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International Journal of Modern Physics B

SQUEEZING AND QUASIPROBABILITIES FOR A TWO-PHOTON JAYNES-CUMMINGS MODEL WITH ATOMIC MOTION

Amitabh Joshi, S. V. Lawande

Published Nov 10, 1992• 13 citations
Publisher

Abstract

We study the squeezing and the quasiprobability distribution Q-function for an extended two-photon Jaynes-Cummings model (JCM) that includes atomic motion and the field mode structure. A comparative study of this model with respect to the standard model (in which the atom is at rest) has been presented here to isolate the effect of limited atom-radiation interaction time.

DOI
10.1142/s0217979292001560

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We study the squeezing and the quasiprobability distribution Q-function for an extended two-photon Jaynes-Cummings model (JCM) that includes atomic motion and the field mode structure. A comparative study of this model with respect to the standard model (in which the atom is at rest) has been presented here to isolate the effect of limited atom-radiation interaction time.
By means or investigating the time evolution of the atomic dipole squeezing and the field squeezing in the one-photon Jaynes-Cummings model and the nondege-nerate two-photon Jaynes-Cummings model, the relations between atomic dipole squeezing and squeezing in the radiating field are examined. The conditions under which the atom in atomic dipole squeezed state can radiate squeezed light are presented. The properties of the squeezing transformation between atomic dipole quadrature components and field quadrature components are also discussed. And in the atom-field coupling system, the two-photon transtion processes in producing squeezed light are superior to the one-photon transition processes.
The quatum statistical properties of two-photon radiation from two-level atomic system are investigated by using complete set in the nth subspace of generalized Jaynes-Cummings hamiltonian, and the general expression for field variance is obtained. The conditions for optimum squeezing as well as the optimum squeezed quantity are found out for an arbitrary initial state, and the time evolution of the optimum squeezed state is then analysed. As an example, the squeezing in an initial state with bare atomic system in thermal equilibrium is discussed, which demonstrates the dependence of squeezing on several parameters, such as, temperature, detuning, coupling strength. The conditions for squeezing are given analytically and numerically. Finally, the physical picture of the squeezing is pointed out.
The correlations between two atoms in a generalized two-mode Jaynes-Cummings model (JCM), in the presence of a two-mode squeezed state, are studied. It is found that for a small amount of initial squeezing the correlations go back and forth between the radiation and the atoms. For large initial squeezing the atoms are found to be highly correlated at all times, while the squeezing of the radiation is destroyed as a function of time. In addition, the squeezing of the field is studied in the two-mode JCM and is compared to the one-mode squeezing that is obtained for the ordinary JCM. It is found that in the two-mode model the squeezing is preserved for longer times under the condition that g1{\mathit{g}}_{1}g1​ and g2{\mathit{g}}_{2}g2​ (the two coupling constants) are almost equal.