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Quantum Optics Journal of the European Optical Society Part B

Squeezing in intracavity four-wave mixing with non-degenerate pumps

Gagik Yu. Kryuchkyan, Karen V. Kheruntsyan

Published Oct 1, 1992• 3 citations
Publisher

Abstract

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.

DOI
10.1088/0954-8998/4/5/005

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Quantum Electronics•Jun 30, 1995•0 citations
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.
We show that an optomechanical cavity pumped by a bichromatic light beam can generate a signal whose frequency lies halfway between the two driving frequencies. This process can be understood as a degenerate four-wave mixing, in which two pump photons (one from each frequency) are combined to yield two identical signal photons. This process takes place between a lower and an upper threshold in terms of the pump intensity, which depend on the pump frequency difference. Close to the signal oscillation threshold a clear noise reduction in one of its quadratures is shown numerically.
It is shown that a four-wave-mixing oscillator [R. Ghosh and G. S. Agarwal, Phys. Rev. A 39, 1582 (1989)] operating above threshold exhibits nonclassical effects in the average phase and the amplitude difference of two radiation fields and shows two-mode squeezing. A maximum of 50% intracavity squeezing is found in the fluctuations of two Hermitian operators corresponding to the average phase and the relative amplitude, which becomes 75% squeezing outside the cavity. The variance in the intensity difference between the two fields is half the shot-noise limit inside the cavity but is perfectly suppressed outside the cavity, and both variances inside and outside the cavity are independent of how far above threshold the oscillator is.
We extend the quantum theory of nondegenerate four-wave mixing by including the effects of the finite bandwidth of the driving-pump field. The interaction of a beam of two-level atoms with the two opposite driving-pump fields that have finite bandwidth inside a bimodal cavity is considered. The master equation for the cavity-field modes, averaged over the stochastic process, is derived. We use our theory to study the effects of phase fluctuations, associated with the driving-pump field, on the generation of two-mode squeezing inside the cavity. The steady-state squeezing is achieved with the same driving-pump field as a local oscillator in the balanced homodyne-detection system. Our results show that, in spite of instantaneous phase locking between the cavity field and the local oscillator, the time-delay effects associated with the exponential decay of atomic coherence relate the steady-state squeezing to the diffusion constant of the driving-pump field.
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.
A theoretical investigation is made of parametric generation of light by four-wave mixing in an optical cavity with two pump fields of different frequencies. Mixing configurations resulting in the excitation of one and three cavity modes are considered taking into account the effects of phase modulation and of depletion of the pump fields. An analysis is made of stable steady-state oscillation regimes. Calculations are reported of the intensities of the generated radiation modes at the exit from the cavity above the threshold. An analysis is made of the conditions for the appearance of optical bistability at nonzero values of the cavity detuning.