No singularities in observables at the phase transition in the Dicke model
- 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, Vol. 83, Issue 5; Other Information: DOI: 10.1103/PhysRevA.83.051601; (c) 2011 American Institute of Physics; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
ANNIHILATION OPERATORS
ATOMS
CAVITIES
COMPARATIVE EVALUATIONS
EIGENSTATES
EXCITED STATES
FLUCTUATIONS
HAMILTONIANS
INTERACTIONS
NUMERICAL SOLUTION
PHASE TRANSFORMATIONS
PHOTONS
RESONATORS
SINGULARITY
BOSONS
ELECTRONIC EQUIPMENT
ELEMENTARY PARTICLES
ENERGY LEVELS
EQUIPMENT
EVALUATION
MASSLESS PARTICLES
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
QUANTUM OPERATORS
VARIATIONS