Stationary states of the Jaynes–Cummings model with atomic centre-of-massquantum motion: analytical approximation to transfer counterpropagating wavesinto a standing wave in a large photon number limit

Abstract

The eigenstate problem of the Jaynes–Cummings model on the basis of acomplete Hamiltonian, including the centre-of-mass kinetic energy operator, isconsidered. The energy spectrum and wavefunctions in the standing-wave (SW)and counterpropagating-wave (CPW) cases are calculated and compared witheach other. It is shown that in the CPW case: (i) the atomic momentumdistribution is asymmetric; (ii) the concept of quasimomentum is notapplicable and instead the problem concerns the ordinary momentum;(iii) atomic and photonic state distributions are self-consistent; and as aconsequence (iv) the mean number of photons in counterpropagatingtravelling waves and mean atomic momentum are matched. Explicit analyticexpressions are proposed to describe the transition from counterpropagatingquantized waves to a standing wave. It is also shown that, if the recoilenergy is taken into account, the Doppleron resonance is split into twobranches, one of which diverges to Bragg-like resonance in high-order range.