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Acta Optica Sinica

Amplitude-squared squeezing in multiphoton nonlinear processes

Yang Zhan

Published Jan 1, 1992• 0 citations
OpenAlex

Abstract

In this paper the amplitude-squared squeezing in the multiphoton nonlinear optical processes is studied. It is examined that amplitude-squared squeezing can be created in the first order approximation by k-photon unitary operators Sk(z) (K 2) acting on the coherent state |α(|α|≠0) and one can not be created by Sk(z) (K 2, K≠4) acting on the vacuum state. It is found that amplitude-squared squeezing can be created by 4-photon unitary operator S4(z) acting on the vacuum state and this shows that the amplitude-squared squeezing is a new nonclassioal effect of light field which is independent of the second order squeezing, antibunohing and sub-Poisson statistics.

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In this paper the amplitude-squared squeezing in the multiphoton nonlinear optical processes is studied. It is examined that amplitude-squared squeezing can be created in the first order approximation by k-photon unitary operators Sk(z) (K 2) acting on the coherent state |α(|α|≠0) and one can not be created by Sk(z) (K 2, K≠4) acting on the vacuum state. It is found that amplitude-squared squeezing can be created by 4-photon unitary operator S4(z) acting on the vacuum state and this shows that the amplitude-squared squeezing is a new nonclassioal effect of light field which is independent of the second order squeezing, antibunohing and sub-Poisson statistics.
Operators are defined which correspond to the real and imaginary parts of the square of the field amplitude. These operators obey an uncertainty relation. Squeezing with respect to these operators is defined and minimum uncertainty states are discussed. A number of nonlinear optical processes are examined and shown to produce this effect. Interactions which couple one mode amplitude to the square of another convert this type of squeezing into normal squeezing. An example of such an interaction is given.
Squeezing of the electromagnetic field is a purely quantum mechanical phenomenon and this quantum effect is expected to manifest itself in optical processes in which the nonlinear response of the system to the radiation field plays an important role. It has generated a great deal of interest in view of the possibility of reducing the noise of an optical signal below the vacuum limit i.e. zero-point oscillations. In this paper the concept of nth-order amplitude squeezing is introduced in the fundamental mode in four- and six-wave mixing processes as a generalization of the higher-order squeezing under short-time approximation based on a fully quantum mechanical approach. It established the coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators. The condition for occurrence of nth-order squeezing is obtained from which higher-order squeezing upto n=3 are studied. Dependence of squeezing on photon number is also established. The conditions for obtaining maximum and minimum squeezing are obtained. The method of present investigation can be applied to any higher-order non-linear optical processes and the technique can also be extended for studying squeezing in any N-photon process in general. Further, nth-order squeezing of radiation in N-photon process can also be investigated. The results obtained may help in selecting a suitable process to generate optimum squeezing in the radiation field.
We investigate theoretically the generation of squeezed states in spontaneous and stimulated six-wave mixing process quantum mechanically. It has been found that squeezing occurs in field amplitude, amplitude-squared, amplitude-cubed, and fourth power of field amplitude of fundamental mode in the process. It is found to be dependent on coupling parameter “g” (characteristics of higher-order susceptibility tensor) and phase values of the field amplitude under short-time approximation. Six-wave mixing is a process which involves absorption of three pump photons and emission of two probe photons of the same frequency and a signal photon of different frequency. It is shown that squeezing is greater in a stimulated interaction than the corresponding squeezing in spontaneous process. The degree of squeezing depends upon the photon number in first and higher orders of field amplitude. We study the statistical behaviour of quantum field in the fundamental mode and found it to be sub-Poissonian in nature. The signal-to-noise ratio has been studied in different orders. It is found that signal-to-noise ratio is higher in lower orders. This study when supplemented with experimental observations offers possibility of improving performance of many optical devices and optical communication networks.
The real and imaginary parts of the square of the field amplitude obey an uncertainty relation. If the uncertainty in either of these variables is less than it would be in a minimum uncertainty state with equal uncertainties in both variables, the state is amplitude-squared squeezed. This is a nonclassical effect which can be produced by second harmonic generation, two-photon absorption, and degenerate parametric amplification, as well as by higher-order processes. Amplitude-squared squeezing can be converted into normal squeezing by interactions in which the square of the amplitude of one field is coupled to the amplitude of another. Second harmonic generation and some forms of four-wave mixing provide examples of such processes.