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International Journal of Modern Physics B

nTH-ORDER AMPLITUDE SQUEEZING EFFECTS OF RADIATION IN MULTIPHOTON PROCESSES

Dilip Kumar Giri, Partha Sarathi Gupta

Published Jun 30, 2006• 2 citations
Publisher

Abstract

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.

DOI
10.1142/s0217979206034686

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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.
The concept of nth-order amplitude squeezing is introduced in the fundamental mode in Raman process as a generalization of the higher-order squeezing under short-time approximation based on a fully quantum mechanical approach. The condition for occurrence of nth-order squeezing is obtained from which higher-order squeezing up to n = 5 are studied. The coupled Heisenberg equation of motion involving real and imaginary parts of the quadrature operators is established. Dependence of squeezing on photon number is also established.
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.
Squeezing of electro-magnetic field, which is a purely quantum phenomenon has attracted considerable attention owing to its low noise property with applications in high quality telecommunication. 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. In this paper squeezing of electro- magnetic field in some multi-photon processes are investigated under short-time approximation. The processes studied include Raman and hyper Raman processes and sum- frequency generation. The coupled Heisenberg equations of motion for field operators are set up and solved under short-time approximation. The occurrence of squeezing of field is investigated using the required conditions of squeezing in each of the cases. The squeezing is found to exist in the fundamental mode and the squeezing in the generated field depends on squeezing in fundamental mode. Squeezing in higher order amplitudes are also studied. This corresponds to the squeezing of the variables which describe the real and imaginary parts of square and cube of the complex amplitudes of the radiation field. The higher order multimode sum squeezing of radiation field is dealt with for harmonic and sum frequency generation. It s shown that squeezing in the sum frequency field depends directly on the sum squeezing of fundamental modes. The results can be utilized in selecting a suitable process which will generate a radiation field with optimum squeezing and can be useful in high quality telecommunication.
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.
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.
Squeezing of electro-magnetic field, which is a purely quantum phenomenon has attracted considerable attention owing to its low noise property with applications in high quality telecommunication. 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. In this paper squeezing of electro-magnetic field in multi-wave mixing processes like Raman and hyper Raman processes and sum- frequency generation are investigated under short-time approximation. The coupled Heisenberg quantum mechanical equations of motion for field operators are set up and solved under short-time approximation. The occurrence of squeezing of field is investigated using the required conditions of squeezing in each of the cases. The squeezing is found to exist in the fundamental mode and the squeezing in the generated field depends on squeezing in the fundamental mode. Squeezing in the higher order amplitudes are also studied. This corresponds to the squeezing of the variables which describe the real and imaginary parts of square and cube of the complex amplitudes of the radiation field. The higher order multimode sum-squeezing of radiation field is dealt with for harmonic and sum frequency generation. It is shown that squeezing in the sum frequency field depends directly on the sum squeezing of fundamental modes. The results can be utilized in selecting a suitable material and suitable process which will generate a radiation field with optimum squeezing and can be useful in high quality tele-communication.