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

Abstract

We measure the collective excitation spectrum of a spin-orbit coupled Bose-Einstein condensate using Bragg spectroscopy. The spin-orbit coupling is generated by Raman dressing of atomic hyperfine states. When the Raman detuning is reduced, mode softening at a finite momentum is revealed, which provides insight towards a supersolid-like phase transition. We find that for the parameters of our system, this softening stops at a finite excitation gap and is symmetric under a sign change of the Raman detuning. Finally, using a moving barrier that is swept through the BEC, we also show the effect of the collective excitation on the fluid dynamics.PACS numbers: 03.75. Kk, 03.75.Mn, 32.80.Qk, 71.70.Ej Since the achievement of Bose-Einstein condensation (BEC) in dilute atomic gases, the investigation of collective excitations has been a key tool to gain insight into this unusual state of matter [1]. For most atomic species used in BEC experiments the interactions between the ultracold atoms can be described by isotropic, short-range s-wave scattering, which leads to the well-known linear phonon excitation spectrum at low momentum. However, if long-range interactions, such as dipolar interactions, are present, the collective excitation spectrum of a BEC can exhibit a more complex structure: in addition to the typical low energy phonon spectrum, a roton-like structure can appear. It is characterised by a shoulder in the spectrum, which for certain parameters can turn into a parabolic minimum at a finite momentum [2][3][4][5].Interestingly, a similar parabolic minimum at a finite momentum can also exist in spin-orbit coupled (SOC) systems. 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]). In the single-particle picture, the effect of the Raman dressing is to displace two copies of the parabolic dispersion originating from the kinetic energy of the particle in opposite directions in momentum space. The Raman coupling opens a gap at the crossing of these two parabolas so that the resulting single-particle dispersion has the form of a double well in momentum space. The double well can be biased towards either minimum by changing the Raman detuning. When the Raman detuning or the Raman coupling exceed a critical value, one of the minima disappears and a single well dispersion results. * engels@wsu.eduIn the presence of nonlinear effects stemming from the s-wave scattering between the atoms in a Raman dressed BEC, the double well structure continues to exist. In a biased double wel...

Properties of spin–orbit-coupled Bose–Einstein condensates

“…The Massachusetts Institute of Technology (MIT) group performed spin-injection spectroscopy in a SOC Fermi gas with 6 Li atoms to measure the energy spectrum of SOC and the coexistence of SOC with a Zeeman lattice generated by a radio-frequency field [20]. The Washington State University (WSU) group investigated the physics of the ZB effect in 87 Rb [21], realized the Dicke model and the Dicke phase transition [22], measured the collective excitation spectrum (indicating the existence of roton-like structures) [23], and demonstrated the lack of Galilean invariance in SOC systems by measuring dynamical instabilities of a BEC in a moving optical lattice [24]. The Purdue group used a SOC 87 Rb BEC to study the physics of Landau-Zener tunneling [25] and to implement interferometry by periodically modulating the power of the laser beams that generate SOC [26].…”

“…To set the stage, we will first briefly describe the experimental approaches to generate SOC [9,[16][17][18][19][20][21][22][23][24][25][26][27][28][29][31][32][33][34][35].…”

Nonlinear waves in coherently coupled Bose-Einstein condensates

“…(28), more precisely, from the specific form of Ξ (1) 0 which is tailored to be representative of the kernel of M 0 . And, as can be checked by a comparison of the forms and definitions of M 1 (14) and M 0 (26), M 0 is the k → 0 limit of M 1 when ω = ω − (k): hence the background contributions in the ansatz (22) (and in the higher order terms) is indeed a low k contribution in the lowest branch and the divergence of W (k) in (57) indeed corresponds to a resonance between the upper branch and the (long wavelength limit of) the lower branch.…”

“…This feature has driven a rich body of experimental studies of phenomena such as the formation of spin domains, vortices and other nonlinear structures [2], internal Josephson effect [3], formation of squeezed and entangled states [4], motion of spin impurities [5], persistent currents [6], effective gauge potentials [7] and spin-orbit coupled systems [8], which has itself opened an avenue of new researches: observation of a superfluid Hall effect [9]; of Zitterbewegung [10]; of spin Hall effect [11]; of tunable Landau-Zener transitions [12]; of a Dicketype phase transition [13]; of the softening of a roton-like dispersion relation [14]...…”

Moving obstacle potential in a spin-orbit-coupled Bose-Einstein condensate

“…First, the ground state of the SO-coupled BEC breaks rotational symmetry, and the excitation spectrum above the ground state has an anisotropic characteristic form with a roton minimum [27][28][29][30]. Because of this feature, the Landau critical velocity and excitation properties depend on the direction of obstacle motion.…”