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Physical Review A

Squeezed states from nondegenerate four-wave mixers

J. R. Klauder, S. L. McCall, Bernard Yurke

Published May 1, 1986• 46 citations
Publisher

Abstract

By closely following the work of Reid and Walls, a fully quantum-mechanical treatment of an atomic radiation-field interaction is developed with the aim of deriving basic equations for a nondegenerate four-wave mixer. The resultant equations are examined in forward and cavity geometries for their implications regarding squeezed states. Good agreement between our theory and the experiments of Slusher et al. is demonstrated.

DOI
10.1103/physreva.33.3204

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Physical Review A•Mar 1, 1987•55 citations
By closely following the work of Reid and Walls, a fully quantum-mechanical treatment of an atomic radiation-field interaction is developed with the aim of deriving basic equations for a nondegenerate four-wave mixer. The resultant equations are examined in forward and cavity geometries for their implications regarding squeezed states. Good agreement between our theory and the experiments of Slusher et al. is demonstrated.
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.
We apply our quantum theory of multiwave mixing to the generation of squeezed states of light via three- and four-wave mixing in cavities and in propagation. We compare the cavity predictions to the experimental results of Slusher et al. [Phys. Rev. Lett. 55, 2409 (1985)], finding reasonably good agreement. The squeezing found there is due to the fact that the number operators are driven by resonance fluorescence, which nearly vanishes for the large detunings chosen, while the combination tone operators are driven by relatively large source terms. We give a physical discussion as to why the spectral quantities outside the cavity are given by those inside multiplied by the cavity linewidth. We have found analytic formulas for the variances for arbitrary propagation distances, detunings, and pump intensities. We derive these formulas both from the density operator and from the Langevin methods. To obtain significant squeezing, the propagation distances must be large compared with the resonant Beer's law length.