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The Amplitude Nth-Power Squeezing of Radiation Fields in the Degenerate Raman Process

Zhi‐Ming Zhang, Jin-Fang Pan, Lei Xu

Published Jan 1, 1996• 0 citations
OpenAlex

Abstract

In this paper we study the amplitude Nth-power squeezing of radiation fields in the degenerate Raman process by using the modified effective Hamiltonian approach recently suggested by us. We found that if the field is initially in a coherent state it will not get squeezing for any Nth-power; if the field is initially in a squeezed vacuum, it may get Nth-power squeezing. The time evolution of the field fluctuation was discussed. Its dependences on power-order N, mean photon number bar-n, and squeezing angle xi are analyzed.

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nTH-ORDER SQUEEZING OF THE FIELD AMPLITUDE IN RAMAN PROCESS AS A GENERALIZATION OF THE HIGHER-ORDER SQUEEZING

Dilip Kumar Giri, Partha Sarathi Gupta

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.

International Journal of Modern Physics B•Apr 30, 2005•4 citations

nTH-ORDER AMPLITUDE SQUEEZING EFFECTS OF RADIATION IN MULTIPHOTON PROCESSES

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Biswajit Sen, Swapan Mandal

An initially prepared coherent state coupled to a second-order nonlinear medium is responsible for stimulated and spontaneous hyper Raman processes. By using an intuitive approach based on perturbation theory, the Hamiltonian corresponding to the hyper Raman processes is analytically solved to obtain the temporal development of the field operators. It is true that these analytical solutions are valid for small coupling constants. However, the interesting part is that these solutions are valid for reasonably large time. Hence, the present analytical solutions are quite general and are fresh compared to those solutions under short-time approximations. By exploiting the analytical solutions of field operators for various modes, we investigate the squeezing, photon antibunching and nonclassical photon statistics for pure modes of the input coherent light responsible for hyper Raman processes. At least in one instance (stimulated hyper Raman processes for vibration phonon mode), we report the simultaneous appearance of classical (photon bunching) and nonclassical (squeezing) effects of the radiation field responsible for hyper Raman processes.

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COMMENTS ON "NTH-ORDER SQUEEZING OF THE FIELD AMPLITUDE IN RAMAN PROCESS AS A GENERALIZATION OF THE HIGHER-ORDER SQUEEZING"

Biswajit Sen, Swapan Mandal

In a recent paper, Giri and Gupta [Int. J. Mod. Phys. B19, 1943 (2005)] discussed the possibility of obtaining nth-order squeezing of the field amplitude of the fundamental mode in spontaneous Raman processes. These investigations are based on the earlier works of Kumar and Gupta [Quantum & Semiclassical Opt.7, 835 (1995)] and Giri and Gupta [J. Mod. Opt.51, 1705 (2004)]. As a consequence of our re-investigation on the same model, we found that the calculations and hence the conclusion of Giri and Gupta [Int. J. Mod. Phys. B19, 1943 (2005) and J. Mod. Opt.51, 1705 (2004)] and Kumar and Gupta are entirely baseless and misleading. There will be no squeezing of the fundamental mode in stimulated and/or in spontaneous Raman processes.

International Journal of Modern Physics B•May 20, 2008•0 citations

Determination of Sum Squeezing of the Field Amplitude in Frequency Upconversion Process

Dilip Kumar Giri, Binod Kumar Choudhary

Sum squeezing of the field amplitude is studied in the nondegenerate and degenerate frequency upconversion process under the short interaction time. A state is squeezed when the quantum fluctuation (amplitude noise or phase noise) in one variable is reduced below the symmetric limit at the expense of the increased quantum fluctuation in the conjugate variable such that the Heisenberg uncertainty relation is not violated. It is shown that sum squeezing can be converted into normal squeezing via sum-frequency generation in the nondegenerate frequency upconversion process, while the amplitude-squared squeezing of the fundamental mode directly changed into the squeezing of the harmonic in the degenerate frequency upconversion process. All reachable conditions of uncorrelated modes for obtaining a sum squeezing in two modes and its dependence on the squeezing of individual field modes are investigated. It is found that the squeezed states are associated with large number of pump photons. It is also confirmed that the higher-order squeezing (sum squeezing) is directly associated with coupling of the field and interaction time. The results obtained in this chapter are of interest for new experiments on the study of nonlinear optical processes in dielectric media using ultrashort intense laser pulses as exciting radiation, and the effects of damping and decoherence as well as higher-order time terms could be investigated.

