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International Meeting on Instabilities and Dynamics of Lasers and Nonlinear Optical Systems

Generation of Squeezed States by Four-Wave-Mixing in a Cavity

R. E. Slusher, Bernard Yurke, Leo W. Hollberg, Jerome C. Mertz

Published Jan 1, 1985• 0 citations
Publisher

Abstract

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.

DOI
10.1364/idlnos.1985.wd20

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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.
Squeezed states of the electromagnetic field have been generated by nondegenerate four-wave mixing due to Na atoms in an optical cavity. The optical noise in the cavity, comprised of primarily vacuum fluctuations and a small component of spontaneous emission from the pumped Na atoms, is amplified in one quadrature of the optical field and deamplified in the other quadrature. These quadrature components are measured with a balanced homodyne detector. The total noise level in the deamplified quadrature drops below the vacuum noise level.
Squeezed states of the electromagnetic field have been generated by nondegenerate four-wave mixing due to Na atoms in an optical cavity. The optical noise in the cavity, comprised of primarily vacuum fluctuations and a small component of spontaneous emission from the pumped Na atoms, is amplified in one quadrature of the optical field and deamplified in the other quadrature. These quadrature components are measured with a balanced homodyne detector. The total noise level in the deamplified quadrature drops below the vacuum noise level.
Squeezed states of light have been predicted to be generated by four-wave mixing in cavity configurations. Any noise fields in the cavity can degrade or modify these squeezed states. An experiment using a Na atomic beam as the nonlinear mixing medium shows that spontaneous emission from the excited atoms results in a broadband frequency spectrum of noise in the cavity used for squeezing. The limits this noise places on the observed amount of squeezing and possible techniques for avoiding this noise source are discussed.
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.
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.
There is presently a growing interest in nearly degenerate four-wave mixing, both for application in optical phase conjugation and the generation of squeezed states. In particular, the self-oscillation of a system interacting with one or two pump beams has been investigated in great detail in the case of photorefractive materials, but very few experiments have been done in vapors in the cw regime. The results that we obtained using sodium are presented here. They are strikingly different from the results obtained with photorefractive materials. For example, the oscillating beam and pump beam frequencies coincide with a precision better than 10−2 Hz. Another interesting aspect of this oscillating beam is that it exhibits a phase sensitive noise: just above threshold, the noise on one quadrature of the field can be 10−2 times smaller than the noise on the other quadrature.