Quasienergy collapse in the driven Jaynes--Cummings--Rabi model: correspondence with a charged Dirac particle in an electromagnetic field

TL;DR

This paper investigates a phase transition in the driven Jaynes--Cummings model, revealing a quasienergy collapse linked to a Dirac particle analogy, and characterizes the system's phases through Lorentz transformations.

Contribution

It establishes a novel correspondence between the driven Jaynes--Cummings model and a charged Dirac particle in an electromagnetic field, providing new insights into the system's phase transition behavior.

Findings

Identifies a quasienergy collapse at a critical drive amplitude.

Maps the Jaynes--Cummings model to a Dirac particle in an electromagnetic field.

Characterizes phases using Lorentz transformations.

Abstract

A system evolving under the driven Jaynes--Cummings model will undergo a phase transition at a critical driving field amplitude. This transition is foreshadowed by a collapse of the quasienergy level spectra of the system and remains present as the model is extended to include a counter-rotating interaction. We study this critical response and obtain the eigenvalues and eigenstates of the extended model by presenting a correspondence between the Jaynes--Cummings model and a charged Dirac particle subject to an external electromagnetic field. Under this correspondence, the field and two-level system that compose the Jaynes--Cummings model map to the external and internal degrees of freedom describing the Dirac particle, respectively. The phases of the system below (above) the critical drive are then characterized by discrete (continuous) solutions, with the manipulations required to obtain these solutions appearing naturally as Lorentz transformations.