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By developing a hydrodynamic formalism, we investigate the expansion dynamicsof the single-minimum phase of a binary spin-orbit coupled Bose-Einsteincondensate, after releasing from an external harmonic trap. We find that theexpansion of the condensate along the direction of the spin-orbit coupling isdramatically slowed down near the transition between the single-minimum phaseand the plane-wave phase. Such a slow expansion, resembling a form of aneffective localization, is due to the quenching of the superfluid motion whichresults in a strong increase of the effective mass. In the single-minimum phasethe anisotropic expansion of the Bose gas, which is spin balanced atequilibrium, is accompanied by the emergence of a local spin polarization. Ouranalytic scaling solutions emerging from hydrodynamic picture are compared witha full numerical simulation based on the coupled Gross-Pitaevskii equations.

Spin-orbit-coupling induced localization in the expansion of an interacting Bose-Einstein condensate