Phase and amplitude modes in the anisotropic Dicke model with matter interactions

TL;DR

This paper investigates phase and amplitude modes in an anisotropic Dicke model with matter interactions, revealing novel phenomena and critical features that could be observed in quantum information systems.

Contribution

It introduces a detailed analysis of the low-lying spectrum and geometric phases in an anisotropic Dicke model, highlighting the interplay between anisotropy and matter interactions.

Findings

Identification of unique critical phenomena due to anisotropy and matter interactions

Analysis of the low-lying spectrum using Holstein-Primakoff transformation

Exploration of geometric phases in parameter space

Abstract

Phase and amplitude modes are emergent phenomena that manifest across diverse physical systems, from condensed matter and particle physics to quantum optics. Also called polariton modes, we study their behavior in an anisotropic Dicke model that includes collective matter interactions. We study the low-lying spectrum in the thermodynamic limit via the Holstein-Primakoff transformation and contrast the results with the semiclassical energy surface obtained via coherent states. We also explore the geometric phase for both boson and spin contours in the parameter space as a function of the phases in the system. We unveil novel phenomena due to the unique critical features provided by the interplay between the anisotropy and matter interactions. We expect our results to serve for the observation of phase and amplitude modes in current quantum information platforms.