Quantum phase transitions in driven Fock-state lattices with synthetic gauge fields

Quantum phase transitions (QPTs) typically emerge in the thermodynamic limit, yet a single-atom QPT can arise when it is coupled to a coherently driven cavity, which provides a simple and unique platform to engineer quantum states with quantum criticality. In this driven Jaynes-Cummings (JC) model, the cavity field becomes squeezed near the critical point. However, vanishing energy gaps at the critical points lead to nonadiabaticity, hindering the practical realization of squeezing. In this work, we introduce a spin-dependent cavity drive, which induces a synthetic gauge field in the Fock-state lattice and enriches the phase diagram of the driven JC model. Remarkably, the energy spectrum can remain discrete for all driving strengths, allowing an adiabatic preparation of squeezed states with robust energy gaps. Moreover, we identify a topological phase transition characterized by projected winding numbers in the presence of broken chiral symmetry. Our results unveil topology and QPTs in a quantized light-matter system and offer a robust strategy for realizing squeezed states.