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

TL;DR

This paper derives exact solutions for strongly interacting two-level ultracold gases in waveguides, revealing quantum phase transitions and potential superradiance when coupled to a quantized electromagnetic field.

Contribution

It introduces a generalized Fermi-Bose mapping for these models and explores their phase transitions, including effects of electromagnetic coupling.

Findings

Identification of quantum phase transitions in the models.

Existence of a possible thermal phase transition with electromagnetic coupling.

Exact ground state solutions for generalized models.

Abstract

A generalized Fermi-Bose mapping method is used to determine the exact ground states of six models of strongly interacting ultracold gases of two-level atoms in tight waveguides, which are generalizations of the Tonks-Girardeau (TG) gas (1D Bose gas with point hard cores) and fermionic Tonks-Girardeau (FTG) gas (1D spin-aligned Fermi gas with infinitely strong zero-range attractions). Three of these models exhibit a quantum phase transition in the presence of an external magnetic field, associated with a cooperative ground state rearrangement wherein Fermi energy is traded for internal excitation energy. After investigation of these models in the absence of an electromagnetic field, one is generalized to include resonant interactions with a single photon mode, leading to a possible thermal phase transition associated with Dicke superradiance.