Analytical solutions and genuine multipartite entanglement of the three-qubit Dicke model

TL;DR

This paper derives analytical solutions for a three-qubit Dicke model beyond the RWA, analyzing entanglement dynamics and revealing differences between bipartite and multipartite entanglement behaviors.

Contribution

It introduces a generalized rotating-wave approximation (GRWA) for the three-qubit Dicke model and studies entanglement dynamics using these solutions.

Findings

GRWA provides accurate energy levels near resonance.

Bipartite entanglement exhibits sudden death, GME does not.

Analytical solutions match numerical results for entanglement dynamics.

Abstract

We present analytical solutions to three qubits and a single-mode cavity coupling system beyond the rotating-wave approximation (RWA). The zero-th order approximation gives correct solutions when the qubits are far detuned from the cavity. The first order approximation, called generalized rotating-wave approximation (GRWA), produces an effective solvable Hamiltonian with the same form as the ordinary RWA one and exhibits substantial improvements of energy levels over the RWA even on resonance. Based on these analytical eigen-solutions, we study both the bipartite entanglement and genuine multipartite entanglement (GME). The dynamics of the concurrence and the GME using the GRWA are in consistent with the numerical ones. Interestingly, the well known sudden death of entanglement occurs in the bipartite entanglement dynamics but not in GME dynamics.