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Physical Review Letters

From Nearly Tilted Waves to Cavity Phase Solitons in Broad Area Lasers with Squeezed Vacuum

Óscar G. Calderón, E. Cabrera, M. A. Antón, Isabel Gonzalo, F. Carreño, J. M. Guerra

Published Apr 23, 2004• 3 citations
Publisher

Abstract

Phase domains and phase solitons in two-level amplifying media damped by a squeezed vacuum are predicted for the first time. Two different types of pattern formation are found depending on the relative value of the cavity detuning to the squeezed parameter: the usual one in lasers via a supercritical Hopf bifurcation and a new one via pitchfork bifurcation.

DOI
10.1103/physrevlett.92.163901

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Phase domains and phase solitons in two-level amplifying media damped by a squeezed vacuum are predicted for the first time. Two different types of pattern formation are found depending on the relative value of the cavity detuning to the squeezed parameter: the usual one in lasers via a supercritical Hopf bifurcation and a new one via pitchfork bifurcation.
Lasers with two-photon saturable absorbers exhibit a phase instability similar to that of two-photon optical bistability. Beyond the phase instability threshold the output intensity breaks into spontaneous oscillations. Analytical perturbative solutions have been found and we have linearized the Fokker-Planck equation around these solutions. The drift and diffusion matrices have been perturbatively developed and we obtained a time-dependent Ornstein-Uhlenbeck stochastic process. We have calculated the amplitude correlations and squeezing spectrum near but above the threshold for a Hopf bifurcation in bad cavity conditions.
Summary form only given. In a recent paper [1] it has been shown how a bichromatic fast driving of optomechanical (optical domain) and superconducting circuit systems (microwave domain), operating in a limit where they present a non-linear Kerr-type interaction, can give rise to very strong vacuum squeezing. The driving with two close frequencies of a Kerr cavity changes the usual bistability bifurcation behaviour that takes place under monochromatic driving, into a degenerate four-wave mixing bifurcation, where a phase-bistable component starts oscillating spontaneously at a frequency that lies halfway between the two driving frequencies [2]. This resembles the physics of the optical parametric oscillator threshold, devices that has produced experimentally the strongest squeezing up to now. Associated to this bifurcation there is a strong reduction of the quantum fluctuations for a given quadrature of the electromagnetic field, resulting in vacuum squeezing, the reduction takes place at the central non-injected frequency.Here we show the application of this bichromatic driving protocol to a semiconductor micro-cavity system [3,4], where the nonlinear interaction between photons is caused through the excitons induced at the semiconductor embedded in the optical cavity.
We present a method for the study of quantum fluctuations of dissipative structures forming in nonlinear optical cavities, which we illustrate in the case of a degenerate, type I optical parametric oscillator. The method consists in (i) taking into account explicitly, through a collective variable description, the drift of the dissipative structure caused by the quantum noise, and (ii) expanding the remaining---internal---fluctuations in the biorthonormal basis associated to the linear operator governing the evolution of fluctuations in the linearized Langevin equations. We obtain general expressions for the squeezing and intensity fluctuations spectra. Then we theoretically study the squeezing properties of a special dissipative structure, namely, the bright cavity soliton. After reviewing our previous result that in the linear approximation there is a perfectly squeezed mode irrespective of the values of the system parameters, we study which are the better squeezed modes at the different bifurcations that the cavity soliton can suffer, as well as the squeezing level attainable when the homodyne detection is made with a plane-wave local oscillator field. In this last case, the squeezing level is quite large in most of the existence domain of the cavity soliton. We then take into account the effect of the detector size and find that, in general, squeezing degrades as the detector is made smaller, except for detector sizes around the cavity soliton size, in which case there is an interesting deviation from the general trend.
The classical behavior and the quantum fluctuations are analyzed for the system of nondegenerate second-harmonic generation inside a cavity, where two frequency degenerate but orthogonally polarized harmonic modes are coupled to a second-harmonic mode via a ${\mathrm{\ensuremath{\chi}}}^{(2)}$ medium. We consider the consequences of asymmetrically pumping the two harmonic modes. Asymmetric pumping causes large changes in the classical dynamical behavior of the system; the pitchfork bifurcation, predicted by Ou [Phys. Rev. A 49, 4902 (1994)] and Eschmann and Reid [Phys. Rev. A 49, 2881 (1994)] for symmetric pumping, is transformed into a saddle node for any antisymmetric pumping. This new dynamics brings about the possibility of the system reaching a Hopf and a saddle-node--Hopf bifurcation point. Squeezed-state production is investigated at the critical points of the system. Large squeezing is predicted at the saddle-node and Hopf bifurcation points. The wealth of squeezing predicted by this model at the pitchfork bifurcation point is interpreted in terms of the dynamics of the system. For symmetric pumping, this system is shown to be able to produce two coherent amplitude and phase correlated beams both above and below the pitchfork bifurcation point and so is a candidate for an Einstein-Podolsky-Rosen experiment. \textcopyright{} 1996 The American Physical Society.
The stationary emission and stability of a three-level cascade laser in which two fields of different frequencies can be simultaneously amplified is investigated under conditions of cavity detuning. Different monomode and bimode solutions are found and analysed for the effects of different pitchfork and Hopf bifurcations. At moderate cavity detunings, features different from those observed in other classes of lasers are found, such as for instance a decrease in the instability threshold when detuning is introduced. Particular attention is paid to the case of resonance of the two-photon transition, which allows us to study the continuous evolution, when detuning is increased, of a resonant cascade laser towards a pure two-photon laser. In particular, this establishes the origin of some features which are characteristic of two-photon lasers.