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Journal of Modern Optics

Comments on ‘Higher order squeezing of the electromagnetic field in spontaneous and in stimulated Raman processes’

Biswajit Sen, Swapan Mandal

Published Nov 28, 2006• 3 citations
Publisher

Abstract

Of late, Giri and Gupta [J. Mod. Opt. 52 1769 (2005)] discussed the possibility of getting higher order (fourth and fifth orders) squeezing of the fundamental mode in spontaneous Raman and in stimulated Raman processes. These investigations are based on the earlier works of Kumar and Gupta [Quantum Semiclass. Opt. 7 835 (1995)]. We reinvestigate the model and we found that the entire calculations and hence the conclusion of Giri and Gupta and Kumar and Gupta are not only baseless but also misleading. There will be no squeezing of the fundamental mode in spontaneous and in Raman processes.

DOI
10.1080/09500340600904185

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Of late, Giri and Gupta [J. Mod. Opt. 52 1769 (2005)] discussed the possibility of getting higher order (fourth and fifth orders) squeezing of the fundamental mode in spontaneous Raman and in stimulated Raman processes. These investigations are based on the earlier works of Kumar and Gupta [Quantum Semiclass. Opt. 7 835 (1995)]. We reinvestigate the model and we found that the entire calculations and hence the conclusion of Giri and Gupta and Kumar and Gupta are not only baseless but also misleading. There will be no squeezing of the fundamental mode in spontaneous and in 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.
Under the short-time approximation, Giri and Gupta1 investigated the sum and difference squeezing of the field amplitude in the Raman process. The relations between the normal squeezing and the sum and difference squeezing of the field amplitude are explicitly exhibited. They argued that the sum and difference squeezing of the field amplitude are essentially the squeezing in higher-order sense. Upon verification of the results of Giri and Gupta, we observe that the entire calculations and the conclusions thereof are misleading and baseless. To substantiate our claim, we give the correct expressions for the useful variances. Interestingly, there is no possibility of getting normal squeezing, sum squeezing and difference squeezing of the input state prepared in coherent state.
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.
The nonclassical effect of squeezing of light in hyper-Raman processes is investigated under the short-time approximation based on a fully quantum mechanical approach. Effects of squeezing in spontaneous and stimulated processes are studied. A hyper-Raman process is looked upon as a three-photon and one-phonon interaction process. Squeezing in amplitude, squared amplitude and cubed amplitude have been investigated. Squeezing occurs invariably in the fundamental mode in both spontaneous and stimulated processes, whereas the squeezing in the Stokes mode is found to be dependent on amplitude-squared squeezing of the initial pump field.
Squeezing in four wave mixing process was studied recently using perturbation method by Giri and Gupta [D. K. Giri and P. S. Gupta, J. Opt. B: Quantum Semiclass. Opt.6 (2004) 91.] We reexamine this using a coherent intense pump mode and with a much better approximation which results in validity of our results for much larger interaction times. We find that for the range of phase where these authors obtained squeezing, only a small squeezing is obtained for a brief period but larger squeezing at large times is obtained in the other range of phase. We also obtain larger amplitude squared squeezing.
The non-classical effect of squeezing of light in spontaneous Raman and stimulated Raman processes are investigated under a short-time approximation based on a fully quantum mechanical approach. A Raman process is looked upon as a two-photon and one-phonon interaction process. Squeezing in amplitude, amplitude squared and amplitude cubed have been investigated. The occurrence of squeezing is observed in the fundamental mode in spontaneous Raman and stimulated Raman scattering. The squeezing in a Stokes field is found to be dependent on squeezing of the initial pump field.