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Modern Physics Letters B

SQUEEZING EFFECTS IN THE SUM AND DIFFERENCE OF THE FIELD AMPLITUDE IN THE RAMAN PROCESS

Biswajit Sen, Swapan Mandal

Published Jul 20, 2007• 0 citations
Publisher

Abstract

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.

DOI
10.1142/s0217984907013614

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SQUEEZING EFFECTS IN THE SUM AND DIFFERENCE OF THE FIELD AMPLITUDE IN THE RAMAN PROCESS

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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.
Sum and difference squeezing of the field amplitude are higher-order squeezing effects. These effects are studied in the Raman process under the short-time approximation based on a fully quantum mechanical approach. It is shown that for uncorrelated modes, the normal squeezing in the sum and difference-frequency field depends on the sum and difference squeezing of input field modes respectively, which can generate normal squeezing in the sum and difference-frequency field mode. All the possibilities for obtaining sum and difference squeezing in two modes and its dependence on squeezing of individual field modes are investigated. We have also shown that if the high-frequency mode is in a coherent state and the low-frequency mode is squeezed, the field state will be difference squeezed if the amplitude of the high-frequency mode is large enough; otherwise the state may or may not be difference squeezed. If both modes are squeezed, then the state may or may not be difference squeezed. These higher-order squeezing effects are useful in the production of squeezing in the Raman process.
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.
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.
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 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 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.