We introduce and study the disordered Dicke model in which the spin-boson
couplings are drawn from a random distribution with some finite width.
Regarding the quantum phase transition we show that when the standard deviation
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.Comment: 11 pages, 6 figure