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The spin-orbit-coupled (SOC) ultracold atomic gases provide unique opportunities for exploring exotic quantum phases and introduce new capabilities into the quantum simulation. In this paper, we study the coherent control of spin states in SOC Bose–Einstein condensate (BEC) by exploiting and implementing the general concept of Landau–Zener–Stüeckelberg–Majorana (LZSM) interference. For a SOC BEC, the Landau–Zener (LZ) transition between the dressed eigenlevels occurs as the BEC is accelerated through the SOC-avoided crossing, which corresponds to a breakdown of the spin momentum locking. In our scheme, two LZ pulses are separated by an intermediate holding period of variable duration. The nice LZSM interference patterns can be generated and controlled by controlling several parameters, corresponding to coherent control of the spin state of the SOC BEC. In particular, the destructive and constructive patterns of LZSM interference are observed and well explained through analytical analysis. Our results suggest a potential application of the LZSM interferometry in calibrating the spin states of a SOC BEC. [ABSTRACT FROM AUTHOR]

We investigate the tunneling dynamics of the Fermi gases in an optical lattice in the Bose–Einstein condensation (BEC) regime. The three critical scattering lengths and the system energies are found in different cases of Josephson oscillation (JO), oscillating-phase-type self-trapping (OPTST), running-phase-type self-trapping (RPTST), and self-trapping (ST). It is found that the s-wave scattering lengths have a crucial role on the tunneling dynamics. By adjusting the scattering length in the adiabatic condition, the transition probability changes with the adiabatic periodicity and a rectangular periodic pattern emerges. The periodicity of the rectangular wave depends on the system parameters such as the periodicity of the adjustable parameter, the s-wave scattering length. [ABSTRACT FROM AUTHOR]