Observation ofZitterbewegungin a spin-orbit-coupled Bose-Einstein condensate

Abstract

Spin-orbit coupled ultra-cold atoms provide an intriguing new avenue for the study of rich spin dynamics in superfluids. In this Letter, we observe Zitterbewegung, the simultaneous velocity (thus position) and spin oscillations, of neutral atoms between two spin-orbit coupled bands in a Bose-Einstein condensate (BEC) through sudden quantum quenches of the Hamiltonian. The observed Zitterbewegung oscillations are perfect on a short time scale but gradually damp out on a long time scale, followed by sudden and strong heating of the BEC. As an application, we also demonstrate how Zitterbewegung oscillations can be exploited to populate the upper spin-orbit band, and observe a subsequent dipole motion. Our experimental results are corroborated by a theoretical and numerical analysis and showcase the great flexibility that ultra-cold atoms provide for investigating rich spin dynamics in superfluids.PACS numbers: 67.85. De, 03.75.Kk, 67.85.Fg Introduction.-The Zitterbewegung (ZB) oscillation, first predicted by Schrödinger in 1930 [1] for relativistic Dirac electrons, describes the fast oscillation or trembling motion of electrons arising from the interference between particle and hole components of Dirac spinors. Although fundamentally important, the ZB oscillation is difficult to observe in real particles. In the past eight decades, analogs of the ZB oscillation have been predicted to exist in various physical systems [2-8], ranging from solid state (e.g., semiconductor quantum wells) to trapped cold atoms, but experimentally a ZB analog has only recently been observed using trapped ions as a quantum emulator of the Dirac equation [9]. A crucial ingredient for the ZB oscillation is the coupling between spin and linear momentum of particles, leading to simultaneous velocity and position oscillations accompanying the spin oscillation, which distinguishes ZB from Rabi oscillations where spin oscillations between two bands do not induce velocity and position oscillations. * These authors contributed equally to this work †

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] .…”

Harmonically trapped two-atom systems: Interplay of short-ranges-wave interaction and spin-orbit coupling

“…To date, spin-orbit coupling terms (although not of Rashba type) have been realized using 87 Rb, 7 Li and 40 K. In 87 Rb, the spin-up and spin-down states are commonly identified with the |F, M F = |1, 0 and |1, −1 states [5,9,10]. The corresponding scattering lengths are a ↑↑ = 100.86a 0 , a ↓↓ = 100.40a 0 and a ↑↓ = 100.41a 0 , where a 0 is the Bohr radius [43] (implying ζ = 0.9954 and η = 0.9955), and Feshbach resonances do not exist.…”

“…By now, the effect of the spin-orbit coupling (or more precisely, spin-momentum coupling) has been investigated for bosonic and fermionic species [5][6][7][8][9][10][11]. The effect of the spin-orbit coupling has been investigated away and near an s-wave FanoFeshbach resonance [7,8].…”

“…The effect of the spin-orbit coupling has been investigated away and near an s-wave FanoFeshbach resonance [7,8]. A variety of intriguing phenomena such as non-equilibrium dynamics [9,10], the spin-orbit coupling assisted formation of molecules [7], and the engineering of band structures [11] have been investigated. At the mean-field level, spin-orbit coupled gases exhibit rich phase diagrams [4,[12][13][14][15][16][17][18].…”