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

We study the dynamics of the Rabi Hamiltonian in the medium coupling regime with $\left|g/\omega \right|\sim 0.07$, where g is the atom-field coupling constant and ω is the field frequency, for the quantum state with average photon number $\overline{n}\sim {10}^4$. 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 amplitude-modulated Bloch oscillations (BOs), which are a superposition of two conventional BOs with a half-BO-period delay between them and are essentially another type of Bloch–Zener oscillation. The probability transition between the two BOs can be controlled and suppressed by the ratio $g\sqrt{\overline{n}}/\omega$, as well as the in-phase resonant oscillating atomic frequency Ω (t), leading to multiple zero-transition points. (paper)