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

Abstract

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.

Delocalization and quantum chaos in atom-field systems

“…Analytical expressions for its eigenenergies have been reported [26][27][28][29][30]. Another important feature in the Hamiltonian is the excited-state quantum phase transitions (ESQPT) [31,32], manifested as a singularity in the level density, order parameters, and wave function properties [33,34]. They could have important effects in decoherence [35] and in the temporal evolution for quantum quenches [36].…”

Quantum Criticality and Dynamical Instability in the Kicked-Top Model

“…In molecular physics, singularities of the density of states (DOS) arise in the vibron model [10], which are closely related to the monodromy in molecular bending degrees of freedom [11]. ESQPTs have been predicted to occur in prominent models of quantum optics such as the Dicke and Jaynes-Cummings models [12,13], too.Despite the striking observation of the QPT in the Dicke and the LMG model [14,15], ESQPTs have so far not been found experimentally for systems different to molecular ones, as the energies at which they occur are difficult to reach with standard techniques. Recently, however, the observation of low-energy singularities of the DOS in twisted graphene layers [16], and monodromy in diverse molecules [11], has opened an increasing interest in the experimental investigation of spectral singularities.…”

“…In molecular physics, singularities of the density of states (DOS) arise in the vibron model [10], which are closely related to the monodromy in molecular bending degrees of freedom [11]. ESQPTs have been predicted to occur in prominent models of quantum optics such as the Dicke and Jaynes-Cummings models [12,13], too.…”

Quantum phase transitions of atom-molecule Bose mixtures in a double-well potential

“…ESQPTs entail dramatic dynamic consequences, like the enhancement of the decoherence if the ESQPT takes place in the environment with which a quantum system interacts [9], the onset of chaos [10], or the emergence of symmetry-breaking equilibrium states after a quench [11]. They appear in models pertaining to different branches of physics, like the interacting boson model (IBM) [12,13], Lipkin-Meshkov-Glick model [14], vibron model [15], Dicke and Jaynes-Cummings models [10,16,17], kicked top [18], and microwave Dirac billiards [19].…”