Quantum phase crossovers with finite atom number in the Dicke model
Jorge G. Hirsch, Octavio Castaños, Eduardo Nahmad-Achar, Ramón López–Peña · Physica Scripta · 2013
Two-level atoms interacting with a one-mode cavity field at zero temperature have order parameters which reflect the presence of a quantum phase transition at a critical value of the atom–cavity coupling strength. Two popular examples are the number of photons inside the cavity and the number of excited atoms. Coherent states provide a mean field description, which becomes exact in the thermodynamic limit. Employing symmetry-adapted (SA) SU (2) coherent states the quantum crossover, precursor of the critical behavior, can be described for a finite number of atoms. A variation after projection treatment, involving a numerical minimization of the SA energy surface, associates the quantum crossover with a discontinuity in the order parameters, which originates from competition between two local minima in the SA energy surface. Although this discontinuity is not present in finite systems, it provides a good description of 1/ N effects in the observables.