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

TL;DR

This paper investigates amplitude modulated Bloch oscillations in a cavity-atom system described by the Rabi Hamiltonian, revealing controllable photon probability dynamics and a novel superposition of Bloch oscillations.

Contribution

It introduces an effective Hamiltonian mapping for the Rabi model in the medium coupling regime and identifies amplitude modulated Bloch oscillations as a new phenomenon.

Findings

Photon probability exhibits amplitude modulated Bloch oscillations.

Transition between oscillations can be controlled by system parameters.

Multiple zero-transition points are achieved through parameter tuning.

Abstract

We study the dynamics of the Rabi Hamiltonian in the medium coupling regime with $\left\vert g/\omega \right\vert \sim 0.07$, 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}}% /\omega $, as well as in-phase resonant oscillating atomic frequency $\Omega \left( t\right) $, leading to multiple zero-transition points.