there is no quantum phase transition at all; the system always lies in the superradiant phase. We derive an approximate expression for the quantum phase transition in the presence of disorder in terms of

\ensuremath{\mu}

and

\ensuremath{\sigma}

, which we numerically verify. Studying the thermal phase transition in the disordered Dicke model, we obtain an analytical expression for the critical temperature in terms of the mean and standard deviation of the coupling strength. We observe that, even when the mean of the coupling strength is zero, there is a finite temperature transition if the standard deviation of the coupling is sufficiently high. Disordered couplings in the Dicke model will exist in quantum dot superlattices, and we also sketch how they can be engineered and controlled with ultracold atoms or molecules in a cavity.

DOI: 10.1103/physreva.109.013715

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The Dicke model generalized to the case where the dependence of the coupling constant on individual atoms is taken into account is investigated. It is shown that the generalized Dicke model exhibits a quantum phase transition from the normal phase to the superradiant phase in the thermodynamic limit, as well as the standard Dicke model. The mean photon number, the atomic inversion, the lowest excitation energy, and the entanglement entropy between the field and the atoms are evaluated analytically or numerically, and the critical behavior is examined. As a result, it turns out that the critical behavior in the generalized model is essentially the same as that in the standard model. This implies universality in the Dicke model.The Dicke model generalized to the case where the dependence of the coupling constant on individual atoms is taken into account is investigated. It is shown that the generalized Dicke model exhibits a quantum phase transition from the normal phase to the superradiant phase in the thermodynamic limit, as well as the standard Dicke model. The mean photon number, the atomic inversion, the lowest excitation energy, and the entanglement entropy between the field and the atoms are evaluated analytically or numerically, and the critical behavior is examined. As a result, it turns out that the critical behavior in the generalized model is essentially the same as that in the standard model. This implies universality in the Dicke model.

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\ensuremath{\sigma}

of the coupling strength gradually increases, the critical value of the mean coupling strength

\ensuremath{\mu}

gradually decreases, and after a certain

\ensuremath{\sigma}

\ensuremath{\mu}

and

\ensuremath{\sigma}

σ

of the coupling strength gradually increases, the critical value of the mean coupling strength

μ

gradually decreases and after a certain

σ

there is no quantum phase transition at all; the system always lies in the super-radiant phase. We derive an approximate expression for the quantum phase transition in the presence of disorder in terms of

μ

and

σ

, which we numerically verify. Studying the thermal phase transition in the disordered Dicke model, we obtain an analytical expression for the critical temperature in terms of the mean and standard deviation of the coupling strength. We observe that even when the mean of the coupling strength is zero, there is a finite temperature transition if the standard deviation of the coupling is sufficiently high. Disordered couplings in the Dicke model will exist in quantum dot superlattices, and we also sketch how they can be engineered and controlled with ultracold atoms or molecules in a cavity.