Searching for structure beyond parity in the two-qubit Dicke model

TL;DR

This paper classifies the spectrum of the two-qubit Dicke model using quantum information measures, identifying spectral sets and trapping states with potential applications in quantum entanglement and quantum information storage.

Contribution

It introduces a spectral classification based on quantum measures and identifies robust trapping states in the two-qubit Dicke model, useful for quantum information processing.

Findings

Four spectral sets identified in each parity subspace.

Singlet states act as trapping states under environmental coupling.

Robustness of trapping states against driving and interactions.

Abstract

We try to classify the spectrum of the two-qubit Dicke model by calculating two quantum information measures of its eigenstates: the Wooters concurrence and the mutual quantum information. We are able to detect four spectral sets in each parity subspace of the model: one set is regular and given by the product of a Fock state of the field times the singlet Bell state of the qubits; the rest are fairly regular and related to the triplet states of the Bell basis. The singlet states become trapping states when we couple the Dicke model to an environment of harmonic oscillators, making them candidates for generating maximally entangled states in experimental realizations of ion trap quantum electrodynamics (QED) and circuit QED. Furthermore, they are robust and survive the inclusion of driving and dipole-dipole interactions, pointing to their use for storing quantum correlations, and it is straightforward to provide a generalization of these trapping states to the Dicke model with even number of qubits.