Jahn-Teller systems from a cavity QED perspective

TL;DR

This paper explores the Jahn-Teller effect within cavity QED systems, analyzing the influence of geometric phases on dynamics and linking it to phase transitions, using both theoretical and numerical methods.

Contribution

It introduces a cavity QED model that maps to the Jahn-Teller $E\times\epsilon$ Hamiltonian, revealing new insights into geometric phases and their effects on system dynamics.

Findings

Geometric phase significantly affects collapse-revival patterns.

Field intensities encode information about the Berry phase.

Connection established between Jahn-Teller effect and Dicke phase transition.

Abstract

Jahn-Teller systems and the Jahn-Teller effect are discussed in terms of cavity QED models. By expressing the field modes in a quadrature representation, it is shown that certain setups of a two-level system interacting with a bimodal cavity is described by the Jahn-Teller $E\times\epsilon$ Hamiltonian. We identify the corresponding adiabatic potential surfaces and the conical intersection. The effects of a non-zero geometrical Berry phase, governed by encircling the conical intersection, are studied in detail both theoretically and numerically. The numerical analysis is carried out by applying a wave packet propagation method, more commonly used in molecular or chemical physics, and analytic expressions for the characteristic time scales are presented. It is found that the collapse-revival structure is greatly influenced by the geometrical phase and as a consequence, the field intensities contain direct information about this phase. We also mention the link between the Jahn-Teller effect and the Dicke phase transition in cavity QED.