Dicke Model for Quantum Hall Systems

TL;DR

This paper models the interaction between nuclear and electron spins in quantum Hall systems using the Dicke model, revealing potential for collective spin phenomena similar to quantum optical systems.

Contribution

It introduces a theoretical framework describing nuclear-electron spin interactions in QH systems as a Dicke model, highlighting novel collective phenomena.

Findings

Nuclear spins collectively couple to the NG mode.

The interaction can be effectively described by the Dicke model.

Quantum optical phenomena may emerge in QH systems.

Abstract

Quantum Hall (QH) systems consist of many-body electron and nuclear spins. They are coupled so weakly through the hyperfine interaction that normally electron spin dynamics are scarcely affected by the nuclear spins. The dynamics of the QH systems, however, may drastically change when the nuclear spins interact with low-energy collective excitation modes of the electron spins. We theoretically investigate the nuclear-electron spin interaction in the QH systems as hybrid quantum systems driven by the hyperfine interaction. In particular, we study the interaction between the nuclear spins and the Nambu-Goldstone (NG) mode with the linear dispersion relation associated with the U(1) spin rotational symmetry breaking. We show that such an interaction is described as nuclear spins collectively coupled to the NG mode, and can be effectively described by the Dicke model. Based on the model we suggest that various collective spin phenomena realized in quantum optical systems also emerge in the QH systems.