Quantum Phase Diagrams of Matter-Field Hamiltonians I: Fidelity, Bures Distance, and Entanglement

Abstract

A general procedure is established to calculate the quantum phase diagrams for finite matter-field Hamiltonian models. The minimum energy surface associated to the different symmetries of the model is calculated as a function of the matter-field coupling strengths. By means of the ground state wave functions, one looks for minimal fidelity or maximal Bures distance surfaces in terms of the parameters, and from them the critical regions of those surfaces characterize the finite quantum phase transitions. Following this procedure for $N_a=1$ and $N_a=4$ particles, the quantum phase diagrams are calculated for the generalised Tavis-Cummings and Dicke models of 3-level systems interacting dipolarly with $2$ modes of electromagnetic field. For $N_a=1$, the reduced density matrix of the matter allows us to determine the phase regions in a $2$-simplex (associated to a general three dimensional density matrix), on the different $3$-level atomic configurations, together with a measurement of the quantum correlations between the matter and field sectors. As the occupation probabilities can be measured experimentally, the existence of a quantum phase diagram for a finite system can be established.

arXiv comment30 pages, 13 figures

References in corpus (16)

• Continuous Quantum Phase Transitions
• Ground state overlap and quantum phase transitions
• Fidelity approach to quantum phase transitions
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Universal scaling and critical exponents of the anisotropic quantum Rabi model
• Some remarks on 'superradiant' phase transitions in light-matter systems
• On the Superradiant Phase in Field-Matter Interactions
• Superradiant phase transitions with three-level systems
• Fidelity Susceptibility in the Quantum Rabi Model
• Quantum phase transitions of three-level atoms interacting with a one-mode electromagnetic field
• Polychromatic phase diagram for $n$-level atoms interacting with $\ell$ modes of electromagnetic field
• Analytic Approximation of the Tavis-Cummings Ground State via Projected States
• A semi-classical versus quantum description of the ground state of three-level atoms interacting with a one-mode electromagnetic field
• On the finite size behavior of quantum collective spin systems
• Variational Study of $\lambda$- and $N$-Atomic Configurations Interacting with an Electromagnetic Field of $2$ Modes
• Optimal basis for the generalized Dicke model

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• Effect of the Atomic Dipole-Dipole Interaction on the Phase Diagrams of Field-Matter Interactions I: Variational procedure