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arXiv:1710.06403 · Europhysics Letters (EPL)

Momentum space Aharonov-Bohm interferometry in Rashba spin-orbit coupled Bose-Einstein condensates

Junpeng Hou, Xi-Wang Luo, Kuei Sun, Chuanwei Zhang

Published Aug 13, 2018• 2 citations
arXivHTMLPDF

Abstract

The recent experimental realization of synthetic Rashba spin-orbit coupling (SOC) paves a new avenue for exploring topological phases in ultracold atoms. The unequivocal characterization of such topological physics requires a simple scheme for measuring the Berry phase originating from the SOC. Here we propose a scheme to realize momentum space Aharonov-Bohm interferometry in a Rashba spin-orbit–coupled Bose-Einstein condensate through a sudden change of the in-plane Zeeman field. We find that the π Berry phase for the Dirac point of the Rashba SOC is directly revealed by a robust dark interference fringe in the momentum space. An external perpendicular Zeeman field opens a band gap at the Dirac point, which reduces the Berry phase along the Rashba ring, leading to lower brightness of the interference fringe. We develop a variational model with semiclassical equations of motion of essential dynamical quantities for describing the interference process, yielding real and momentum space trajectories and geometric phases agreeing with the real-time simulation of the Gross-Pitaevskii equation. Our study may pave the way for the experimental detection of Berry phases in ultracold atomic systems and further exploration of momentum space interference dynamics.

