Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1805.06285 · Physical Review A

Quantum quench dynamics in Dicke superradiance models

Michal Kloc, Pavel Stránský, Pavel Cejnar

Published Jul 20, 2018• 56 citations
arXivHTMLPDF

Abstract

We study the quantum quench dynamics in an extended version of the Dicke model where an additional parameter allows a smooth transition to the integrable Tavis-Cummings regime. We focus on the influence of various quantum phases and excited-state quantum phase transitions (ESQPTs) on the survival probability of the initial state. We show that, depending on the quench protocol, an ESQPT can either stabilize the initial state or, on the contrary, speed up its decay to the equilibrated regime. Quantum chaos smears out the manifestations of ESQPTs in quench dynamics, therefore significant effects can only be observed in integrable or weakly chaotic settings. Similar features are present also in the postquench dynamics of some observables.

DOI
10.1103/physreva.98.013836

Related papers

Quantum quench influenced by an excited-state phase transition

P. Pérez-Fernández, Pavel Cejnar, J. M. Arias +3 more

We analyze excited-state quantum phase transitions (ESQPTs) in three schematic (integrable and nonintegrable) models describing a single-mode bosonic field coupled to a collection of atoms. It is shown that the presence of the ESQPT in these models affects the quantum relaxation processes following an abrupt quench in the control parameter. Clear-cut evidence of the ESQPT effects is presented in integrable models, while in a nonintegrable model the evidence is blurred due to chaotic behavior of the system in the region around the critical energy.

arXiv:1012.3001•Physical Review A•Mar 3, 2011•102 citations

Excited-state quantum phase transitions and their manifestations in an extended Dicke model

Pavel Stránský, Michal Kloc, Pavel Cejnar

An Excited-State Quantum Phase Transition (esqpt) is a singularity observed in quantum energy spectra in the infinite-size limit of the system. It originates in the existence of stationary points in the semiclassical Hamiltonian function. We review the classification of esqpts and present a case study in an extended Dicke model. Finally, we show some preliminary results on the dynamical effect induced by esqpts.

AIP conference proceedings•Jan 1, 2017•2 citations

Classical and Quantum Dynamics of the Dicke Model

Aakash Sarkar, Supervisor Dr. Subhasis Sinha

In this thesis, we explore the Dicke model, well-known for its explanation of the superradiant phase transition and signatures of Classical and Quantum Chaos. We then propose a variational approach to determine the semi-classical (SC) equations of motion, using coherent states. The SC dynamics exhibits signs of classical chaos both with increasing coupling and as the energy of the system is gradually increased, eventually leading to it completely engulfing the 2 dimensional phase space of the pseudospin, which we examine through Poincare sections. We then use numerical diagonalization to study the Quantum Dicke model - it is observed that at and after exactly the critical value of the coupling, the system shows a net macroscopic photon expectation value, and the pseudospin component in the z direction starts to steadily decline - implying a net fraction of the atoms are shifting to the excited state. We then study the dynamics of the Quantum Dicke Hamiltonian using coherent states and compare the expectation values of the dimensional with the classical trajectories from the semi-classical dynamics for stable and chaotic orbits. We then introduce a linear quench which drives the Dicke model across the Superradiant phase transition by changing the coupling strength. The quenched dynamics is simulated using both semi-classical and quantum dynamics - it is seen that dynamically varying quantities are periodically oscillating around their instantaneous steady-state coupling values.

•May 1, 2016•0 citations

Excited-state phase transition and onset of chaos in quantum optical models

P. Pérez-Fernández, Armando Relaño, J. M. Arias +3 more

We study the critical behavior of excited states and its relation to order and chaos in the Jaynes-Cummings and Dicke models of quantum optics. We show that both models exhibit a chain of excited-state quantum phase transitions demarcating the upper edge of the superradiant phase. For the Dicke model, the signatures of criticality in excited states are blurred by the onset of quantum chaos. We show that the emergence of quantum chaos is caused by the precursors of the excited-state quantum phase transition.

Physical Review E•Apr 15, 2011•115 citations

Dynamics of coherent states in regular and chaotic regimes of the non-integrable Dicke model

Sergio Lerma-Hernández, Jorge Chávez-Carlos, M. A. Bastarrachea-Magnani +2 more

The quantum dynamics of initial coherent states is studied in the Dicke model and correlated with the dynamics, regular or chaotic, of their classical limit. Analytical expressions for the survival probability, i.e. the probability of finding the system in its initial state at time t, are provided in the regular regions of the model. The results for regular regimes are compared with those of the chaotic ones. It is found that initial coherent states in regular regions have a much longer equilibration time than those located in chaotic regions. The properties of the distributions for the initial coherent states in the Hamiltonian eigenbasis are also studied. It is found that for regular states the components with no negligible contribution are organized in sequences of energy levels distributed according to Gaussian functions. In the case of chaotic coherent states, the energy components do not have a simple structure and the number of participating energy levels is larger than in the regular cases.

arXiv:1711.10987•AIP conference proceedings•Jan 1, 2018•2 citations

Comparative quantum and semiclassical analysis of atom-field systems. I. Density of states and excited-state quantum phase transitions

