Unidirectional spin transport of a spin-orbit-coupled atomic matter wave using a moving Dirac $\delta$-potential well

We study the transport of a spin-orbit-coupled atomic matter wave using a moving Dirac $\delta$-potential well. In a spin-orbit-coupled system, bound states can be formed in both ground and excited energy levels with a Dirac $\delta$ potential. Because Galilean invariance is broken in a spin-orbit-coupled system, moving of the potential will induce a velocity-dependent effective detuning. This induced detuning breaks the spin symmetry and makes the ground-state transporting channel be spin-$\uparrow$ ($\downarrow$) favored while makes the excited-state transporting channel be spin-$\downarrow$ ($\uparrow$) favored for a positive-direction (negative-direction) transporting. When the $\delta$-potential well moves at a small velocity, both the ground-state and the excited-state channels contribute to the transportation, and thus both the spin components can be efficiently transported. However, when the moving velocity of the $\delta$-potential well exceeds a critical value, the induced detuning is large enough to eliminate the excited bound state, and makes the ground bound state the only transporting channel, in which only the spin-$\uparrow$ ($\downarrow$) component can be efficiently transported in a positive (negative) direction. This work demonstrates a prototype of unidirectional spin transport.