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

摘要

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