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Journal of Physics B Atomic and Molecular Physics

Population trapping with cross-correlated lasers of non-Lorentzian (phase diffusion) bandshape

Tom Kennedy, S. Swain

Published Dec 14, 1985• 4 citations
Publisher

Abstract

The authors have extended the theory of population trapping in three-level systems to include cross-correlated lasers of non-Lorentzian (phase diffusion) bandshape, and find that the conditions for population trapping are the same as for the Lorentzian phase diffusion model. Absorption spectra for the Lorentzian and non-Lorentzian theories are compared.

DOI
10.1088/0022-3700/18/23/015

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The authors have extended the theory of population trapping in three-level systems to include cross-correlated lasers of non-Lorentzian (phase diffusion) bandshape, and find that the conditions for population trapping are the same as for the Lorentzian phase diffusion model. Absorption spectra for the Lorentzian and non-Lorentzian theories are compared.
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.
According to laser theory the lineshape of a laser broadened by Ornstein-Uhlenbeck phase fluctuations is non-Lorentzian. The equations describing the interaction of such a laser with atomic systems are cast into a form which has the same structure as the density-matrix equations in the absence of fluctuations but with modified detunings, damping parameters and interaction matrix elements. By these means the authors derive substitution rules for taking into account the effect of these non-Lorentzian lineshapes which generalize those already known for Lorentzian lineshapes arising from Wiener-Levy fluctuations. The theory is applied to two-photon ionisation and analytic expressions are obtained for the rate of this process. For the extended two-level model the authors' results agree with those of Yeh and Eberly (1981) in the appropriate limit, but they also consider a more general model which leads to enhanced single-photon ionisation rates.
A three-level system driven by two coherent fields on two-photon resonance leads to the trapping of population in a superposition of initial and final states which is immune to further photoexcitation, manifesting itself in a narrow coherence minimum in the absorption spectrum. The authors analyse the effects of laser field bandwidths and cross-correlations on these phenomena. They find that the inclusion of laser bandwidths dephases atomic coherences which leads to the destruction of population trapping and of the narrow coherence minimum in the absorption spectrum. When the driving fields are not cross-correlated, the atomic coherences are similarly dephased in both lambda and ladder systems. If, however, the driving fields are critically cross-correlated, two-photon coherences in the lambda system are unaffected by laser fluctuations; trapping and the coherence minimum persist. For the ladder system, on the other hand, the cross-correlation does not restore the atomic coherences involved.
The authors consider population trapping in a three-level system which is driven by two applied fields of arbitrary intensity, frequency and bandwidth. An irreversible loss of population is allowed to take place from the common level. The conditions are investigated under which population trapping can occur when spontaneous emission and finite radiation bandwidths are allowed. For the lambda configuration with monochromatic lasers the authors find that increasing the spontaneous emission rate can increase the amount of population trapped in the system, whereas spontaneous emission destroys trapping in the ladder configuration. For the case of uncorrelated lasers, finite laser bandwidths destroy trapping for either configuration.
We study the correlation between level populations, absorption and two-photon coherence in closed Λ- and V-shaped three-level systems interacting with two lasers of arbitrary intensity. Whereas it is well known that maximum two-photon coherence leads to population trapping in Λ-shaped three-level systems interacting with two equally detuned lasers, we demonstrate that minimum two-photon coherence, under saturation conditions, can lead to equal populations in all the levels of a Λ- or V-shaped system when the lasers are symmetrically detuned. Moreover we show that steady-state population inversion between one of the upper levels of a V-shaped system and the ground state can occur when either the detunings are asymmetrical or the upper states decay at different rates. It is shown that this population inversion does not lead to stimulated emission into the lasing modes. These effects are also correlated with two-photon coherence and are explained physically by a cross three-photon scattering process involving two laser photons of different frequencies.