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Soviet Journal of Quantum Electronics

Dicke model for a multicomponent system

Igor K. Kudryavtsev, A N Meleshko, A. S. Shumovskiǐ

Published Nov 30, 1979• 1 citation
Publisher

Abstract

A study is made of a phase transition in a multicomponent system of two-level atoms interacting with a finite set of electromagnetic field modes. It is shown that the coupling between the components increases the temperature of a phase transition to a state characterized by ordering in the atomic subsystem and simultaneous filling of the photon modes.

DOI
10.1070/qe1979v009n11abeh009741

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A study is made of a phase transition in a multicomponent system of two-level atoms interacting with a finite set of electromagnetic field modes. It is shown that the coupling between the components increases the temperature of a phase transition to a state characterized by ordering in the atomic subsystem and simultaneous filling of the photon modes.
The Dicke model describing an ensemble of two-state atoms interacting with a single quantized mode of the electromagnetic field (with omission of the ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{A}}^{2}$ term) exhibits a zero-temperature phase transition at a critical value of the dipole coupling strength. We propose a scheme based on multilevel atoms and cavity-mediated Raman transitions to realize an effective Dicke model operating in the phase transition regime. Optical light from the cavity carries signatures of the critical behavior, which is analyzed for the thermodynamic limit where the number of atoms is very large.
A system of NNN two-level atoms interacting with a quantized field, the so-called Dicke model of superradiance, is studied. By making use of a set of Glauber's coherent states for the field, the free energy of the system is calculated exactly in the thermodynamic limit. The results agree precisely with those obtained by Hepp and Lieb, who studied the same model using a different method. The exhibition of a phase transition of the system is presented mathematically in an elementary manner in our approach. The generalization to the case of finitely many radiation modes is also presented.
An analysis is made of the possibility of a phase transition in a system of two-level atoms interacting via a transverse electromagnetic field. The analysis is based on the total (including the polarization energy) Hamiltonian. It is shown that if allowance is made for the difference between the field acting on an atom and the Maxwellian field in the spectrum of collective (polariton) excitations, soft modes may arise and at a temperature T < T cr a phase transition may occur and a macroscopic polarization may appear at zero frequency.
The dipole-coupled two-level atoms (qubits) in a single-mode resonant cavity are studied by extended bosonic coherent states. The numerical solution is presented. The first-order quantum phase transitions may occur in finite systems, in contrast to the original Dicke model. This system also exhibits a second-order quantum phase transition from the normal to the superradiant phase, as in the original Dicke model. Finite-size scaling for several observables---such as average fidelity susceptibility, order parameter, and concurrence---is performed for different interatomic interactions. The scaling exponents obtained suggest that interatomic interactions do not change the universality class.