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IOSR Journal of Applied Physics

Detection of Sum and Difference Squeezing

Ranjana Prakash

Published Jan 1, 2012• 3 citations
Publisher

Abstract

Sum and difference squeezing was defined by Hillery who showed that these turn into normal squeezing in sum and difference frequency generation.We re-examine this using an intense coherent pump mode and with a much better approximation.Our results are valid for much larger interaction times and therefore enable detection of smaller sum and difference squeezings, in principle.,Moreover, if both, our and Hillary's results are regarded holding, our results lead to more squeezing.

DOI
10.9790/4861-0124347

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Sum and difference squeezing was defined by Hillery who showed that these turn into normal squeezing in sum and difference frequency generation.We re-examine this using an intense coherent pump mode and with a much better approximation.Our results are valid for much larger interaction times and therefore enable detection of smaller sum and difference squeezings, in principle.,Moreover, if both, our and Hillary's results are regarded holding, our results lead to more squeezing.
Sum and difference squeezing are both higher-order, two-mode squeezing effects. Sum squeezing is turned into normal squeezing by sum-frequency generation. The operators that are used to define it form a representation of the su(1,1) Lie algebra. Difference squeezing can generate normal squeezing through difference-frequency generation. The operators that characterize it form a representation of the su(2) Lie algebra. Both are nonclassical effects. For uncorrelated modes the presence of squeezing in at least one of the modes is a necessary condition for the existence of either sum or difference squeezing. If the modes are correlated this is no longer true. Both sum and difference squeezing can be generated by combining a squeezed mode with one in a coherent state. Sum squeezing is also produced by a parametric amplifier. In order to better illustrate some of these effects a pictorial representation of sum squeezing is presented.
The multimode difference squeezing of the electromagnetic field in the four-wave mixing process is investigated under the short-time approximation based on a fully quantum mechanical approach. It is shown that for uncorrelated modes the normal squeezing in the difference-frequency field depends on the difference squeezing of input field modes, which can generate normal squeezing in the difference-frequency field mode. Various possibilities for obtaining difference squeezing in three modes and its dependence on squeezing of individual field modes are investigated. If one of the high-frequency modes is squeezed and the other two modes are in coherent states, difference squeezing can be generated when the amplitude of the low-frequency mode is large enough. Difference squeezing can be generated in the three modes if one of the high-frequency modes is in a coherent state and the other two modes are difference squeezed. It is also shown that when the low-frequency mode is in a coherent state and the high-frequency modes are sum squeezed, then difference squeezing can be generated for large amplitude of the low-frequency mode.
We consider squeezing of the electromagnetic field resulting from the interaction of the three-level ssV-shaped atom with two modes initially taken in coherent-state representation. We also consider higher-order squeezing in the sense of Hong and Mandel [Phys. Rev. Lett. 54, 323 (1985)] and then in the sense of Hillery [Phys. Rev. A 36, 3796 (1987)]. We calculate the two-mode squeezing proposed in [J. Mod. Opt. 34, 709 (1987)] and the sum squeezing defined by Hillery [Phys. Rev. A 40, 3147 (1989)] for an atom starting initially at its ground 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.