Order parameters in Dicke model

  • S. F. Lyagushyn Oles Honchar Dnipro National University, Dnipro, Ukraine
  • A. I. Sokolovsky Oles Honchar Dnipro National University, Dnipro, Ukraine
Keywords: ordering, phase transition, Jaynes–Cummings model, Dicke superradiance, quasiaverages, macroscopic dipole moment


Dicke model provides describing the superradiance effect when the spontaneous emission of a great number of excited two-level atoms is running in a correlated way due to their interaction via field. The process is identical to a giant dipole emission. Since the ordering takes place, it is interesting to study the possibility for using the terms of phase transition theory in such physical situation. Equilibrium properties of Dicke type models were studied for a long time because of their relevance for explaining some phenomena in matter-field interaction. The existence of an ordered phase in the emitter subsystem together with macroscopic photon mode filling is established, wherein the correct solution requires the Bogolyubov concept of quasiaverages to exclude the phase uncertainty of quasispin component structures <R+> and <R-> (for the concentrated model). In this paper, the behavior of similar order parameters for the non-equilibrium process description is analyzed and using the order parameter <R+R-> associated with the squared electric dipole moment of the emitter complex is substantiated. Such fact justifies <R3> application in the literature devoted to the superradiance theory. The situation with quasiaverages is compared with the problem of uniformity breaking in the numerical modeling.