Mirror-field-atom interaction: Hamiltonian diagonalization

TL;DR

This paper introduces a transformation using Susskind-Glogower operators to simplify the Hamiltonian of a system involving a movable mirror, a quantized field, and a two-level atom, enabling easier solution of the model.

Contribution

The paper presents a novel application of Susskind-Glogower operators to diagonalize and simplify the Hamiltonian in a hybrid quantum system involving a mirror, field, and atom.

Findings

Hamiltonian simplified via Susskind-Glogower transformation

Elimination of the quantized field subsystem in the Hamiltonian

Effective Hamiltonian solvable with reduced complexity

Abstract

We show that the interaction between a movable mirror with a quantized field that interacts with a two-level atom may be simplified via a transformation that involves Susskind-Glogower operators (SGO). By using this transformation it is easy to show that we can cast the Hamiltonian, after a series of small rotations, into an effective Hamiltonian that may be solved. We would like to stress that the transformation in terms of SGO already simplifies enough the Hamiltonian in the sense that, in an exact way, it "eliminates" one of the three-subsystems, namely the quantized field.