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Physical Review A

Generation of squeezed states via degenerate four-wave mixing

M. D. Reid, Daniel F. Walls

Published Mar 1, 1985• 204 citations
Publisher

Abstract

A microscopic model of degenerate four-wave mixing including the quantization of the medium is given. Thus the full effects of loss and spontaneous emission on the squeezing attainable are analyzed. We examine separately the squeezing in the output fields for counterpropagating four-wave mixing, copropagating four-wave mixing, and four-wave mixing in a single-ended optical ring cavity. Good squeezing is possible only in certain limits of atomic parameters.

DOI
10.1103/physreva.31.1622

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Ways to minimize spontaneous-emission noise due to quantum fluctuations in the medium are a major consideration in experiments designed to produce squeezed states of light. Motivated by the recent experiments of Slusher et al. we present a fully quantized model of nondegenerate four-wave mixing. We show that the spontaneous-emission noise, important at higher intensities in the degenerate case, may be minimized in the nondegenerate case for certain regimes of cavity and medium parameters.

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Squeezed states in optical cavities: A spontaneous-emission-noise limit

R. E. Slusher, Leo W. Hollberg, Bernard Yurke +2 more

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.

Physical Review A•May 1, 1985•59 citations
A microscopic model of degenerate four-wave mixing including the quantization of the medium is given. Thus the full effects of loss and spontaneous emission on the squeezing attainable are analyzed. We examine separately the squeezing in the output fields for counterpropagating four-wave mixing, copropagating four-wave mixing, and four-wave mixing in a single-ended optical ring cavity. Good squeezing is possible only in certain limits of atomic parameters.
Degenerate four-wave mixing has been suggested as a possible generation scheme for squeezed-state light. A recent analysis of the quantum effects of probe-conjugate loss in backward degenerate four-wave mixing has shown that such loss puts an absolute limit on the squeezing that can be obtained via this generation scheme. In this Rapid Communication we show that it is the counter-propagating beam geometry of backward degenerate four-wave mixing that makes it ill suited for squeezed-state generation. On the other hand, the nominally copropagating beam geometry of forward degenerate four-wave mixing is shown to alleviate the absolute probe-conjugate loss limit on squeezing.
Squeezed light generated by four-wave mixing near the Na atomic resonance is compared with a full quantum-theoretical model. Losses and dephasing that are due to spontaneous emission near the atomic resonance are included in this theoretical treatment. The experimental results show noise reduction greater than 1 dB below the standard quantum limits and are in good agreement with the quantum model at low pump intensities and large detuning. Theory and experiment show that limits to squeezed-light noise reduction resulting from spontaneous-emission losses can be largely avoided by using nondegenerate four-wave mixing and pump intensities near the atomic saturation values.
We consider the generation of squeezed states in degenerate four-wave mixing, retaining all significant phase-matched terms in the third-order polarization. It is shown that, for output modes combined with appropriate phase shifts, ideal squeezed states are produced when the pump field is treated classically. An approximation scheme is used to investigate the effect of pump-field quantization. We show that for reasonable crystal lengths, the effect of pump-field quantization is insignificant in the region of significant squeezing.
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.