Ultracold two-level atom in a quadratic potential

TL;DR

This paper introduces a right unitary decomposition method to analyze an ultracold two-level atom in a quadratic potential, providing an analytic solution for the atom-field interaction dynamics with position-dependent coupling.

Contribution

The paper presents a novel right unitary approach that simplifies numerical evolution and derives an explicit analytic time evolution operator for quadratic position-dependent couplings.

Findings

Simplifies numerical simulation of atom-field interactions

Provides a closed-form analytic time evolution operator

Applicable to arbitrary position-dependent couplings

Abstract

We use a right unitary decomposition to study an ultracold two-level atom interacting with a quantum field. We show that such a right unitary approach simplifies the numerical evolution for arbitrary position-dependent atom-field couplings. In particular, we provide a closed form, analytic time evolution operator for atom-field couplings with quadratic dependence on the position of the atom.