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Journal of the Optical Society of America B

Interaction of cross-correlated laser fields with atomic systems

S. Swain

Published Oct 1, 1985• 13 citations
Publisher

Abstract

Cross correlation refers to the situation in which the fluctuations in the fields of two or more lasers are correlated in some way. Recently, Thomas et al. [ Opt. Lett.6, 298 ( 1981); Phys. Rev. Lett.48, 867 ( 1982)] proposed the generation of cross correlation between two laser fields interacting with a three-level system as a means of reducing noise and went on to exploit this property in the observation of narrow Ramsay fringes. Dalton and Knight [ J. Phy. B15, 3997 ( 1982)] discussed the theoretical aspects of cross correlation and showed that it produced interesting effects in population trapping for example. We have demonstrated that it has significant effects on the optical double-resonance (ODR) spectra [ J. Phys. B17, L389 ( 1984)]. On the other hand, the effects of non-Lorentzian laser line shapes have been shown by various workers to have significant effects on a wide range of phenomena, such as multiphoton ionization, resonance fluorescence, and ODR. In this paper we present a theory of the interactions of lasers whose fluctuations are governed by the phase-diffusion process with atomic systems that includes the effects of cross correlation and non-Lorentzian line shapes. We derive the basic equations (which in general have to be solved numerically) and obtain analytic results in the case in which the line shape is approximately Lorentzian near line center but falls off faster than a Lorentzian in the wings. We believe that this analytic model shows all the essential features of the interplay between cross correlation and non-Lorentzian line shapes. The theory is applied to the ODR experiment. In particular, we find that the asymmetry of the spectra is strongly affected by these two features, and so is the ODR spectral line shape when the saturating laser intensity is close to the threshold for producing two peaks.

DOI
10.1364/josab.2.001666

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Physical Review A•Jun 1, 1990•17 citations
Cross correlation refers to the situation in which the fluctuations in the fields of two or more lasers are correlated in some way. Recently, Thomas et al. [ Opt. Lett.6, 298 ( 1981); Phys. Rev. Lett.48, 867 ( 1982)] proposed the generation of cross correlation between two laser fields interacting with a three-level system as a means of reducing noise and went on to exploit this property in the observation of narrow Ramsay fringes. Dalton and Knight [ J. Phy. B15, 3997 ( 1982)] discussed the theoretical aspects of cross correlation and showed that it produced interesting effects in population trapping for example. We have demonstrated that it has significant effects on the optical double-resonance (ODR) spectra [ J. Phys. B17, L389 ( 1984)]. On the other hand, the effects of non-Lorentzian laser line shapes have been shown by various workers to have significant effects on a wide range of phenomena, such as multiphoton ionization, resonance fluorescence, and ODR. In this paper we present a theory of the interactions of lasers whose fluctuations are governed by the phase-diffusion process with atomic systems that includes the effects of cross correlation and non-Lorentzian line shapes. We derive the basic equations (which in general have to be solved numerically) and obtain analytic results in the case in which the line shape is approximately Lorentzian near line center but falls off faster than a Lorentzian in the wings. We believe that this analytic model shows all the essential features of the interplay between cross correlation and non-Lorentzian line shapes. The theory is applied to the ODR experiment. In particular, we find that the asymmetry of the spectra is strongly affected by these two features, and so is the ODR spectral line shape when the saturating laser intensity is close to the threshold for producing two peaks.
The interaction of an atomic system with a laser having phase fluctuations is studied within the phase-diffusion model, with the finite correlation time of the time derivative of the phase taken into account. This finite correlation time introduces a line shape which is Lorentzian near the center and falls off faster than the Lorentzian at its wings. The authors apply this model to calculate the spectrum of double optical resonance for excitation by a laser having this non-Lorentzian line shape. It is observed that the reversed peak asymmetry reverts to normal far off resonance owing to the cutoff of the laser spectrum, in agreement with recent experiments. Numerical results are presented.
Thomas et al. (1981, 1982) proposed the generation of cross correlation between two laser fields interacting with a three-level system as a means of reducing noise and subsequently exploited this property in the observation of very narrow Ramsey fringes. Cross correlation has been discussed theoretically by Dalton and Knight (1982, 1983) and shown to have interesting effects in population trapping. For such effects to be important, the cross correlation coefficient must be as large as possible. The authors discuss the degree of correlation between the two modes of a two-mode laser using the approach of Scully and Lamb (1967, 1968) and show it can be large. They also evaluate the linewidths of the two laser modes. They find that if the laser parameters for the two modes are equal, the two-mode linewidth is one half the value of the linewidth of the corresponding single-mode laser, well above threshold.
The effects of different laser line shapes on the intensity and spectrum of resonance fluorescence from a two-level atom are investigated. The laser model considered is that of an ideal single-mode laser operating high above threshold, with constant amplitude and undergoing phase-frequency fluctuations analogous to Brownian motion. As the correlation time of the frequency fluctuations increases from zero to infinity, the laser line shape changes from Lorentzian to Gaussian in a continuous way. It is shown that for intermediate and strong fields, the average intensity of fluorescence in the case of a resonant broadband Lorentzian line shape is higher than that in the case of a Gaussian line shape with the same bandwidth and total power. This is in contrast to the weak-field case where the higher peak power of the Gaussian line shape makes it more effective than the Lorentzian line shape. It is also shown that in the case of a nonzero frequency correlation time (non-Lorentzian line shape) the intensity of fluorescence undergoes non-Markovian fluctuations. In relation to the spectrum of resonance fluorescence, it is shown that as the line shape is varied from Lorentzian to Gaussian the following changes take place: In the case of off-resonance excitation, the asymmetry of the spectrum decreases. In the case of resonant excitation, the center-peak to side-peak height ratio for the triplet structure increases. Moreover, the recently predicted center-line dip, which develops in the spectrum in the case of broadband excitation when the Rabi frequency and the bandwidth are nearly equal, becomes increasingly deeper.
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.