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.

DOI: 10.48550/arxiv.2308.12996

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σ

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

μ

gradually decreases and after a certain

σ

μ

and

σ