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Journal of Physics B Atomic and Molecular Physics

Cross correlation in the two-mode laser

T. A. B. Kennedy, S. Swain

Published Nov 14, 1984• 16 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/17/21/011

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Journal of Physics B Atomic and Molecular Physics•Nov 14, 1982•152 citations
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.
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.
We consider the theory of the two-photon laser using the Scully–Lamb theory developed for ordinary single-photon lasers, concentrating on the calculation of the linewidths and the cross-correlation coefficient. In a previous publication we have shown that the quantum-mechanical noise in the modes of a two-mode laser may be highly correlated. Here we show that the same situation appertains to the two-photon laser, that is the two modes are strongly positively cross-correlated when the laser is operating well above threshold. The two-photon laser has the advantage of tunability over the two-mode or quantum-beat laser. The point of using modes whose noise properties are strongly correlated is that in an appropriate two-photon experiment the noises may effectively ‘cancel out’ leaving a very low noise signal. We present a brief development of the two-photon laser theory and show the connection between our work and that of other approaches.
As the laser linewidth arises under the influence of spontaneous emission, it is of considerable interest to find effects that decrease it. In this paper it is considered the effect of cooperative atomic interactions on the linewidth of a single-mode laser. It can be shown by suitably generalizing the Scully-Lamb theory that the cooperative effects tend to decrease the natural linewidth of the laser at high intensities. Considering the interaction of two-two- level atoms with a single-mode quantized field and the effect of cooperative atomic interactions it was obtained an expression for the natural linewidth of the system. Based on the theoretical models we obtain the numerical results for the laser linewidth as a function of the cooperation parameter. We then present a set of graphs by suitably plotting these data and we discuss the results.
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.