a Study of the Dicke Superradiant Phase Transition and the Development of a Density Operator Formalism for Phase States.

H. J. Carmichael, Crispin W. Gardiner, Daniel F. Walls

Klaus Hepp, Élliott H. Lieb

William R. Mallory

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

Alexandre Baksic, Pierre Nataf, Cristiano Ciuti

Peng-Fei Wei, Zhihai Wang

The emergence of multiple superradiant phases in Dicke lattice models has attracted considerable attention in the quantum optics community. However, a unified understanding of the origin of multistability and its relation to different superradiant phases is still lacking. Here, we develop a configuration-based understanding to classify the superradiant phases in Dicke lattices. We show that photon hopping naturally organizes the possible superradiant configurations according to the lattice symmetry, providing a unified interpretation of the nonequilibrium phase diagram and the emergence of multistability. For the dissipative four-site Dicke lattice, we obtain the complete phase diagram and identify the coexistence of up to four stable superradiant phases. The proposed classification is further extended to five- and six-site lattices. Moreover, we demonstrate that the same configuration-based understanding also applies to the closed Dicke lattice, where the ground state uniquely selects one of the allowed configurations. Finally, we show that different configurations may belong to either same or distinct nonequilibrium universality classes in the dissipative Dicke lattice, while they share the same equilibrium universality class in the closed Dicke lattice. Our results provide a unified picture for understanding equilibrium and nonequilibrium superradiant phase transitions in Dicke lattices.

Anqi Mu, Nathan Ng, Andrew J. Millis +1 more

We present a density matrix based time dependent projection operator formalism to calculate the beyond mean-field dynamics of systems with non-Markovian local baths and one-to-all interactions. Such models encapsulate the physics of condensed phase systems immersed in optical cavities. We use this method, combined with tensor network influence functionals, to study the dynamics of the Dicke model coupled to non-Markovian local dephasing baths at zero temperature, which has a superradiant phase transition in the mean-field limit. The method corrects a spurious initial state dependence found in the mean-field dynamics and describes the emergence of new time scales which are absent in the mean-field dynamics. Our formalism, based on density matrices, is applicable to other quantum optical systems with one-to-all interactions at finite temperatures.