No singularities in observables at the phase transition in the Dicke model

Journal Article · Sun May 15 04:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.051601· OSTI ID:21546680

Castanos, O; Nahmad-Achar, E; Lopez-Pena, R; Hirsch, J G ^[1]

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1. Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-543, Mexico D. F., C.P. 04510 (Mexico)

The Dicke Hamiltonian describes the simplest quantum system with atoms interacting with photons: N two-level atoms inside a perfectly reflecting cavity, which allows only one electromagnetic mode. It has also been successfully employed to describe superconducting circuits that behave as artificial atoms coupled to a resonator. The system exhibits a transition to a superradiant phase at zero temperature. When the interaction strength reaches its critical value, both the number of photons and atoms in excited states in the cavity, together with their fluctuations, exhibit a sudden increase from zero. By employing symmetry-adapted coherent states, it is shown that these properties scale with the number of atoms, their reported divergences at the critical point represent the limit when this number goes to infinity, and, in this limit, they remain divergent in the superradiant phase. Analytical expressions are presented for all observables of interest, for any number of atoms. Comparisons with exact numerical solutions strongly support the results.

• OSTI ID: 21546680
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 5 Vol. 83; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANNIHILATION OPERATORS
ATOMS
BOSONS
CAVITIES
COMPARATIVE EVALUATIONS
EIGENSTATES
ELECTRONIC EQUIPMENT
ELEMENTARY PARTICLES
ENERGY LEVELS
EQUIPMENT
EVALUATION
EXCITED STATES
FLUCTUATIONS
HAMILTONIANS
INTERACTIONS
MASSLESS PARTICLES
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
NUMERICAL SOLUTION
PHASE TRANSFORMATIONS
PHOTONS
QUANTUM OPERATORS
RESONATORS
SINGULARITY
VARIATIONS