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. 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.Many interesting quantum phases can emerge in solid state materials when electrons are placed in a strong magnetic field or possess strong spin-orbit (SO) coupling, such as the fractional quantum Hall effect [1] and the topological insulator [2]. In cold atom systems, albeit neutral atoms have neither charges nor SO coupling, the recent exciting experimental progress demonstrates that artificial gauge potentials can be synthesized in laboratory by laser control technique [3][4][5][6][7][8][9][10]. Synthetic gauge potential is becoming a powerful tool for simulating real materials with cold atoms. Moreover, the system of SO coupled bosons does not have an analogy in conventional condensed matter systems, and can exhibit many novel phases [11] such as striped superfluid phase [12,13] and half vortex phase [14][15][16][17].Collective excitations play an important role in studying physical properties of trapped atomic Bose-Einstein condensates (BEC) and degenerate Fermi gases. Collective dipole oscillation is a center-of-mass motion of all atoms. For a conventional condensate, the dipole oscillation is trivial: the frequency is just the harmonictrap frequency, independent of oscillation amplitude and interatomic interaction. This is known as Kohn theorem [18,19]. For a SO coupled condensate, however, it was found [4] that the dipole-oscillation frequency deviates from the trap frequency and the experimental data thereby can be explained by effective-mass approximation. Recently, much theoretical effort has been taken to understand dynamics of a SO coupled BEC [20][21][22][23][24][25], and many predicted unconventional properties remain to be experimentally explored. In particular, the so-called sum-rule approach predicts [25] a unique feature of SO coupled condensate: spin polarization susceptibility-a static physical quantity-can be measured via dynamics of dipole oscillatio...

Topological superfluids with finite-momentum pairing and Majorana fermions

“…The pseudospins of atoms are defined through atomic hyperfine ground states. By transferring Raman photons between two hyperfine ground states, an effective 1D SO coupling (used below) has been created in experiments for both bosonic and fermionic atoms [24][25][26][27][28] , where the effective in-plane and outof-plane Zeeman fields can be tuned independently by varying the detuning and intensity of the Raman coupling lasers. The schemes for the realization of 2D Rashba SO coupling are similar, but involve more laser beams, as proposed in several different theoretical schemes [40][41][42] .…”

“…Here we propose a possible platform for the realization of topological FF superfluids using two-dimensional (2D) or one-dimensional (1D) spin-orbit (SO)-coupled degenerate Fermi gases subject to in-plane and out-of-plane Zeeman fields. Recently, the SO coupling and Zeeman fields for cold atoms have already been realized in experiments [24][25][26][27][28] , which provide a completely new avenue for studying topological superfluid physics. It is known that SOcoupled degenerate Fermi gases with an out-of-plane Zeeman field support MFs with zero total momentum pairing [29][30][31][32] .…”

Measurement of collective excitations in a spin-orbit-coupled Bose-Einstein condensate

“…In cold atomic gases, spin-orbit coupling can be implemented by Raman dressing of two or more atomic hyperfine states, which play the role of different (pseudo-)spins. The Raman lasers are arranged in such a way that a Raman transition between the states is accompanied by a change of momentum [6][7][8][9][10][11]. Since the Raman coupling strength and the detuning from the Raman resonance can be independently adjusted in an experiment, this provides a very flexible platform to engineer interesting dispersion relations and test spin-orbit coupled physics (for a review, see, e.g., [12][13][14][15]).…”

Topological Fulde–Ferrell–Larkin–Ovchinnikov states in spin–orbit-coupled Fermi gases

“…Recently, evidence for the FFLO superfluid has been reported in quasi-one-dimensional geometry at Rice Univeristy 13 . Meanwhile, the realization of synthetic SOC adds another important piece to the already versatile toolbox of controllability in cold atoms [14][15][16][17] . By Ramancoupling two hyperfine states in the ground state manifold of alkali atoms, experimentalists have implemented an equal mixture of Rashba and Dresselhaus SOC with both out-of-plane and in-plane effective Zeeman fields.…”