Critical phenomena in an extended Dicke model

Abstract

Spectral characterization is a fundamental step in the development of useful quantum technology platforms. Here, we study an ensemble of interacting qubits coupled to a single quantized field mode, an extended Dicke model that might be at the heart of Bose-Einstein condensate in a cavity or circuit-QED experiments for large and small ensemble sizes, respectively. We present a semi-classical and quantum analysis of the model. In the semi-classical regime, we show analytic results that reveal the existence of a third regime, in addition of the two characteristic of the standard Dicke model, characterized by one logarithmic and two jump discontinuities in the derivative of the density of states. We show that the finite quantum system shows two different types of clustering at the jump discontinuities, signaling a precursor of two excited quantum phase transitions. These are confirmed using Peres lattices where unexpected order arises around the new precursor. Interestingly, Peres conjecture regarding the relation between spectral characteristics of the quantum model and the onset of chaos in its semi-classical equivalent is valid in this model as a revival of order in the semi-classical dynamics occurs around the new phase transition.

arXiv comment15 pages, 6 figures

References in corpus (25)

• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• Chaos and the Quantum Phase Transition in the Dicke Model
• Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system
• Quantum Chaos Triggered by Precursors of a Quantum Phase Transition: The Dicke Model
• Entanglement and the Phase Transition in Single Mode Superradiance
• The Dicke model phase transition in the quantum motion of a Bose-Einstein condensate in an optical cavity
• Excited state quantum phase transitions in many-body systems
• Observation of Dicke Superradiance for Two Artificial Atoms in a Cavity with High Decay Rate
• Realization of the Dicke model using cavity-assisted Raman transitions
• Self-organization of a Bose-Einstein condensate in an optical cavity
• Collective Dynamics of Bose--Einstein Condensates in Optical Cavities
• Accurate numerical solution to the finite-size Dicke model
• Excited-State Quantum Phase Transitions in Dicke Superradiance Models
• Digital Quantum Rabi and Dicke Models in Superconducting Circuits
• Quantum phase transition in the Dicke model with critical and non-critical entanglement
• Quantum quench influenced by an excited-state 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
• Excited-state phase transition leading to symmetry-breaking steady states in the Dicke model
• Digital-analog quantum simulation of generalized Dicke models with superconducting circuits
• Analog quantum simulation of generalized Dicke models in trapped ions
• Ground state in the finite Dicke model for interacting qubits
• Classical dynamics of a two-species condensate driven by a quantum field
• Dispersive Regimes of the Dicke Model
• Peres Lattices and chaos in the Dicke model

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• Signatures of excited state quantum phase transitions in quantum many body systems: Phase space analysis
• Experimental realization of the classical Dicke model
• Squeezed displaced entangled states in the quantum Rabi model
• Quantum Chaos in the Extended Dicke Model
• Quantum Simulation of an Extended Dicke Model with a Magnetic Solid
• Critical phenomena in light-matter systems with collective matter interactions