Stern-Gerlach Effect of Weak-Light Ultraslow Vector Solitons

We propose a scheme to exhibit Stern-Gerlach (SG) deflection of high-dimensional vector optical soliton (VOS) at weak-light level in a cold atomic gas via electromagnetically induced transparency. We show that the propagating velocity and generation power of such VOS can be reduced to $10^{-6}\,\,c$ ($c$ is light speed in vacuum) and lowered to magnitude of nanowatt, respectively. The stabilization of the VOS may be realized by using an optical lattice formed by a far-detuned laser field, and its trajectory can be deflected significantly by using a SG magnetic field. Deflection angle of the VOS can be of magnitude of $10^{-3}$ rad when propagating several millimeters. Different from atomic SG deflection, deflection angle of the VOS can be distinct for different polarization components and can be manipulated in a controllable way. The results obtained can be described in terms of a SG effect for the VOS with quasispin and effective magnetic moment.