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Journal of the Optical Society of America B

Spectrum of squeezing in detuned degenerate four-wave mixing

Kaige Wang, Yafei Wang

Published Nov 1, 1993• 3 citations
Publisher

Abstract

We calculate the squeezing spectra for a detuned degenerate four-wave mixing system. In the detuning case sizable squeezing still exists for both the pump and the signal fields. Especially in the limits for which the ratio of the damping rates becomes very small and large, the squeezing for the signal and the pump fields, respectively, is nearly perfect.

DOI
10.1364/josab.10.002130

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We calculate the squeezing spectra for a detuned degenerate four-wave mixing system. In the detuning case sizable squeezing still exists for both the pump and the signal fields. Especially in the limits for which the ratio of the damping rates becomes very small and large, the squeezing for the signal and the pump fields, respectively, is nearly perfect.
Abstract We analyze a simple model for degenerate four wave mixing, introduced by Savage and Walls. In the resonant case, the system exhibits a phase instability when the pump intensity is increased well beyond the threshold for generation of the signal mode. Still in the resonant configuration, we calculate the amplitude and phase squeezing spectra both for the signal and the pump mode. In the signal (pump) mode, the squeezing becomes especially large when the signal (pump) mode is much more damped than the pump (signal) mode. The signal field can exhibit both phase and amplitude squeezing, in distinct domains of the parameter space. On the other hand, the pump field can show squeezing only in the amplitude quadrature component. In general, the model exhibits sizable squeezing over very extended regions of the parameter space.
We analyze the classical behavior and the quantum fluctuations for the system of degenerate four-wave mixing inside a doubly resonant optical cavity. Two frequency-degenerate but orthogonally polarized modes are coupled together in a ${\mathrm{\ensuremath{\chi}}}^{(3)}$ medium. We include all significant phase-matched interactions that occur in a third-order polarization (self-phase modulation, cross-phase modulation, and four-wave mixing). Two critical points are predicted to occur in the system. The first occurs for low pumping, associated with the excitation of the single mode. The second critical point occurs for higher pumping, associated with the onset of self-pulsing. Quantum fluctuations are analyzed for the various regions of pumping. At the first critical point, perfect squeezing is possible in both the pump and the signal modes when the damping of the signal mode is greater than the damping of the pump (${\ensuremath{\gamma}}_{\mathit{a}}$>${\ensuremath{\gamma}}_{\mathit{b}}$). In the case where the damping of the signal mode is much greater than that of the pump (${\ensuremath{\gamma}}_{\mathit{a}}$\ensuremath{\gg}${\ensuremath{\gamma}}_{\mathit{b}}$), nearly perfectly squeezed states of the signal mode are possible in the entire region between the two critical points.
A quantum theory of degenerate four-wave mixing is presented in which the atomic medium consists of stationary four-level atoms, each with three degenerate excited states, and the interacting light beams are allowed to be in different states of polarization. This vector-field theory differs from the scalar-field theory of Reid and Walls [Phys. Rev. A 31, 1622 (1985)] in that there are new atomic variables in the Langevin equations which are related to the induced coherence between the upper atomic states. It is found, for the assumed set of atomic levels, that this seemingly different mechanism of four-wave-mixing gain does not circumvent the degrading effect of spontaneous emission on squeezing obtainable via degenerate four-wave mixing. The theory is applied to both forward and backward degenerate four-wave mixing with nearly collinear geometry, and specialized to the case in which the polarization states of the two pump modes are mutually orthogonal. It is found that for both forward and backward configurations, the range of pump intensity for which squeezing can be achieved in the vector-field case is larger than that in the scalar-field case, and the maximum amount of squeezing obtainable at a particular pump detuning is comparable in both cases.
The authors present a quantum analysis of four-wave mixing in a non-resonant nonlinear medium inside a cavity which is driven by two driving fields. In this process a nonlinear medium couples two pump modes with a signal mode of the frequency equal to the half-sum of the two pump field frequencies. Three types of stable steady-state solutions of the deterministic problem, describing three regimes of oscillation, are found: one below threshold and two different above-threshold regimes. The spectra of fluctuations of the quadrature-phase amplitudes for all three modes are calculated. It is found that in the above-threshold regime each of three modes may display a squeezed noise reduction. Below threshold a squeezing is realized for the central mode.