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Stationary states of Jaynes-Cummings model with atomic center-of-mass quantum motion: direct comparison of standing-wave and counterpropagating-waves cases

A. Zh. Muradyan·G. A. Muradyan
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Abstract

The eigenstate problem of the Jaynes-Cummings model on the basis of complete Hamiltonian, including the center-of -mass kinetic energy operator, is treated. The energy spectrum and wave functions in standing-wave (SW)- and counterpropagating waves (CPW)- cases are calculated and compared with each other. It is shown that in CPW-case i) the atomic momentum distribution is asymmetric and somewhat narrower in general; ii) the concept of quasimomentum is not applicable and instead the ordinary momentum concerns the problem; iii) atomic and photonic state distributions are self-consistent, and, in consequence iiii) mean number of photons in the counterpropagating traveling waves and mean atomic momentum match. Explicit analytic expressions for energy eigenvalues and eigenfunctions are found in Tavis -Cummings-type approximation [Phys. Rev. 170, 379(1968)] and is pointed, that it implies only the bounded-like states for atomic center-of-mass motion. It is also shown that if the recoil energy is taken into account, the Doppleron resonance is split into two branches, one of which diverges to Bragg-like resonance in the high-order range.

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A. Zh. Muradyan, G. A. Muradyan. 2001-12-26. Stationary states of Jaynes-Cummings model with atomic center-of-mass quantum motion: direct comparison of standing-wave and counterpropagating-waves cases. https://arxiv.org/abs/quant-ph/0112164

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