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Recent experiments on $p$-orbital atomic bosons have suggested the emergenceof a spectacular ultracold superfluid with staggered orbital currents inoptical lattices. This raises fundamental questions like the effects ofcollective thermal fluctuations, and how to directly observe such chiral order.Here, we show via Monte Carlo simulations that thermal fluctuations destroythis superfluid in an unexpected two-step process, unveiling an intermediatenormal phase with spontaneously broken time-reversal symmetry, dubbed "chiralBose liquid". For integer fillings ($n\geq 2$) in the chiral Mott regime,thermal fluctuations are captured by an effective orbital Ising model, andOnsager's powerful exact solution is adopted to determine the transition fromthis intermediate liquid to the para-orbital normal phase at high temperature.A suitable lattice quench is designed to convert the staggered angularmomentum, previously thought by experts difficult to directly probe, intocoherent orbital oscillations, providing a smoking-gun signature of chiralorder.

Formation and detection of a chiral orbital Bose liquid in an optical lattice