Book Publisher International (a part of SCIENCEDOMAIN International)•May 22, 2021•0 citations
In this paper we study the amplitude Nth-power squeezing of radiation fields in the degenerate Raman process by using the modified effective Hamiltonian approach recently suggested by us. We found that if the field is initially in a coherent state it will not get squeezing for any Nth-power; if the field is initially in a squeezed vacuum, it may get Nth-power squeezing. The time evolution of the field fluctuation was discussed. Its dependences on power-order N, mean photon number bar-n, and squeezing angle xi are analyzed.
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.
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.
An initially prepared coherent state coupled to a second-order nonlinear medium is responsible for stimulated and spontaneous hyper Raman processes. By using an intuitive approach based on perturbation theory, the Hamiltonian corresponding to the hyper Raman processes is analytically solved to obtain the temporal development of the field operators. It is true that these analytical solutions are valid for small coupling constants. However, the interesting part is that these solutions are valid for reasonably large time. Hence, the present analytical solutions are quite general and are fresh compared to those solutions under short-time approximations. By exploiting the analytical solutions of field operators for various modes, we investigate the squeezing, photon antibunching and nonclassical photon statistics for pure modes of the input coherent light responsible for hyper Raman processes. At least in one instance (stimulated hyper Raman processes for vibration phonon mode), we report the simultaneous appearance of classical (photon bunching) and nonclassical (squeezing) effects of the radiation field responsible for hyper Raman processes.
In a recent paper, Giri and Gupta [Int. J. Mod. Phys. B19, 1943 (2005)] discussed the possibility of obtaining nth-order squeezing of the field amplitude of the fundamental mode in spontaneous Raman processes. These investigations are based on the earlier works of Kumar and Gupta [Quantum & Semiclassical Opt.7, 835 (1995)] and Giri and Gupta [J. Mod. Opt.51, 1705 (2004)]. As a consequence of our re-investigation on the same model, we found that the calculations and hence the conclusion of Giri and Gupta [Int. J. Mod. Phys. B19, 1943 (2005) and J. Mod. Opt.51, 1705 (2004)] and Kumar and Gupta are entirely baseless and misleading. There will be no squeezing of the fundamental mode in stimulated and/or in spontaneous Raman processes.
Sum squeezing of the field amplitude is studied in the nondegenerate and degenerate frequency upconversion process under the short interaction time. A state is squeezed when the quantum fluctuation (amplitude noise or phase noise) in one variable is reduced below the symmetric limit at the expense of the increased quantum fluctuation in the conjugate variable such that the Heisenberg uncertainty relation is not violated. It is shown that sum squeezing can be converted into normal squeezing via sum-frequency generation in the nondegenerate frequency upconversion process, while the amplitude-squared squeezing of the fundamental mode directly changed into the squeezing of the harmonic in the degenerate frequency upconversion process. All reachable conditions of uncorrelated modes for obtaining a sum squeezing in two modes and its dependence on the squeezing of individual field modes are investigated. It is found that the squeezed states are associated with large number of pump photons. It is also confirmed that the higher-order squeezing (sum squeezing) is directly associated with coupling of the field and interaction time. The results obtained in this chapter are of interest for new experiments on the study of nonlinear optical processes in dielectric media using ultrashort intense laser pulses as exciting radiation, and the effects of damping and decoherence as well as higher-order time terms could be investigated.