Topological properties of the spin-1/2 hourglass Creutz-like ladder model assisted by an optical cavity

In the present paper, we investigate a one-dimensional spinful degenerate Fermi gas coupled to an optical cavity, thereby realizing a cavity-assisted hourglass Creutz-like ladder model characterized by a Peierls-like instability between identical spins and a modulated spin-orbit coupling. Furthermore, we demonstrate that flat-band states induced by the optical cavity emerge through appropriate detuning of the parameters within our system. We perform a comprehensive analysis for the effects of cavity-assisted Raman processes that involve either distinct or identical spins on the topological superradiant properties. Notably, our findings reveal that our system exhibits rich nontrivial topological superradiant characteristics by varying different coupling strengths. Specifically, we identify a topological superradiant phase with winding numbers two and four corresponding to degenerate edge states. Additionally, we discuss various quantum phases and provide the corresponding steady-state phase diagram. Finally, we briefly outline parameter estimation techniques and address potential experimental observations related to these predicted quantum phases and their associated phase diagrams.