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Physical Review A

Phase-difference fluctuations of the quantum-beat laser

Miguel Orszag, C. Saavedra

Published Mar 1, 1991• 15 citations
Publisher

Abstract

We calculate the phase-difference and phase-sum fluctuations of the quantum-beat laser, using the nonlinear model of Bergou et al. [Phys. Rev. A 38, 754 (1988)], and also making use of the phase operators defined by Pegg and Barnett [Phys. Rev. A 39, 1665 (1989)]. We found a vanishing phase-difference diffusion constant, in agreement with Bergou et al. However, the present formalism is more general, and includes shot noise as well as saturation effects for the relative and sum phase fluctuations.

DOI
10.1103/physreva.43.2557

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We calculate the phase-difference and phase-sum fluctuations of the quantum-beat laser, using the nonlinear model of Bergou et al. [Phys. Rev. A 38, 754 (1988)], and also making use of the phase operators defined by Pegg and Barnett [Phys. Rev. A 39, 1665 (1989)]. We found a vanishing phase-difference diffusion constant, in agreement with Bergou et al. However, the present formalism is more general, and includes shot noise as well as saturation effects for the relative and sum phase fluctuations.
We calculate phase fluctuations of the phase operator defined by Pegg and Barnett [Europhys. Lett. 6, 483 (1988); J. Mod. Opt. 36, 7 (1989); Phys. Rev. A 39, 1665 (1989)] in a laser with atomic memory effects. First, we compute the phase fluctuations of a laser, using the Scully-Lamb theory. In a single curve of 〈(\ensuremath{\Delta}\ensuremath{\varphi})2{)}^{2})2〉 versus time, we obtain the expected behavior: namely, for Dt\ensuremath{\sim}1 the Schawlow-Townes linewidth and for t\ensuremath{\gg}${\mathit{D}}^{\mathrm{\ensuremath{-}}1}$ the phase fluctuations corresponding to a random phase. As we include the atomic memory effects, we obtain a noise reduction for times of the order of the atomic decay time.
In papers by Lynch [ Phys. Rev. A 41 2841 (1990)] and Gerry and Urbanski [ Phys. Rev. A 42 662 (1990)] it has been argued that the phase-fluctuation laser experiments of Gerhardt, Büchler and Lifkin [ Phys. Lett. 49A 119 (1974)] are in good agreement with the variance of the Pegg–Barnett phase operator for a coherent state, even for a small number of photons. We argue that this is not conclusive. In fact, we show that the variance of the phase in fact depends on the relative phase between the phase of the coherent state and the off-set phase ϕ 0 of the Pegg–Barnett phase operator. This off-set phase is replaced with the phase of a reference beam in an actual experiment and we show that several choices of such a relative phase can be fitted to the experimental data. We also discuss the Noh, Fougères and Mandel [ Phys. Rev. A 46 2840 (1992)] relative phase experiment in terms of the Pegg–Barnett phase taking post-selection conditions into account.
The expectation value and variance of a new phase operator introduced recently by Pegg and Barnett [Europhys. Lett. 6, 483 (1988); Phys. Rev. A 39, 1665 (1989)] and by Barnett and Pegg [J. Mod. Opt. 36, 7 (1989)] is calculated for a coherent state. The values for the variance so obtained are compared with the phase-fluctuation measurements of Gerhardt, B\"uchler, and Liftin [Phys. Lett. 49A, 119 (1974)] and Gerhardt, Welling, and Frolich [Appl. Phys. 2, 91 (1973)]. Agreement is found to be good, provided that account is taken of the details of the experimental values.
A quantum-beat laser without inversion is proposed for producing two-mode suqeezing. Using the dressed-atom-dressed-mode approach, the master equation is derived and the variances in the sum mode intensity and in the relative amplitude and phase are calculated. When the laser is operated well above threshold, the intensity fluctuations in the sum mode are reduced below the shot noise limit with an optimum Mandel parameter of -0.5. At the same time, the fluctuations in the relative amplitude and phase are retained at their vaccum noise levels.