Polaritons are the collective excitations of many atoms dressed by resonant photons, which can be used toexplain the slow light propagation with the mechanism of electromagnetically induced transparency. As qua-siparticles, these collective excitations possess the typical feature of the matter particles, which can be reflectedand deflected by the inhomogeneous medium in its spatial motion with some velocity. In this paper we developa quantum theory to systematically describe the spatial motion of polaritons in inhomogeneous magnetic andoptical fields. This theoretical approach treats these quasiparticles through an effective Schrodinger equationwith anisotropic dispersion that the longitudinal motion is similar to an ultrarelativistic motion of a "slow lightvelocity" while the transverse motion is of nonrelativity with certain effective mass. We find that, after passingthrough the EIT medium, the light ray bends due to the spatial-dependent profile of external field. Thisphenomenon explicitly demonstrates the exotic corpuscular and anisotropic property of polaritons.
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