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Physics Letters A

Instability and non-equilibrium phase transition in the Dicke Hamiltonian

M.A. Panzarella, Franco Persico

Published Jan 1, 1983• 0 citations
Publisher
DOI
10.1016/0375-9601(83)90801-0

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We study dynamical phase transitions in the generalized dissipative Dicke model in an array of trapped Rydberg ions, where their density-density interactions compete with the collective spin-phonon coupling, laser driving and dissipation. This setting offers a versatile approach to study equilibrium as well as non-equilibrium many-body phenomena, as parameters, such as the Ising interaction, laser-ion and spin-phonon coupling can be tuned. Through analyzing the mean-field phase diagram, we find a variety of distinct phases and the emergence of a tricritical point that are sensitively dependent of the interaction between Rydberg ions. We then study the quantum dynamics for a finite system size and characterize parameter dependent dynamics using the spin average, entropy, and Loschmidt echo. Distinctive signatures of the dynamical phases, such as slow relaxation and metastability, arise near the phase transition. This analysis predicts rich quantum dynamics of the finite system that link to the non-equilibrium mean-field phases. Our study widens the exploration of collective and non-equilibrium phases in Dicke models, and reveals that the Rydberg ion interaction drastically affects the phase diagram and dynamics.
The thermodynamic equilibrium properties of the Dicke Hamiltonian for a collection of spin- 1 / 2 particles interacting via magnetic dipole interaction with a single mode of the radiation field and with each other by spin-spin interaction are analysed and the conditions for the existence of a super-radiant phase transition are derived. It is shown, using the approximate long-range spin-spin interaction (MI), in the Dicke Hamiltonian, that the conditions for the existence of the super-radiant phase transition are invariant with respect to isotropic MI whether or not the A 2 term is included.
It is shown that the rotating wave approximation in the minimal coupling Hamiltonian with the A 2 term leads to an incorrect energy spectrum of the polariton mode: in particular, to a spurious polariton instability which should not occur for a photon-matter system consisting of radiation and atoms without the Coulomb interaction. Thus the counter-rotating term in the presence of the A 2 term plays a crucial role in the instability property of the system. The super-radiant phase transition in the Dicke model is shown to be accompanied by polariton instability, and therefore by instability of the ground state of the photon-matter system. The rotating wave approximation, as well as the neglect of the A 2 term, should therefore not be made for the study of the thermodynamic phase transition and instability properties of the ground state of the system.