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Physical Review A

Linewidth of a laser with a squeezed reservoir

Christian Ginzel, Julio R. Gea-Banacloche, Axel Schenzle

Published Oct 1, 1990• 11 citations
Publisher

Abstract

We present a detailed analysis of a laser model with a squeezed reservoir. The steady-state behavior is described by means of the moments and the variance of the field intensity as a function of the pump parameter and the amount of squeezing. The dynamic properties are contained in the eigenfunctions and eigenvalues of the corresponding Fokker-Planck equation. Because of a loss of phase symmetry, the model exhibits interesting features concerning its stationary as well as its dynamic behavior.

DOI
10.1103/physreva.42.4164

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Chinese Physics•Nov 2, 2006•5 citations
We present a detailed analysis of a laser model with a squeezed reservoir. The steady-state behavior is described by means of the moments and the variance of the field intensity as a function of the pump parameter and the amount of squeezing. The dynamic properties are contained in the eigenfunctions and eigenvalues of the corresponding Fokker-Planck equation. Because of a loss of phase symmetry, the model exhibits interesting features concerning its stationary as well as its dynamic behavior.
The influence of injected atomic coherence on a laser's operation is discussed by analyzing the semiclassical equations of motion of this system. Both stationary-steady-state and time-dependent regimes of operation are investigated. We present the dependence of the stationary laser intensity and phase on the external parameters (population inversion, amplitude of atomic coherence, and detuning). For small cavity-field detuning and large atomic coherence, both frequency and phase locking occurs. The laser frequency is locked to the atomic frequency, and the phase is locked to a value determined primarily by the phase of the atomic coherence. Under certain conditions, in the inverted regime, the output intensity is an ssS-shaped function of the atomic coherence, leading to the possibility of a bistable behavior. However, only a portion of the bistable curve gives stable stationary operation, and in critical points (the location of which depends crucially on the external parameters) time-dependent instabilities branch away. When the detuning is larger than a critical value there is neither phase nor frequency locking. We find that the time-dependent behavior of the laser intensity in this case is oscillatory (quasiperiodic), and show that there is a stable limit cycle in the phase plane of the quadratures. There is a small parameter region where a stationary steady state and an oscillatory state may coexist. We also consider the nonlinear quantum theory of a laser with injected atomic coherence, and include the effect of pumping statistics. We derive the Fokker-Planck equation for the P representation, and express the noise in terms of moments. We find that in the steady state the intensity noise can be suppressed below the shot-noise limit but that the phase fluctuations are not affected by pump regularity. For nonzero detuning, we find that transient squeezing of the phase fluctuations is possible.
We investigate the effect of injected squeezed vacuum on the phase and intensity fluctuations of a laser. By using a stochastic simulation of the Langevin equations, we find that the phase diffusion noise of a laser with injected squeezed vacuum can be transiently reduced by a factor of 2, in agreement, with earlier predictions. Further, we find that the laser linewidth is broadened. The key observation is that the phase-diffusion rate is time dependent. We find that the steady-state intensity fluctuations are increased by the injected squeezing, in qualitative (but not quantitative) agreement with an earlier prediction. The problem of locking is examined. We find that the injected squeezed vacuum does not cause the laser to lock to any particular phase. We present an approximate solution of the Fokker-Planck equation in steady state, and a simple geometrical, vector kick model from which most of our results can be obtained.
The effect of squeezing on the degenerate parametric oscillator is studied. It is shown that when the ordinary-vacuum reservoir is replaced by a squeezed-vacuum reservoir, the maximum 50% limit of the second-order squeezing inside the cavity can be crossed. It is also shown that the mean number of photons increases considerably. An exact steady-state solution for the Fokker-Planck equation for the field mode is also presented. The photon distribution for the intracavity field and the higher-order variances have been obtained by using the solution of this equation.
We consider the dynamics of a single-mode cavity field damped via its coupling to a broad-band squeezed heat bath. The density operator equation of motion is transformed to a Fokker-Planck equation (FPE) for the s-parametrized quasiprobability distributions. We show that the field amplitude, intensity, spectrum and quadrature variances can be evaluated easily using the differential equations derived directly from the FPE. The FPE is then solved subject to different initial conditions, and the solution is used to investigate squeezing and field state evolution. The time behaviour of the purity Tr ([pcirc] 2) is treated in detail both analytically and numerically. The general steady-state solution is found in the operator form. We also show that, when certain conditions are met, dissipation without change in fluctuation properties is possible. A comparison is made with the cases of single-atom damping and off-resonance field damping.
We study the effects of correlations between quantum and pump noises on fluctuations of the laser intensity in a saturation laser model. An approximative Fokker–Planck equation and analytic expressions of the steady-state probability distribution function (SPD) of the laser system are derived. Based on the SPD, the normalized mean, the normalized variance, and the normalized skewness of the steady-state laser intensity are calculated numerically. The results indicate that (i) the correlation strength λ of correlated noises always enhances the fluctuation of laser intensity; (ii) the correlation time τ of correlated noises strengthens the fluctuation of laser intensity for the below-threshold case but τ weakens it for the above-threshold case.