slow and fast fluctuations; slow fluctuations are followed adiabatically by the atom and fast fluctuations appear as a relaxation mechanism for the population difference and for the optical dipole moment obeying the motional-narrowing condition. The perturbation of the spectral distribution of the fluorescence light is determined quantitatively and the great sensitivity of this spectrum to higher order correlation functions of the light wave is exhibited.
The relaxation process and resonance fluorescence of a two-level atom strongly driven by stochastically fluctuating laser light is studied. A laser with small intensity fluctuations about a constant mean value and a diffusing phase is assumed. Depending on the relative time scales of the intensity fluctuations and the atomic response to these fluctuations, the time decay of the atomic population is found to be non-exponential. The broadening of the sidebands in the triplet spectrum of resonance fluorescence is shown to be non-Lorentzian.