Metamorphosis of Goldstone and soft fluctuation modes in polariton lasers

For a driven-dissipative quantum many-body system prepared in a spontaneous broken-symmetry steady state, in addition to the Goldstone mode, the soft fluctuation modes provide important insight into the system's dynamics. Using a microscopic polariton laser theory, we find a rich transformation behavior of discrete and continuum soft modes in a two parameter (pump density and cavity dissipation rate) space. Our theory yields a unified picture of a variety of seemingly disconnected physical concepts including Mott transition, Mollow spectra or relaxation oscillations, polaritonic Bardeen-Cooper-Schrieffer gaps, and Goldstone companion modes. In particular, transformation paths connect the Goldstone companion modes with the Mollow analog modes across a line of exceptional points.