M. A. Bastarrachea-Magnani, Sergio Lerma-Hernández, Jorge G. Hirsch

We study the nonintegrable Dicke model and its integrable approximation, the Tavis-Cummings model, as functions of both the coupling constant and the excitation energy. Excited-state quantum phase transitions (ESQPT) are found analyzing the density of states in the semiclassical limit and comparing it with numerical results for the quantum case in large Hilbert spaces, taking advantage of efficient methods recently developed. Two different ESQPTs are identified in both models, which are signaled as singularities in the semiclassical density of states; one static ESQPT occurs for any coupling, whereas a dynamic ESQPT is observed only in the superradiant phase. The role of the unstable fixed points of the Hamiltonian semiclassical flux in the occurrence of the ESQPTs is discussed and determined. Numerical evidence is provided that shows that the semiclassical results describe very well the tendency of the quantum energy spectrum for any coupling in both models. Therefore, the semiclassical density of states can be used to study the statistical properties of the fluctuation in the spectra, a study that is presented in a companion paper.

arXiv:1312.2665•Physical Review A•Mar 3, 2014•102 citations
We study the quantum quench dynamics in an extended version of the Dicke model where an additional parameter allows a smooth transition to the integrable Tavis-Cummings regime. We focus on the influence of various quantum phases and excited-state quantum phase transitions (ESQPTs) on the survival probability of the initial state. We show that, depending on the quench protocol, an ESQPT can either stabilize the initial state or, on the contrary, speed up its decay to the equilibrated regime. Quantum chaos smears out the manifestations of ESQPTs in quench dynamics, therefore significant effects can only be observed in integrable or weakly chaotic settings. Similar features are present also in the postquench dynamics of some observables.
We analyze excited-state quantum phase transitions (ESQPTs) in three schematic (integrable and nonintegrable) models describing a single-mode bosonic field coupled to a collection of atoms. It is shown that the presence of the ESQPT in these models affects the quantum relaxation processes following an abrupt quench in the control parameter. Clear-cut evidence of the ESQPT effects is presented in integrable models, while in a nonintegrable model the evidence is blurred due to chaotic behavior of the system in the region around the critical energy.
In this thesis, we explore the Dicke model, well-known for its explanation of the superradiant phase transition and signatures of Classical and Quantum Chaos. We then propose a variational approach to determine the semi-classical (SC) equations of motion, using coherent states. The SC dynamics exhibits signs of classical chaos both with increasing coupling and as the energy of the system is gradually increased, eventually leading to it completely engulfing the 2 dimensional phase space of the pseudospin, which we examine through Poincare sections. We then use numerical diagonalization to study the Quantum Dicke model - it is observed that at and after exactly the critical value of the coupling, the system shows a net macroscopic photon expectation value, and the pseudospin component in the z direction starts to steadily decline - implying a net fraction of the atoms are shifting to the excited state. We then study the dynamics of the Quantum Dicke Hamiltonian using coherent states and compare the expectation values of the dimensional with the classical trajectories from the semi-classical dynamics for stable and chaotic orbits. We then introduce a linear quench which drives the Dicke model across the Superradiant phase transition by changing the coupling strength. The quenched dynamics is simulated using both semi-classical and quantum dynamics - it is seen that dynamically varying quantities are periodically oscillating around their instantaneous steady-state coupling values.
We study the critical behavior of excited states and its relation to order and chaos in the Jaynes-Cummings and Dicke models of quantum optics. We show that both models exhibit a chain of excited-state quantum phase transitions demarcating the upper edge of the superradiant phase. For the Dicke model, the signatures of criticality in excited states are blurred by the onset of quantum chaos. We show that the emergence of quantum chaos is caused by the precursors of the excited-state quantum phase transition.
The quantum dynamics of initial coherent states is studied in the Dicke model and correlated with the dynamics, regular or chaotic, of their classical limit. Analytical expressions for the survival probability, i.e. the probability of finding the system in its initial state at time t, are provided in the regular regions of the model. The results for regular regimes are compared with those of the chaotic ones. It is found that initial coherent states in regular regions have a much longer equilibration time than those located in chaotic regions. The properties of the distributions for the initial coherent states in the Hamiltonian eigenbasis are also studied. It is found that for regular states the components with no negligible contribution are organized in sequences of energy levels distributed according to Gaussian functions. In the case of chaotic coherent states, the energy components do not have a simple structure and the number of participating energy levels is larger than in the regular cases.
We study the nonintegrable Dicke model and its integrable approximation, the Tavis-Cummings model, as functions of both the coupling constant and the excitation energy. Excited-state quantum phase transitions (ESQPT) are found analyzing the density of states in the semiclassical limit and comparing it with numerical results for the quantum case in large Hilbert spaces, taking advantage of efficient methods recently developed. Two different ESQPTs are identified in both models, which are signaled as singularities in the semiclassical density of states; one static ESQPT occurs for any coupling, whereas a dynamic ESQPT is observed only in the superradiant phase. The role of the unstable fixed points of the Hamiltonian semiclassical flux in the occurrence of the ESQPTs is discussed and determined. Numerical evidence is provided that shows that the semiclassical results describe very well the tendency of the quantum energy spectrum for any coupling in both models. Therefore, the semiclassical density of states can be used to study the statistical properties of the fluctuation in the spectra, a study that is presented in a companion paper.