title: Collective dipole oscillations of a spin-orbit coupled Bose-Einstein condensate.
abstract: In this Letter, we present an experimental study of the collective dipole oscillation of a spin-orbit coupled Bose-Einstein condensate in a harmonic trap. The 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 the oscillation amplitude. The anharmonic properties beyond the effective-mass approximation are revealed, such as the amplitude-dependent frequency and finite oscillation frequency at a place with a divergent effective mass. These anharmonic behaviors agree quantitatively with variational wave-function calculations. Moreover, we experimentally demonstrate a unique feature of the spin-orbit coupled system predicted by a sum-rule approach, stating that spin polarization susceptibility--a static physical quantity--can be measured via the dynamics of dipole oscillation. The divergence of polarization susceptibility is observed at the quantum phase transition that separates the magnetic nonzero-momentum condensate from the nonmagnetic zero-momentum phase. The good agreement between the experimental and theoretical results provides a benchmark for recently developed theoretical approaches.
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230027, People's Republic of China.
authors.forename: Jin-Yi
authors.initials: JY
authors.lastname: Zhang
authors.forename: Si-Cong
authors.initials: SC
authors.lastname: Ji
authors.forename: Zhu
authors.initials: Z
authors.lastname: Chen
authors.forename: Long
authors.initials: L
authors.lastname: Zhang
authors.forename: Zhi-Dong
authors.initials: ZD
authors.lastname: Du
authors.forename: Bo
authors.initials: B
authors.lastname: Yan
authors.forename: Ge-Sheng
authors.initials: GS
authors.lastname: Pan
authors.forename: Bo
authors.initials: B
authors.lastname: Zhao
authors.forename: You-Jin
authors.initials: YJ
authors.lastname: Deng
authors.forename: Hui
authors.initials: H
authors.lastname: Zhai
authors.forename: Shuai
authors.initials: S
authors.lastname: Chen
authors.forename: Jian-Wei
authors.initials: JW
authors.lastname: Pan