Superradiance phase transition in the presence of parameter fluctuations

One of the remarkable phenomena in the study of light-matter
interaction under strong-coupling conditions is the possibility of a
phase transition to a superradiant phase, where the atoms and light
become strongly correlated even in the ground state. This phase
transition has generally been studied under the assumption of
identical atoms. We theoretically analyze the effect of parameter
fluctuations on the superradiance phase transition in a cavity quantum
electrodynamics setup with many emitters (or qubits) coupled to a single cavity
[1]. We include parameter fluctuations qubit gaps,
bias points, and qubit-cavity coupling strengths. We find that the
phase transition should occur in this case, although it manifests
itself differently from the case with no fluctuations. We
also find that fluctuations in the qubit gaps and qubit-cavity
coupling strengths do not make it more difficult to reach
the transition point. Fluctuations in the bias points, however,
increase the coupling strength required to reach the quantum phase
transition point and enter the superradiant phase. Similarly, these
fluctuations lower the critical temperature for the thermal phase
transition. [1] S. Ashhab and K. Semba, Phys. Rev. A 95, 053833 (2017).