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Higher Order Squeezing in - and Four-Wave Mixing Processes with Loss

Jiaju Gong

Published Jan 1, 1991• 0 citations
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An investigation is carried out of higher-order squeezing in a class of three- and four-wave mixing processes that can be modeled by a master equation. In (2N)th-order squeezing, as defined by Hong and Mandel, the Nth-power of the variance of a field quadrature falls below the value it would have for a coherent state. Higher-order squeezing is of interest because (i) it occurs in many processes in which ordinary (or second-order) squeezing occurs, and (ii) it allows a much larger fractional noise reduction to be achieved than ordinary squeezing. The master equation we use models a degenerate three- or four-wave process and takes into account the losses in the signal mode. We convert the master equation into a Fokker-Planck equation for the Wigner distribution function and solve it for a wide range of initial signal states (including thermal, coherent, Fock states, and mixtures of these). Results are presented for the enhancement of fourth- and sixth-order squeezing over second-order squeezing. Differences in the character of higher-order squeezing for different input states are pointed out. The role of losses in limiting the amount of achievable squeezing in all orders is especially investigated.
It is found that the field of the combined mode of the probe wave and the phase conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The higher-order squeezed parameter and squeezed limit due to the modulation frequency are investigated. The smaller the modulation frequency is, the stronger the degree of higher-order squeezing becomes. Furthermore, the higher-order uncertainty relations in the process of non-degenerate four-wave mixing are presented for the first time. The product of higher-order noise moments is related to even order number N and the length L of the medium.