Solution of the Dicke model for N=3

TL;DR

This paper analytically solves the N=3 Dicke model, revealing unique spectral degeneracies and extending understanding of multi-qubit quantum optical systems beyond simpler models.

Contribution

It provides an analytical solution for the N=3 Dicke model, highlighting new spectral degeneracies not linked to symmetries, unlike previous models.

Findings

Analytical spectrum determination for N=3 Dicke model

Identification of novel spectral degeneracies

Contrast with N=1 Rabi model results

Abstract

The N=3 Dicke model couples three qubits to a single radiation mode via dipole interaction and constitutes the simplest quantum-optical system allowing for Greenberger-Horne-Zeilinger states. In contrast to the case N=1 (the Rabi model), it is non-integrable if the counter-rotating terms are included. The spectrum is determined analytically, employing the singularity structure of an associated differential equation. While quasi-exact eigenstates known from the Rabi model do not exist, a novel type of spectral degeneracy becomes possible which is not associated with a symmetry of the system.