Calculations on the Hanle effect in a J - J:i atomic transition are performed for laser fields with a) Brownian motion phase diffusion b) Gaussian amplitude fluctuations and c) fluctuating real and imaginary parts of the laser electric field amplitude (chaotic field model). We use the Fokker-Planck operator approach to stochastic differential equations. The zero-field level-crossing dip broadens at high laser intensity significantly less so as the laser bandwidth increases or if the amp]itu(le fluctuates.
Calculations on the Hanle effect in a J - J:i atomic transition are performed for laser fields with a) Brownian motion phase diffusion b) Gaussian amplitude fluctuations and c) fluctuating real and imaginary parts of the laser electric field amplitude (chaotic field model). We use the Fokker-Planck operator approach to stochastic differential equations. The zero-field level-crossing dip broadens at high laser intensity significantly less so as the laser bandwidth increases or if the amp]itu(le fluctuates.
We report results of calculations on the Hanle effect in a J=0\ensuremath{\leftrightarrows}J=1 atomic transition with three types of model fluctuating light fields: (a) the Brownian-motion phase-diffusion field, as produced in recent experiments by Arnett et al. [Phys. Rev. A 41, 2580 (1990)]; (b) Gaussian amplitude fluctuations; and (c) the chaotic field model, in which real and imaginary parts of the electric-field amplitude fluctuate. For the stochastic density-matrix equations, we use methods developed by Zoller and co-workers [e.g., Dixit, Zoller, and Lambropoulos, Phys. Rev. A 21, 1289 (1980)] employing the Fokker-Planck operator and leading to matrix continued-fraction expansions. The Hanle effect is of interest as a prototype for multisublevel atomic transitions. The width of the Hanle dip at zero magnetic field reflects the tendency of the light field to preserve the coherence between excited-state sublevels. For monochromatic light, the Hanle dip width increases as the square root of light intensity. When the laser bandwidth increases, power broadening of the coherence dip normally decreases. However, with the Brownian-motion phase-diffusion model, if the laser spectral profile is nearly Gaussian, broadening the laser up to several times the natural width of the atomic line does not diminish the Hanle dip width. With amplitude fluctuations, even in the limit of monochromatic light, power broadening of the Hanle dip with intensity is reduced by one-third to one-half depending on the particular model.
We have carried out experimental and theoretical investigations of the Hanle effect in the 1S0${\ensuremath{\rightarrow}}^{3}$P1 transition at \ensuremath{\lambda}=555.6 nm in 174Yb, emphasizing the dependence of the Hanle signal on the intensity and on the statistical parameters of a well-characterized phase-diffusing optical field. The phase and frequency fluctuations imposed on the laser beam by a system of modulators are described by two parameters corresponding to the bandwidth \ensuremath{\beta} and the spectral density b of the noise spectrum. The shape of the laser power spectrum is continuously variable between nearly Gaussian (b/\ensuremath{\beta}\ensuremath{\gg}1) and nearly Lorentzian (b/\ensuremath{\beta}\ensuremath{\ll}1). Measurements are made with a well-collimated Yb atomic beam crossed at right angles by a linearly polarized laser beam. In accord with theoretical predictions, the full width at half maximum (FWHM) of the Hanle effect coherence dip is found to increase as the square root of the laser intensity for monochromatic excitation. For a given intensity, the FWHM decreases as the laser bandwidth increases. With the same laser intensity and spectral width, the FWHM of the Hanle coherence dip increases as the laser spectral profile approaches the Gaussian limit, particularly when \ensuremath{\beta}/2\ensuremath{\pi} is within an order of magnitude of the natural width of the atomic line. The Hanle signal shapes agree well with theoretical calculations using a Brownian motion phase-diffusion model of the laser field. For large \ensuremath{\beta}, it suffices to apply substitution rules for simple phase diffusion to the density-matrix equations.
A generalized Fokker-Planck equation is derived for a system undergoing optical bistability when the dominant source of fluctuations is due to fluctuations in the incident field rather than spontaneous emission. The fluctuations are treated as a time-dependent Gaussian process whose properties are determined by the individual laser's characteristics. Both amplitude and phase fluctuations are included on the incident laser field. The effect of fluctuations of the incident laser on optical bistability are different for amplitude and phase fluctuations and are different for absorptive and dispersive optical bistability. The combination of incident laser phase fluctuations and dispersive optical bistability leads to large amplitude fluctuations near the turning points of the optical bistability curve and causes the system to make a transition from one branch of the optical bistability curve to the other before reaching the mean-field turning points. We take the high-Q cavity limit of our generalized Fokker-Planck equation, solve the linearized equations, and provide criteria for the magnitude of fluctuations in optical bistability in terms of laser and cavity parameters. The magnitude of incident laser fluctuations are typically orders of magnitude larger than fluctuations due to spontaneous emission and are therefore important for practical applications of optical bistability devices.
The authors present a theory of the potential scattering in the presence of a laser field taken with a well stabilised amplitude and a randomly fluctuating phase (phase diffusion model, PDM), and investigate the structure of the scattering lineshapes in the weak- and strong-field limits. The field, with its statistics, enters the theoretical treatment in a non-perturbative way. This gives the possibility of obtaining new information on the role of the statistical properties of the radiation fields in highly non-linear domains of the matter-field interaction, which complements in a significant way what is presently known. The PDM results are compared with those relative to a chaotic field (multimode laser field with a large number of uncorrelated modes). The broadening of the scattering lines is found to be controlled in an essential way by several parameters (field bandwidth, strength of the particle-field coupling, field intensity and so on); among them, the multiplicity of the exchanged photons becomes the most important only in the limit of weak coupling. In the strong-coupling limit, a chaotic field (i.e. a field undergoing amplitude and phase fluctuations) is found to broaden the scattering lines in a more effective way than a PDM field.
We study the effects of cross-correlations between the real and imaginary parts of quantum noise on the intensity fluctuation of a saturation laser model. By virtue of the locked phase method,we derived an approximate Fokker–Planck equation and analytic expressions of the stationary probability distribution function (SPD) of the laser system. Based on the SPD, the mean, the normalized variance, and the normalized skewness of the steady-state laser intensity are calculated numerically. The results indicate that the correlation strength of the cross-correlations between the real and imaginary parts of quantum noise increases the intensity fluctuations.
In this paper we describe an experimental investigation of a zero- field level crossing resonance in the observed fluorescence at 555.6 nm resulting from excitation of the /sup 1/S/sub O/ ..-->.. /sup 3/P/sub 1/ transition in transition in Yb/sup 174/ by a linearly polarized laser field. The essential new feature of this investigation is the use of an optical field for which the phase coherence is well-characterized and variable over a wide range. We have developed, and apply here, experimental techniques for synthesizing constant amplitude laser fields with phase/frequency fluctuations which follow Gaussian (normal) statistics and which have spectral dependences which can be varied over a range from nearly Lorentzian to nearly Gaussian profiles. These synthesized fields correspond, to a good approximation, to the so-called phase-diffusion fields described in theoretical studies of the ac Stark effect with Lorentzian and non-Lorentzian laser line shapes, and have been applied previously in several related experimental investigations. 13 refs., 6 figs., 1 tab.