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Zeitschrift für Naturforschung A

Laser-Phase-Noise-Induced Stochastic-Resonance Fluorescence

Chang Su, Abbas A. Rangwala, K. Wódkiewicz

Published Feb 1, 1997• 1 citation
Publisher

Abstract

Abstract Stochastic fluctuations of coherent and incoherent components of the resonance fluorescence intensity induced by Wiener-Levy laser phase noise are investigated. Statistical properties of the atomic dipole moment and stochastic Mollow spectra of atomic dipole fluctuations for different values of the laser linewidth and Rabi frequency are calculated. It is shown that these spectra exhibit a triplet structure which is purely classical and entirely laser-noise dependent.

DOI
10.1515/zna-1997-1-232

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Abstract Stochastic fluctuations of coherent and incoherent components of the resonance fluorescence intensity induced by Wiener-Levy laser phase noise are investigated. Statistical properties of the atomic dipole moment and stochastic Mollow spectra of atomic dipole fluctuations for different values of the laser linewidth and Rabi frequency are calculated. It is shown that these spectra exhibit a triplet structure which is purely classical and entirely laser-noise dependent.
Stochastic fluctuations of coherent and incoherent components of the resonance fluorescence intensity induced by Wiener-Levy laser phase noise are investigated. Statistical properties of the atomic dipole moment for different values of the laser linewidth and different strength of the driving field are calculated. The stochastic Mollow spectra of atomic dipole fluctuations are derived. It is shown that these spectra exhibit a triplet structure which is purely classical and entirely laser-noise dependent.
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.
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.
Strong laser fields, when tuned on resonance to an atomic (molecular) transition, give rise to the well-known triplet of resonance fluorescence. The laser field is normally assumed to be strong and monochromatic, even though the spectrum of real lasers is never a \ensuremath{\delta} function. A standard way to treat laser fluctuations has been to assume a well-defined nominal frequency and a randomly fluctuating phase. Recently we introduced the generalized jump model (GJM) for correlated phase fluctuations, where correlated phase jumps are considered, leading to Markovian as well as non-Markovian stochastic behavior. In the GJM, each phase jump may be correlated to the previous jump, and the degree of correlation, the typical jump size, and the mean time between jumps are the three parameters defining the stochastic character of the laser field. In this paper we apply the GJM model to the case of resonance fluorescence from an atom excited by a stochastic field. The ``standard'' Mollow triplet is obtained in the monochromatic limit of small jumps, and several new predictions are made in the different limits of the stochastic parameters. In the small-jump limit, a new ``field effect'' is predicted. The spectral line shape and the triplet separation deviate from the Mollow predictions for a monochromatic field in a substantial way, giving rise to observable differences.In the highly correlated small-jump limit, which is approximated by the Kubo oscillator model, the previous results are corrected to include nonzero line shifts and extended to the case of non-Lorentzian line shapes. In all regions, even input fields of the same line shape (which would be considered identical in the one-parameter linewidth description) give rise to very different output spectra, justifying the more complete stochastic description. Effective relaxation constants ${\mathrm{\ensuremath{\Gamma}}}_{1}^{\mathrm{*}}$ and ${\mathrm{\ensuremath{\Gamma}}}_{2}^{\mathrm{*}}$ that simplify the description of the spectrum are calculated in all appropriate cases, and ${\mathrm{\ensuremath{\Gamma}}}_{1}^{\mathrm{*}}$ is found to equal the input laser linewidth. In addition to predicting the resonance fluorescence spectra, the present analysis provides a way to extract the stochastic parameters from the nonlinear measurement in those cases where the linear characterization of the input field cannot do it. The analytic work is fully supported by extensive numerical simulations.
Resonance fluorescence by an atom near the surface of a phase conjugator is studied. The atom is irradiated by a finite-linewidth laser beam, and the bandwidth is modelled by a randomly fluctuating phase. Expressions for the steady-state atomic density operator and the resonance fluorescence spectrum are obtained. For a small laser linewidth the spectrum contains two delta peaks: the usual peak at the laser frequency and its phase-conjugate image. In the limit of separated lines the spectrum consists of the Mollow triplet and its phase-conjugate replica. In the image triplet the positions of the fluorescence line and the three-photon line are reversed, as compared with the original triplet. Also, the intensity of the image spectrum is distributed differently over the three lines.
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.