Energy cat states induced by a parity-breaking excited-state quantum phase transition

Abstract

We show that excited-state quantum phase transitions (ESQPTs) in a system in which the parity symemtry has been broken can be used to engineer an energy-cat state -a Schrödinger cat state involving a quantum superposition of both different positions and energies. By means of a generalization of the Rabi model, we show that adding a parity-breaking term annihilates the ground-state quantum phase transition between normal and superradiant phases, and induces the formation of three excited-state phases, all of them identified by means of an observable with two eigenvalues. In one of these phases, level crossings are observed in the thermodynamic limit. We profit from them to separate a wavefunction in two parts: one, with lower energy, trapped within one region of the spectrum, and a second one, with higher energy, trapped within another. Finally, we show that a generalized microcanonical ensemble, including two different average energies, is required to properly describe equilibrium states in this situation. Our results illustrate yet another physical consequence of ESQPTs.

Anharmonicity-induced excited-state quantum phase transition in the symmetric phase of the two-dimensional limit of the vibron model

“…As previously mentioned, the anharmonic 2DVM symmetric phase provides a case in point of the occurrence of an ESQPT without an associated QPT. In systems with more than one control parameter, there are other examples of ESQPTs without an associated QPT that can be traced back to critical points in particular trajectories in the parameter space [80][81][82]. In the present case, as can be seen in the energy functionals in Fig.…”