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A generalized Fermi-Bose mapping method is used to determine the exact groundstates of six models of strongly interacting ultracold gases of two-level atomsin tight waveguides, which are generalizations of the Tonks-Girardeau (TG) gas(1D Bose gas with point hard cores) and fermionic Tonks-Girardeau (FTG) gas (1Dspin-aligned Fermi gas with infinitely strong zero-range attractions). Three ofthese models exhibit a quantum phase transition in the presence of an externalmagnetic field, associated with a cooperative ground state rearrangementwherein Fermi energy is traded for internal excitation energy. Afterinvestigation of these models in the absence of an electromagnetic field, oneis generalized to include resonant interactions with a single photon mode,leading to a possible thermal phase transition associated with Dickesuperradiance.

Soluble Models of Strongly Interacting Two-level Ultracold Gases in Tight Waveguides with Coupling to the Quantized Electromagnetic Field