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Journal of Physics B Atomic and Molecular Physics

Theory of bandwidth induced asymmetry reversal in optical double resonances

D P O'Brien, S. Swain

Published Jul 28, 1983• 14 citations
Publisher

Abstract

The authors examine the theory of optical double resonance using two lasers whose finite linewidths are produced by the process of phase-diffusion. Their lineshapes, which are nonLorentzian, are characterised by a bandwidth B and a cut off C. The authors are concerned with obtaining an analytic theory; they achieve this by assuming the ratio B/C to be small and work to first order in B/C (although the method can be extended to higher order in B/C). They obtain analytic expressions for the optical double resonance spectrum and discuss the results of recent experiments by Hogan et al. (1978) and Nitz et al. (1981) in which it was found that the asymmetry of the peaks in the optical double resonance spectrum changed with detuning. It is found that a qualitative understanding can be achieved but that a full quantitative comparison is not yet possible.

DOI
10.1088/0022-3700/16/14/011

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The authors examine the theory of optical double resonance using two lasers whose finite linewidths are produced by the process of phase-diffusion. Their lineshapes, which are nonLorentzian, are characterised by a bandwidth B and a cut off C. The authors are concerned with obtaining an analytic theory; they achieve this by assuming the ratio B/C to be small and work to first order in B/C (although the method can be extended to higher order in B/C). They obtain analytic expressions for the optical double resonance spectrum and discuss the results of recent experiments by Hogan et al. (1978) and Nitz et al. (1981) in which it was found that the asymmetry of the peaks in the optical double resonance spectrum changed with detuning. It is found that a qualitative understanding can be achieved but that a full quantitative comparison is not yet possible.
The effect of a cut off of the Lorentzian laser lineshape (as predicted by the phase-diffusion model of ideal laser theory) on the laser-atom interaction is investigated. The damping terms in the averaged density matrix equation of the atom, arising from the finite laser bandwidth are shown to be multiplied by a detuning-dependent cut-off. For detunings of the laser well within the Lorentzian part of the spectrum, the authors recover the previously derived results, while these damping terms are seen to drop out for detuning larger than the cut-off. Within their model, therefore, a laser with a lineshape falling faster than a Lorentzian, and for large detunings, appears monochromatic to the atom. In particular, the authors obtain qualitative agreement with recent experiments in which the reversed peak asymmetry in the doublet of double optical resonance persists only within a certain range of detuning from resonance.
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.
A simple analytic expression for the double optical resonance spectrum obtained when a two-level atom is excited by a noisy pump laser is derived for two different models of laser noise, the phase diffusion model, and a model in which the laser bandwidth arises from a random telegraph signal in the laser phase. The double optical resonance spectrum is identical for both models and therefore double optical resonance experiments cannot distinguish between them. The importance of transients in cases where the laser bandwidth is comparable with or less than the atomic linewidth is stressed. Experiments which can distinguish between the two sources of bandwidth are identified.
We have studied the effect of well-characterized laser frequency fluctuations on the saturation of an atomic resonance in a double optical resonance experiment. The peak-height asymmetry of the observed Autler-Townes signal was reversed at small detunings when the shape of the saturating laser power spectrum was changed from nearly Gaussian to nearly Lorentzian. This behavior agrees qualitatively with theoretical calculations and also with previous observations using lasers without such well-characterized fluctuations.
Optical-double-resonance measurements using ionization detection have been carried out in the $3{S}_{\frac{1}{2}}\ensuremath{-}3{P}_{\frac{1}{2}}\ensuremath{-}4D$ atomic-sodium system. Asymmetries observed in production of 4D4D4D atoms from the two components of the Stark-split 3P123{P}_{\frac{1}{2}}3P21​​ state are found to be controlled by the far, very weak wings of the 17-MHz full-width-at-half-maximum laser line which is used to drive the $3{S}_{\frac{1}{2}}\ensuremath{-}3{P}_{\frac{1}{2}}$ transition at detunings in the range 0-70 GHz. Suppression of the wings with a Fabry-Perot filter causes a pronounced reversal of the asymmetry.
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.