DOI
10.1209/0295-5075/123/10005

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The recent experimental realization of synthetic Rashba spin-orbit coupling (SOC) paves a new avenue for exploring topological phases in ultracold atoms. The unequivocal characterization of such topological physics requires a simple scheme for measuring the Berry phase originating from the SOC. Here we propose a scheme to realize momentum space Aharonov-Bohm interferometry in a Rashba spin-orbit–coupled Bose-Einstein condensate through a sudden change of the in-plane Zeeman field. We find that the π Berry phase for the Dirac point of the Rashba SOC is directly revealed by a robust dark interference fringe in the momentum space. An external perpendicular Zeeman field opens a band gap at the Dirac point, which reduces the Berry phase along the Rashba ring, leading to lower brightness of the interference fringe. We develop a variational model with semiclassical equations of motion of essential dynamical quantities for describing the interference process, yielding real and momentum space trajectories and geometric phases agreeing with the real-time simulation of the Gross-Pitaevskii equation. Our study may pave the way for the experimental detection of Berry phases in ultracold atomic systems and further exploration of momentum space interference dynamics.
Recent experimental realization of one-dimensional spin-orbit coupling (SOC) for ultracold alkaline-earth(-like) atoms in optical lattice clocks opens a new avenue for exploring exotic quantum matter because of the strongly suppressed heating of atoms from lasers comparing with alkaline-earth atoms. Here we propose a scheme to realize two-dimensional (2D) Rashba and three-dimensional (3D) Weyl types of SOC in a 3D optical lattice clock and explore their topological phases. With 3D Weyl SOC, the system can support topological phases with various numbers as well as types (I or II) of Weyl points. The spin distributions of such topological bands for 2D Rashba and 3D Weyl SOCs can be detected using suitably designed spectroscopic sequences. Our proposal may pave the way for the experimental realization of robust topological quantum matters and their exotic quasiparticle excitations in ultracold atomic gases.
Spin-orbit coupling (SOC), the interaction between the spin and momentum of a quantum particle, is crucial for many important condensed matter phenomena. The recent experimental realization of SOC in neutral bosonic cold atoms provides a new and ideal platform for investigating spin-orbit coupled quantum many-body physics. In this Letter, we derive a generic Gross-Pitaevskii equation as the starting point for the study of many-body dynamics in spin-orbit coupled Bose-Einstein condensates. We show that different laser setups for realizing the same SOC may lead to different mean-field dynamics. Various ground state phases (stripe, phase separation, etc.) of the condensate are found in different parameter regions. A new oscillation period induced by the SOC, similar to the Zitterbewegung oscillation, is found in the center-of-mass motion of the condensate.
Topological phenomena arise in a wide range of systems, with fascinating physical consequences. There is great interest in finding new ways to measure such consequences in ultracold atomic gas experiments. These experiments have significant advantages over the solid-state as ultracold atoms are controllable, tuneable and clean. They can also be used to investigate properties which are inaccessible in other quantum systems. We explore some of the novel features of topological energy bands and topological solitons in ultracold gases. Topological energy bands have important geometrical properties described by the Berry curvature. Bands with nonzero Berry curvature arise in key areas of current research, such as optical lattices with more than one band; strong artificial magnetic fields and 2D spin-orbit coupling. Topological solitons are also relevant to cutting-edge experiments as they can be created and studied with high temporal and spatial resolution. In this thesis, we investigate the consequences of Berry curvature for the semiclassical dynamics of a wavepacket and the collective modes of an ultracold gas. We also study theoretically the dynamics of skyrmion-antiskyrmion pairs in a Bose Einstein condensate. Firstly, we propose a general method by which experiments can map the Berry curvature across the Brillouin zone, and thereby determine the topological properties of the energy bands of optical lattices. The Berry curvature modifies the semiclassical dynamics and hence the trajectory of a wavepacket undergoing Bloch oscillations. Our general protocol allows a clean measurement from the semiclassical dynamics of the Berry curvature over the Brillouin zone. We discuss how this protocol may be implemented and explore the semiclassical dynamics for three relevant systems. We discuss general experimental considerations for observing Berry curvature effects before reviewing some of the progress in the field since the publication of our work. Secondly, we show that the Berry curvature changes the hydrodynamic equations of motion for a trapped Bose-Einstein condensate, and causes significant modifications to the collective mode frequencies. We illustrate our results for the case of two-dimensional Rashba spin-orbit coupling in a Zeeman field, where we also apply both a sum rule and an operator approach to the dipole mode. Extending the operator method, we derive the effects of Berry curvature on the dipole mode in very general settings. We show that the sizes of these effects can be large and readily detected in experiment. Collective modes therefore provide a sensitive way to measure geometrical properties of topological energy bands. Lastly, we study theoretically the dynamics of two-component Bose-Einstein condensates in two dimensions, which admit topological excitations related to the skyrmions of nuclear physics. We explore a branch of uniformly propagating solitary waves, which, at high momentum, can be viewed as skyrmion-antiskyrmion pairs. We study these solitary waves for a range of interaction regimes and show that, for experimentally relevant cases, there is a transition to spatially extended spin-wave states at low momentum. We explain how this can be understood by analogy to the two-dimensional ferromagnet and discuss how such solitary waves can be generated and studied in experiment.
We propose a hierarchy set of minimal optical Raman lattice schemes to pave the way for experimental realization of high-dimensional spin-orbit (SO) couplings for ultracold atoms, including two-dimensional (2D) Dirac type, 2D Rashba type, and three-dimensional (3D) Weyl type. The proposed Dirac-type SO coupling exhibits precisely controllable high symmetry, for which a large topological phase region is predicted. The generation of 2D Rashba and 3D Weyl types requires that two sources of laser beams have distinct frequencies of factor 2 difference. Surprisingly, we find that 133Cs^{133}\mathrm{Cs}133Cs atoms provide an ideal candidate for the realization. A common and essential feature is of high controllability and absent of any fine-tuning in the realization, and the resulting SO coupled ultracold atoms have a long lifetime. In particular, a long-lived topological Bose gas of 2D Dirac SO coupling has been proved in the follow-up experiment. These schemes essentially improve over the current experimental accessibility and controllability, and open a realistic way to explore novel high-dimensional SO physics, particularly quantum many-body physics and quantum far-from-equilibrium dynamics with novel topology for ultracold atoms.
We explore a way of producing the Rashba spin-orbit coupling (SOC) for ultracold atoms by using a two-component (spinor) atomic Bose-Einstein condensate (BEC) confined in a bilayer geometry. The SOC of the Rashba type is created if the atoms pick up a $\ensuremath{\pi}$ phase after completing a cyclic transition between four combined spin-layer states composed of two spin and two layer states. The cyclic coupling of the spin-layer states is carried out by combining an intralayer Raman coupling and an interlayer laser assisted tunneling. We theoretically determine the ground-state phases of the spin-orbit-coupled BEC for various strengths of the atom-atom interaction and the laser-assisted coupling. It is shown that the bilayer scheme provides a diverse ground-state phase diagram. In an intermediate range of the atom-light coupling two interlacing lattices of half-skyrmions and half-antiskyrmions are spontaneously created. In the strong-coupling regime, where the SOC of the Rashba type is formed, the ground state represents plane-wave or standing-wave phases depending on the interaction between the atoms. A variational analysis is shown to be in good agreement with the numerical results.
Spin-orbit coupling (SOC) plays a crucial role in many branches of physics. In this context, the recent experimental realization of the coupling between spin and linear momentum of ultracold atoms opens a completely new avenue for exploring new spin-related superfluid physics. Here we propose that another important and fundamental SOC, the coupling between spin and orbital angular momentum (SOAM), can be implemented for ultracold atoms using higher-order Laguerre-Gaussian laser beams to induce Raman coupling between two hyperfine spin states of atoms. We study the ground-state phase diagrams of SOAM-coupled Bose-Einstein condensates on a ring trap and explore their applications in gravitational force detection. Our results may provide the basis for further investigation of intriguing superfluid physics induced by SOAM coupling, such as collective excitations.