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We theoretically analyze the effect of parameter fluctuations on thesuperradiance phase transition in a setup where a large number ofsuperconducting qubits are coupled to a single cavity. We include parameterfluctuations that are typical of superconducting architectures, such asfluctuations in qubit gaps, bias points and qubit-cavity coupling strengths. Wefind that the phase transition should occur in this case, although it manifestsitself somewhat differently from the case with no fluctuations. We also findthat fluctuations in the qubit gaps and qubit-cavity coupling strengths do notnecessarily make it more difficult to reach the transition point. Fluctuationsin the bias points, however, increase the coupling strength required to reachthe quantum phase transition point and enter the superradiant phase. Similarly,these fluctuations lower the critical temperature for the thermal phasetransition.

Superradiance phase transition in the presence of parameter fluctuations