Exact solvability, non-integrability, and genuine multipartite entanglement dynamics of the Dicke model

Abstract

In this paper, the finite size Dicke model of arbitrary number of qubits is solved analytically in an unified way within extended coherent states. For the $N=2k$ or $2k-1$ Dicke models ($k$ is an integer), the $G$-function, which is only an energy dependent $k\times k$ determinant, is derived in a transparent manner. The regular spectrum is completely and uniquely given by stable zeros of the $G$-function. The closed-form exceptional eigenvalues are also derived. The level distribution controlled by the pole structure of the $G$-functions suggests non-integrability for $N>1$ model at any finite coupling in the sense of recent criterion in literature. A preliminary application to the exact dynamics of genuine multipartite entanglement in the finite $N$ Dicke model is presented using the obtained exact solutions.

arXiv comment18 pages, 5 figures

References in corpus (49)

• Quantum entanglement
• Separability Criterion for Density Matrices
• Quantum-enhanced measurements: beating the standard quantum limit
• Entanglement detection
• Scaling of Entanglement close to a Quantum Phase Transitions
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• Entanglement in a simple quantum phase transition
• Measurement-based quantum computation
• Strongly Interacting Polaritons in Coupled Arrays of Cavities
• On the Integrability of the Rabi Model
• Quantum phase transitions of light
• Chaos and the Quantum Phase Transition in the Dicke Model
• Preparation and Measurement of Three-Qubit Entanglement in a Superconducting Circuit
• Quantum Chaos Triggered by Precursors of a Quantum Phase Transition: The Dicke Model
• Entanglement and the Phase Transition in Single Mode Superradiance
• Generation of Three-Qubit Entangled States using Superconducting Phase Qubits
• Exploring Symmetry Breaking at the Dicke Quantum Phase Transition
• The Dicke model phase transition in the quantum motion of a Bose-Einstein condensate in an optical cavity
• Taming multiparticle entanglement
• Separability criteria for genuine multiparticle entanglement
• Exact solvability of the quantum Rabi models within Bogoliubov operators
• Detection of high-dimensional genuine multi-partite entanglement of mixed states
• Scaling of geometric phases close to quantum phase transition in the XY chain
• Entanglement, quantum phase transition and scaling in XXZ chain
• Geometric phases and criticality in spin chain systems
• Measurement of the decay of Fock states in a superconducting quantum circuit
• Finite-Size Scaling Exponents in the Dicke Model
• Accurate numerical solution to the finite-size Dicke model
• Analytical eigenstates for the quantum Rabi model
• Entanglement and Entropy in a Spin-Boson Quantum Phase Transition
• Comparative quantum and semi-classical analysis of Atom-Field Systems I: density of states and excited-state quantum phase transitions
• Comparative quantum and semi-classical analysis of Atom-Field Systems II: Chaos and regularity
• Instability and entanglement of the ground state of the Dicke model
• Large-N scaling behavior of the ground-state energy and fidelity in the Dicke Model
• Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems: scaling of entanglement
• Analytical characterization of the genuine multiparticle negativity
• Genuine multiparticle entanglement of permutationally invariant states
• Solution of the Dicke model for N=3
• On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations
• Recoherence in the entanglement dynamics and classical orbits in the N-atom Jaynes-Cummings model
• Quantum correlations in the collective spin systems
• Scaling of Berry's Phase Close to the Dicke Quantum Phase Transition
• Scaling behavior in the adiabatic Dicke Model
• On solvability and integrability of the Rabi model
• Solutions to the quantum Rabi model with two equivalent qubits
• Concise analytic solutions to the quantum Rabi model with two arbitrary qubits
• Searching for structure beyond parity in the two-qubit Dicke model
• Adiabatic approximation for three qubits ultrastrongly coupled to a harmonic oscillator

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