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International Journal of Optics

Minimum Total Noise in Wave-Mixing Processes

Savita Gill, Sunil Rani, Nafa Singh

Published Jan 1, 2012• 6 citations
Publisher

Abstract

Higher-order squeezing in different optical processes such as seven-wave mixing and five-wave mixing has been studied. The total noise of a field state is a measure of the fluctuations of the field amplitude. It is shown that the minimum total noise ( Tmin ) of a higher-order squeezed state always increases with the increase in nonclassicality associated with higher-order squeezing. Thus, from Tmin , one can conclude that highly nonclassical states have large amplitude fluctuations.

DOI
10.1155/2012/431826

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Higher-order squeezing in different optical processes such as seven-wave mixing and five-wave mixing has been studied. The total noise of a field state is a measure of the fluctuations of the field amplitude. It is shown that the minimum total noise ( Tmin ) of a higher-order squeezed state always increases with the increase in nonclassicality associated with higher-order squeezing. Thus, from Tmin , one can conclude that highly nonclassical states have large amplitude fluctuations.
The total noise of a field state is a measure of the fluctuations of the field amplitude. It is a minimum for coherent states. As the behavior of a state becomes more nonclassical, its total noise increases. This is shown first for several specific types of nonclassical states, among them squeezed and sub-Poissonian states. These results are generalized by using nonclassical distance to measure how nonclassical a field state is. A lower bound for the total noise is derived that is an increasing function of nonclassical distance. From it one can conclude that highly nonclassical states have large amplitude fluctuations.
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.
The total noise of a state is the sum of the fluctuations in the real part of the field amplitude and those in the imaginary part. It is a measure of the total fluctuations in the field amplitude and is a minimum for coherent states. Several examples of nonclassical fields are considered, and it is shown that as nonclassical behavior increases so does total noise. For example, total noise increases as a state becomes more squeezed or as the photon statistics become more sub-Poissonian. This result is then generalized by using the concept of nonclassical distance. Nonclassical distance δ is a measure of the extent to which the behavior of a field state differs from that of classical states. A lower bound for the total noise is derived which is an increasing function of δ. This means that the more nonclassical a state is the greater its total noise must be.
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.
Squeezing of radiation is a purely quantum mechanical phenomenon which has no classical counterpart. 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. The concept of squeezing started in mid 1980s. Since then there has been an enormous upsurge of interest in this field owing to its low noise property. In the present paper various aspects of squeezing of radiation are studied and possible means of generation of squeezed light in which the quantum fluctuations are reduced below shot noise limit are investigated. The amplitude of the electric field of a mode of an electromagnetic field is always associated with quantum mechanical fluctuations. Squeezing states are characterised by reduced quantum fluctuations in one quadrature component of the field at the expense of increased fluctuations in the other noncommuting component. A fully quantum mechanical approach is followed. In the present paper we intend to review different aspects of squeezing and higher order squeezing in higher order Raman processes as well as in multiwave mixing processes. A comparative study between different processes are made which will pave a way for easier generation of squeezed light.
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.