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QUANTUM CRITICALITY OF TWO GENERALIZED DICKE MODELS: WITH EITHER QUADRATIC FIELD TERMS OR WITH DIPOLE-DIPOLE INTERACTION

Yueming Wang, Minglong Zhao

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

In this work we analytically derived the critical behavior of zero-temperature quantum phase transition for two generalized Dicke models: one model includes quadratic field terms (the A 2 -term) and the other one has dipole-dipole interaction. It was pointed out that both the A 2 -term and dipole-dipole interaction lead to a corrected position of the critical point, amounting to inducing a shift of radiation field frequency and atomic transition frequency.

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In this work we analytically derived the critical behavior of zero-temperature quantum phase transition for two generalized Dicke models: one model includes quadratic field terms (the A 2 -term) and the other one has dipole-dipole interaction. It was pointed out that both the A 2 -term and dipole-dipole interaction lead to a corrected position of the critical point, amounting to inducing a shift of radiation field frequency and atomic transition frequency.
We consider the full Dicke spin-boson model composed by a single bosonic mode and an ensemble of N identical two-level atoms with different couplings for the resonant and anti-resonant interaction terms, and incorporate a dipole–dipole interaction between the atoms. Assuming that the system is in thermal equilibrium with a reservoir at temperature β −1 , we compute the free energy in the thermodynamic limit N → ∞ in the saddle-point approximation to the path integral and determine the critical temperature for the super-radiant phase transition. In the zero temperature limit, we recover the critical coupling of the quantum phase transition, presented in the literature.
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.
In this paper, we reveal a second-order phase transition for the Dicke model with the dipole–dipole interaction between the atoms. By means of Holstein–Primakoff transformation, the energy spectra for both the normal and superradiant phases are explicitly obtained and therefore the scaling behaviour near the critical transition point can be given clearly. It is also shown that the dipole–dipole interactions between the atoms deeply affect the critical transition point, the ground-state and excitation energies and the scaled atomic inversion in the ground state.
The full Dicke model is composed of a single bosonic mode and an ensemble of NNN identical two-level atoms. In the model, the coupling between the bosonic mode and the atoms generates resonant and nonresonant processes. We also consider a dipole-dipole interaction between the atoms, which is able to generate entangled states in the atomic system. By assuming thermal equilibrium with a reservoir at temperature ${\ensuremath{\beta}}^{\ensuremath{-}1}$, the transition from fluorescent to superradiant phase and the quantum phase transition are investigated. It is shown that the critical behavior of the full Dicke model is not modified by the introduction of the dipole-dipole interaction.
Phase transitions of a generalized Dicke model in the Coulomb gauge-including A(2) terms in the matter-radiation coupling, as well as direct dipole-dipole interaction terms-are studied. After a brief review of previous work on the 'no-go theorem' for phase transitions in the Dicke model, it is shown that a consistent truncation of the radiation modes and of the direct interactions leads to a model that does have a phase transition. When transformed to the electric dipole gauge, such a system takes exactly the form of the original Dicke Hamiltonian, which displays the expected phase transition.