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Physical Review A

Comment on “Influence of nonlinearity in one-photon processes on the relationship between field and dipole squeezing in the two-level thermal Jaynes-Cummings model”

Rui Hua Xie

Published Jun 7, 2000• 7 citations
Publisher

Abstract

Recently, in a very interesting article [Phys. Rev. A 56, 796 (1997)], Bhattacherjee has discussed the influence of nonlinearity in one-photon processes on the relationship between field and dipole squeezing in the two-level thermal Jaynes-Cummings model. Here we correct Eqs. (14)--(17) of that paper and exactly show that the squeeze period and duration in the case of $\mathrm{n\ifmmode \bar{}\else \={}\fi{}}=0$ and $\ensuremath{\lambda}\ensuremath{\ne}0$ are inversely proportional to the nonlinear parameter $\ensuremath{\lambda}.$

DOI
10.1103/physreva.62.017801

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Recently, in a very interesting article [Phys. Rev. A 56, 796 (1997)], Bhattacherjee has discussed the influence of nonlinearity in one-photon processes on the relationship between field and dipole squeezing in the two-level thermal Jaynes-Cummings model. Here we correct Eqs. (14)--(17) of that paper and exactly show that the squeeze period and duration in the case of n\ifmmodeˉ\elseˉ\fi=0\mathrm{n\ifmmode \bar{}\else \={}\fi{}}=0n\ifmmodeˉ\elseˉ\fi=0 and \ensuremathλ\ensuremath≠0\ensuremath{\lambda}\ensuremath{\ne}0\ensuremathλ\ensuremath=0 are inversely proportional to the nonlinear parameter \ensuremathλ.\ensuremath{\lambda}.\ensuremathλ.
Historically, the Heisenberg lower limit is used as the reference level for the definitionof squeezing in observables. However, in the measurement of observables correspondingto noncanonical operators, it may not work [Puri, Phys. Rev. A49, 2178 (1994)]. Then,one should employ the Schrodinger uncertainty relation for further studies, where theSchrodinger lower limit sets a higher bound on quantum fluctuations than the Heisen-berg one does. In this paper, using Heisenberg ™s and Schrodinger uncertainty relations,we have made a comparative study on the squeezing properties of quantum fluctuationsin atomic dipole variables in the thermal two-photon Jaynes-Cummings model, includ-ing the discussion of the difference between both cases,the influence of initial atomiccoherence or thermal photons on the atomic dipole squeezing, and the possibility of real-ization of atomic dipole squeezing in two-photon micromaser experiments with Rydbergatoms in a high-Q cavity.PACS. 42.50.D~ - Nonclassical field states; squeezed, antibunched, and sub-Poissonianstates; operational definitions of the phase of the field; phasemeasurements.PACS. 42.5O.L~ - Quantum fluctuations, quantum noise, and quantum jumps.PACS. 32.80.-t - Photon interactions with atoms.