Stückelberg interferometry using spin-orbit-coupled cold atoms in an optical lattice

Time evolution of spin-orbit-coupled cold atoms in an optical lattice is studied, with a two-band energy spectrum having two avoided crossings. A force is applied such that the atoms experience two consecutive Landau-Zener tunnelings while transversing the avoided crossings. Stuckelberg interference arises from the phase accumulated during the adiabatic evolution between the two tunnelings. This phase is gauge field dependent and thus provides new opportunities to measure the synthetic gauge field, which is verified via calculation of spin transition probabilities after a double-passage process. Time-dependent and time-averaged spin probabilities are derived, in which resonances are found. We also demonstrate chiral Bloch oscillation and rich spin-momentum locking behavior in this system.