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Physical Review A

Superradiant phase transition in the Dicke Hamiltonian

William R. Mallory

Published Mar 1, 1975• 9 citations
Publisher

Abstract

The condition for a superradiant phase transition to occur in the Dicke model is shown to be a condition on the atomic density. The transition can only occur for high densities.Received 10 December 1974DOI:https://doi.org/10.1103/PhysRevA.11.1088©1975 American Physical Society

DOI
10.1103/physreva.11.1088

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The condition for a superradiant phase transition to occur in the Dicke model is shown to be a condition on the atomic density. The transition can only occur for high densities.Received 10 December 1974DOI:https://doi.org/10.1103/PhysRevA.11.1088©1975 American Physical Society
We investigate the possibility of a Dicke-type superradiant phase transition of an atomic gas with an extended model which takes into account the short-range depolarizing interaction between atoms that approach each other as close as the atomic size scale, which interaction appears in a regularized electric-dipole picture of the QED of atoms. By using a mean-field model, we find that a critical density does indeed exist, though the atom-atom contact interaction shifts it to a higher value than that from the bare Dicke model.
The occurrence of a second-order quantum phase transition in the Dicke model is a well-established feature. On the contrary, a comprehensive understanding of the corresponding open system, particularly in the proximity of the critical point, remains elusive. When approaching the critical point, the system inevitably enters first the system-bath ultrastrong coupling regime and finally the deepstrong coupling regime, causing the failure of usual approximations adopted to describe open quantum systems. We study the interaction of the Dicke model with bosonic bath fields in the absence of additional approximations, which usually relies on the weakness of the system-bath coupling. We find that the critical point is not affected by the interaction with the environment. Moreover, the interaction with the environment is not able to affect the system ground-state condensates in the superradiant phase, whereas the bath fields are i n f e c t e d by the system and acquire macroscopic occupations. The obtained reflection spectra display lineshapes which become increasingly asymmetric, both in the normal and superradiant phases, when approaching the critical point.