Collective Dipole Oscillation of a Spin-Orbit Coupled Bose-Einstein Condensate

We present an experimental study of the collective dipole oscillation of a spin-orbit coupled Bose-Einstein condensate in a harmonic trap. Dynamics of the center-of-mass dipole oscillation is studied in a broad parameter region, as a function of spin-orbit coupling parameters as well as oscillation amplitude. Anharmonic properties beyond effective-mass approximation are revealed, such as amplitude-dependent frequency and finite oscillation frequency at place with divergent effective mass. These anharmonic behaviors agree quantitatively with variational wave-function calculations. Moreover, we experimentally demonstrate a unique feature of spin-orbit coupled system predicted by a sum-rule approach, stating that spin polarization susceptibility--a static physical quantity--can be measured via dynamics of dipole oscillation. The divergence of polarization susceptibility is observed at the quantum phase transition that separates magnetic nonzero-momentum condensate from nonmagnetic zero-momentum phase. The good agreement between the experimental and theoretical results provides a bench mark for recently developed theoretical approaches.