Vestigial Order Melting of a Chiral Atomic Superfluid in a Double-Valley Optical Lattice

Abstract

The interplay of multiple symmetry-breaking channels plays an important role in shaping complex phase diagrams in many-body systems. In multicomponent superfluids, this interplay can generate fluctuation-driven vestigial order relevant to unconventional superconductivity. Here we investigate thermal phase transitions in a Floquet-engineered double-valley band structure realized with ultracold bosons in a shaken optical lattice. The system possesses U(1) and time-reversal $\mathbb{Z}_2$ symmetries, and forms, at low temperature, a chiral superfluid in which Bose-Einstein condensation occurs in a single valley, and the condensate wavefunction develops a real space phase winding. Upon heating, the chiral superfluid melts in two steps: first into a time-reversal-symmetric superfluid and then into a normal phase. By measuring the superfluid and Ising transition temperatures across a range of driving frequencies, we find that the superfluid transition temperature remains higher than the Ising transition temperature throughout the explored regime. Near resonance, the Ising transition temperature is suppressed, whereas the superfluid transition temperature is nearly unchanged; far from resonance, the two transitions merge. These results reveal how thermal and quantum fluctuations govern symmetry breaking in periodically driven quantum many-body systems.