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Journal of Optics B Quantum and Semiclassical Optics

Short-time fourth-order squeezing effects in spontaneous and stimulated four- and six-wave mixing processes

Dilip Kumar Giri, Partha Sarathi Gupta

Published Mar 7, 2003• 11 citations
Publisher

Abstract

The concept of fourth-order squeezing of the electromagnetic field is investigated in the fundamental mode in spontaneous and stimulated four- and six-wave mixing processes under the short-time approximation based on a fully quantum mechanical approach. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The possibility of obtaining fourth-order squeezing is studied. The dependence of fourth-order squeezing on the number of photons is also investigated. It is shown that fourth-order squeezing, which is a higher-order squeezing, allows a much larger fractional noise reduction than lower-order squeezing. It is shown that squeezing is greater in a stimulated process than the corresponding squeezing in spontaneous interaction. The conditions for obtaining maximum and minimum squeezing are obtained. We have also established the non-classical nature of squeezed radiation using the Glauber–Sudarshan representation.

DOI
10.1088/1464-4266/5/2/307

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The concept of fourth-order squeezing of the electromagnetic field is investigated in the fundamental mode in spontaneous and stimulated four- and six-wave mixing processes under the short-time approximation based on a fully quantum mechanical approach. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The possibility of obtaining fourth-order squeezing is studied. The dependence of fourth-order squeezing on the number of photons is also investigated. It is shown that fourth-order squeezing, which is a higher-order squeezing, allows a much larger fractional noise reduction than lower-order squeezing. It is shown that squeezing is greater in a stimulated process than the corresponding squeezing in spontaneous interaction. The conditions for obtaining maximum and minimum squeezing are obtained. We have also established the non-classical nature of squeezed radiation using the Glauber–Sudarshan representation.
The occurrence of fourth and fifth-order squeezing in the fundamental mode of the electromagnetic field in spontaneous and stimulated Raman processes under the short-time approximation is investigated on the basis of a fully quantum-mechanical approach. In an idealized model, the Raman process is looked upon as a two-photon on a one phonon interaction process. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The dependence of fourth- and fifth-order squeezing in terms of the signal-to-noise ratio on the number of photons is investigated. We have also established the amplitude squeezing effects in the Stokes and vibrational modes, which is found to be dependent on higher-order difference squeezing showing a difference squeezing that can be converted to normal squeezing.
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.
Squeezing of the electromagnetic field is investigated in the pump, Stokes and parametric mode in spontaneous and stimulated four-wave mixing processes under a short-time approximation based on a fully quantum mechanical approach. The occurrence of squeezing in amplitude and amplitude squared of the fundamental mode has been investigated. The dependence of squeezing on the photon number is noticed and the degree of squeezing in the first and second-order is also investigated. Squeezing occurs in the fundamental mode in both spontaneous and stimulated processes, whereas squeezing in the Stokes and parametric modes is found to be dependent on squeezing of the initial pump field.
The amplitude squeezing properties of the electromagnetic field is investigated in the fundamental, Stokes (probe) and signal mode in six-wave mixing process under short-time approximation based on a fully quantum mechanical approach. The interaction is looked upon as a process involving absorption of two pump photons and emission of three probe photons and one signal photon at different frequencies. The coupled Heisenberg quantum mechanical equations of motion involving real and imaginary parts of the quadrature operators are established and solved under short-time scale. The occurrence of amplitude squeezing effects in both the quadrature of the radiation field in the fundamental mode as well as in the Stokes (probe) mode is investigated using the required conditions of squeezing in each of the cases. It is also shown that the squeezing in the signal mode is found to be dependent on amplitude-squared squeezing of the initial pump field. This gives a method of converting higher-order (amplitude-squared) squeezing into normal squeezing.
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.
We study a single-mode squeezing, sub-Poissonian and total noise in degenerate six-wave mixing process.We establish the analytic expression of first-order and second-order squeezing in terms of total noise under short-time approximation in degenerate six-wave mixing process.It shows that higher-order squeezing allows a much larger fractional noise reduction than lower-order squeezing.We observe that the squeezed states are associated with large number of photons.We find that squeezing is greater in stimulated process than corresponding squeezing in spontaneous interaction.The photon statistics of the pump mode in the process is investigated and found to be sub-Poissonian in nature.The effect of sub-Poissonian nature of an optical field in terms of total noise is also incorporated.We show that the depth of nonclassicality directly depends on the amount of total noise present in the system.This suggests that the more squeezed the state is, the greater is its total noise in the system.