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Dirac delta-function potential is widely studied in quantum mechanics becauseit usually can be exactly solved and at the same time is useful in modelingvarious physical systems. Here we study a system of delta-potential trappedspinorbit coupled cold atoms. The spin-orbit coupled atomic matter wave has twokinds of evanescent modes, one of which has pure imaginary wavevector and is anordinary evanescent wave; while the other with a complex number wave vector isrecognized as oscillating evanescent wave. We identified the eigenenergyspectra and the existence of bound states in this system. The bound states canbe constructed analytically using the two kinds of evanescent modes and wefound that they exhibit typical features of stripe phase, separated phase orzero-momentum phase. In addition to that, the properties of semi-bound statesare also discussed, which is a localized wave packet on a plane wavebackground.

Bound states of spin-orbit coupled cold atoms in a Dirac delta-function potential