Revisiting the Jaynes-Cummings model with time-dependent coupling

TL;DR

This paper analyzes the resonant time-dependent Jaynes-Cummings model, deriving exact solutions to explore how modulated atom-field couplings influence atomic inversion, entanglement, and thermal effects in quantum light-matter interactions.

Contribution

It provides an analytical solution for the resonant TDJC model with various coupling modulations, enhancing understanding of dynamic quantum light-matter phenomena.

Findings

Time-dependent coupling causes atomic dipole alignment with the field.

Atomic population trapping increases with thermal photon number.

Modulations affect atomic entanglement and purity dynamics.

Abstract

The Jaynes-Cummings (JC) model stands as a fully quantized, fundamental framework for exploring light-matter interactions, a timely reflection on a century of quantum theory. The time-dependent Jaynes-Cummings (TDJC) model introduces temporal variations in certain parameters, which often require numerical methods. However, under the resonance condition, exact solutions can be obtained, offering insight into a variety of physical scenarios. In this work, we study the resonant TDJC model considering different modulations of the atom-field coupling. The model is presented and an analytical solution derived in a didactic way, allowing us to examine how time-dependent couplings affect atomic population inversion and atom-field entanglement. We also consider an atom traversing a partially cooled cavity, which induces periodicity and reveals the combined effects of atomic motion and thermal fluctuations. The Bloch vector is used to analyze the dynamics of the system, including the atomic state purity, and reveals phenomena such as atomic dipole alignment with the field due to the oscillating coupling, as well as atomic population trapping, which arises by increasing the initial mean thermal photon number.