Quantum quenches in the Dicke model: statistics of the work done and of other observables

Abstract

We study the statistics of the work done in a zero temperature quench of the coupling constant in the Dicke model describing the interaction between a gas of two level atoms and a single electromagnetic cavity mode. When either the final or the initial coupling constants approach the critical coupling ${\lambda }_c$ that separates the normal and superradiant phases of the system, the probability distribution of the work done displays singular behavior. The average work tends to diverge as the initial coupling parameter is brought closer to the critical value ${\lambda }_c$. In contrast, for quenches ending close to criticality, the distribution of work has finite moments but displays a sequence of edge singularities. This contrasting behavior is related to the difference between the processes of compression and expansion of a particle subject to a sudden change of its confining potential. We confirm this by studying in detail the time dependent statistics of other observables, such as the quadratures of the photons and the total occupation of the bosonic modes.

8 pages, 2 figures

References in corpus (29)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• Time-dependence of correlation functions following a quantum quench
• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Fluctuation theorems: Work is not an observable
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system
• The Luttinger model following a sudden interaction switch-on
• Universal adiabatic dynamics across a quantum critical point
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Dephasing and the steady state in quantum many-particle systems
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Entanglement Entropy dynamics in Heisenberg chains
• Quench dynamics across quantum critical points
• Strongly correlated fermions after a quantum quench
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Effective thermal dynamics following a quantum quench in a spin chain
• Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench
• Nonthermal steady states after an interaction quench in the Falicov-Kimball model
• Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined
• Quantum quenches from integrability: the fermionic pairing model
• Correlations in an expanding gas of hard-core bosons
• Relaxation in the XX quantum chain
• Microcanonical quantum fluctuation theorems
• Microscopic expression for the heat in the adiabatic basis
• Dipole oscillations of confined lattice bosons in one dimension

Cited by in corpus (29)

• Nonequilibrium dynamics of closed interacting quantum systems
• Irreversible work and inner friction in quantum thermodynamic processes
• Emergent thermodynamics in a quenched quantum many-body system
• Quantum quench influenced by an excited-state phase transition
• Quench Dynamics of Isolated Many-Body Quantum Systems
• General Features of the Relaxation Dynamics of Interacting Quantum Systems
• Work Extraction and Energy Storage in the Dicke Model
• Work and Quantum Phase Transitions: Is there Quantum Latency?
• Quantum transition-edge detectors
• Nonexponential fidelity decay in isolated interacting quantum systems
• Relaxation and Thermalization of Isolated Many-Body Quantum Systems
• Statistics of the work distribution for a quenched Fermi gas
• Overlap distributions for quantum quenches in the anisotropic Heisenberg chain
• Edge exponents in work statistics out of equilibrium and dynamical phase transitions from scattering theory in one dimensional gapped systems
• Asymptotic work statistics of periodically driven Ising chains
• Quench action and large deviations: work statistics in the one-dimensional Bose gas
• Quench echo and work statistics in integrable quantum field theories
• Quantum quenches and work distributions in ultra-low-density systems
• Exact work statistics of quantum quenches in the anisotropic XY model
• Work statistics and symmetry breaking in an excited state quantum phase transition
• Adiabatic invariants for the regular region of the Dicke model
• Effects of the Dzyaloshinsky-Moriya interaction on nonequilibrium thermodynamics in the $XY$ chain in a transverse field
• Bose-Hubbard ladder subject to effective magnetic field: quench dynamics in a harmonic trap
• Thermodynamics and Superradiant Phase Transitions in a three-level Dicke Model
• The role of quantum work statistics in many-body physics
• Singularities in large deviations of work in quantum quenches
• Work statistics and thermal phase transitions
• Work extraction and fully entangled fraction
• Role of topology on the work distribution function of a quenched Haldane model of graphene