Macroscopic Quantum States and Quantum Phase Transition in Dicke Models of Arbitrary Atom-Number

TL;DR

This paper analytically investigates the energy spectrum and quantum phase transition in Dicke models with arbitrary atom numbers, revealing macroscopic quantum states and second-order phase transitions beyond the thermodynamic limit.

Contribution

It provides an analytical approach to the Dicke Hamiltonian for any atom number, identifying macroscopic quantum states and demonstrating quantum phase transitions without requiring infinite atoms.

Findings

Ground-state energies match various approaches

Models exhibit second-order quantum phase transition at zero temperature

Geometric phase shows no singularity at critical point

Abstract

The energy spectrum of Dicke Hamiltonians with and without the rotating wave approximation for arbitrary atom-number is obtained analytically with the variational method, in which the effective pseudo-spin Hamiltonian resulted from the expectation value in the boson-field coherent state is diagonalized by the spin-coherent-state transformation. In addition to the ground-state energy an excited macroscopic quantum-state is found corresponding to the south-and-north-pole gauges of the spin-coherent states respectively. Our results of ground-state energies in exact agreement with various approaches show that these models exhibit a zero-temperature quantum phase transition of second-order for any number of atoms, which however was commonly considered as a phenomenon of the thermodynamic limit with the atom-number tending to infinite. The critical behavior of geometric phase is analyzed, which displays no singularity at the critical point.