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Chinese Journal of Physics

Generation of Atomic Dipole Squeezing in the Thermal Two-Photon Jaynes-Cummings Model

Rui‐Hua Xie

Published Oct 1, 1997• 0 citations

Abstract

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.

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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 $\mathrm{n\ifmmode \bar{}\else \={}\fi{}}=0$ and $\ensuremath{\lambda}\ensuremath{\ne}0$ are inversely proportional to the nonlinear parameter $\ensuremath{\lambda}.$

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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.

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 $\ensuremath{\lambda}.$