Amplitude modulated Bloch oscillations of photon probability distribution in a cavity-atom system

Abstract

We study the dynamics of the Rabi Hamiltonian in the medium coupling regime with $\left|g/\omega \right|\sim 0.07$, where $g$ is atom-field coupling constant, $\omega$ is the field frequency, for the quantum state with average photon number $\bar{n}\sim 10^4$. We map the original Hamiltonian to an effective one, which describes a tight-binding chain subjected to a staggered linear potential. It is shown that the photon probability distribution of a Gaussian-type state exhibits the amplitude modulated Bloch oscillation (BO), which is a superposition of two conventional BOs with a half-BO-period delay between them and is essentially another type of Bloch-Zener oscillation. The probability transition between the two BOs can be controlled and suppressed by the ratio $g\sqrt{\bar{n}}$, as well as in-phase resonant oscillating atomic frequency $\Omega \left(t\right)$, leading to multiple zero-transition points.

8 pages, 5 figures

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