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Physical Review A

Two-mode squeezing in a four-wave-mixing oscillator

Ning Lü

Published Jun 1, 1990• 2 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.41.6261

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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.
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 describe how a two-mode, above-threshold, optical parametric oscillator can generate nonclassical states of light with a large average number of photons: the fluctuation spectrum of the various fields is calculated, and several quantities are shown to have squeezed fluctuations. In particular, a perfect quantum noise suppression is predicted on the difference between the intensities of the two generated beams. We describe an experiment designed to demonstrate such an effect and show how it can be used to generate high-intensity amplitude-squeezed states.
Phase dependent nonlinear optical processes can make large fractional changes in the phase and amplitude of an optical field. An example is the prediction(1) that four-wave-mixing can generate squeezed states of an optical field where the variance in the two quadratures of the field are unequal. In order to observe squeezed states and utilize them in interferometric measurements this inequality in variances must be large (e.g. ≳ 50%). The large phase shifts required to achieve this regime of squeezing can be obtained near the threshold for oscillation of four-wave-mixing in an optical cavity. (2) This paper describes an experimental study(3) of four-wave-mixing in a cavity near threshold using the nonlinear index of the Na atomic resonance.