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arXiv:1511.08492 · Physical Review Letters

Experimental Observation of a Topological Band Gap Opening in Ultracold Fermi Gases with Two-Dimensional Spin-Orbit Coupling

Zengming Meng, Lianghui Huang, Peng Peng, Donghao Li, Liangchao Chen, Yong Xu, Chuanwei Zhang, Pengjun Wang, Jing Zhang

Published Dec 2, 2016• 159 citations
arXivHTMLPDF

Abstract

The recent experimental realization of synthetic spin-orbit coupling (SOC) opens a new avenue for exploring novel quantum states with ultracold atoms. However, in experiments for generating two-dimensional SOC (e.g., Rashba type), a perpendicular Zeeman field, which opens a band gap at the Dirac point and induces many topological phenomena, is still lacking. Here, we theoretically propose and experimentally realize a simple scheme for generating two-dimensional SOC and a perpendicular Zeeman field simultaneously in ultracold Fermi gases by tuning the polarization of three Raman lasers that couple three hyperfine ground states of atoms. The resulting band gap opening at the Dirac point is probed using spin injection radio-frequency spectroscopy. Our observation may pave the way for exploring topological transport and topological superfluids with exotic Majorana and Weyl fermion excitations in ultracold atoms.

DOI
10.1103/physrevlett.117.235304

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The recent experimental realization of synthetic spin-orbit coupling (SOC) opens a new avenue for exploring novel quantum states with ultracold atoms. However, in experiments for generating two-dimensional SOC (e.g., Rashba type), a perpendicular Zeeman field, which opens a band gap at the Dirac point and induces many topological phenomena, is still lacking. Here, we theoretically propose and experimentally realize a simple scheme for generating two-dimensional SOC and a perpendicular Zeeman field simultaneously in ultracold Fermi gases by tuning the polarization of three Raman lasers that couple three hyperfine ground states of atoms. The resulting band gap opening at the Dirac point is probed using spin injection radio-frequency spectroscopy. Our observation may pave the way for exploring topological transport and topological superfluids with exotic Majorana and Weyl fermion excitations in ultracold atoms.
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.
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.
In a recent experiment, a two-dimensional spin-orbit coupling (SOC) was realized for fermions in the continuum [Nat. Phys. 12, 540 (2016)], which represents an important step forward in the study of synthetic gauge fields using cold atoms. In the experiment it was shown that a Raman-induced two-dimensional SOC exists in the dressed-state basis close to a Dirac point of the single-particle spectrum. By contrast, the short-range interatomic interactions of the system are typically expressed in the hyperfine-spin basis. The interplay between synthetic SOC and interactions can potentially lead to interesting few- and many-body phenomena but has so far eluded theoretical attention. Here we study in detail properties of two-body bound states of such a system. We find that, due to the competition between SOC and interaction, the stability region of the two-body bound state is in general reduced. Particularly, the threshold of the lowest two-body bound state is shifted to a positive, SOC-dependent scattering length. Furthermore, the center-of-mass momentum of the lowest two-body bound state becomes nonzero, suggesting the emergence of Fulde-Ferrell pairing states in a many-body setting. Our results reveal the critical difference between the experimentally realized two-dimensional SOC and the more symmetric Rashba or Dresselhaus SOCs in an interacting system, paving the way for future characterizations of topological superfluid states in the experimentally relevant systems.
We theoretically investigate a three-dimensional Fermi gas with Rashba spin–orbit coupling in the presence of both out-of-plane and in-plane Zeeman fields. We show that, driven by a sufficiently large Zeeman field, either out-of-plane or in-plane, the superfluid phase of this system exhibits a number of interesting features, including inhomogeneous Fulde–Ferrell pairing, gapped or gapless topological order, and exotic quasi-particle excitations known as Weyl fermions that have linear energy dispersions in momentum space (i.e., massless Dirac fermions). The topological superfluid phase can have either four or two topologically protected Weyl nodes. We present the phase diagrams at both zero and finite temperatures and discuss the possibility of their observation in an atomic Fermi gas with synthetic spin–orbit coupling. In this context, topological superfluid phase with an imperfect Rashba spin–orbit coupling is also studied.
Spin-orbit coupling (SOC) in ultracold atoms is engineered by light-atom interaction, such as two-photon Raman transitions between two Zeeman spin states. In this paper, we propose and experimentally realize chiral Raman coupling to generate SOC in ultracold atomic gases, which exhibits high quantization axis direction dependence. Chiral Raman coupling for SOC is created by chiral light-atom interaction, in which a circularly polarized electromagnetic field generated by two Raman lasers interacts with two Zeeman spin states $\ensuremath{\delta}{m}_{F}=\ifmmode\pm\else\textpm\fi{}1$ (chiral transition). We present a simple scheme of chiral one-dimensional (1D) Raman coupling by employing two Raman lasers at an intersecting angle ${90}^{\ensuremath{\circ}}$ with the proper polarization configuration. In this case, Raman coupling for SOC exists in one direction of the magnetic quantization axis and disappears in the opposite direction. Then we extend this scheme into a chiral two-dimensional (2D) optical square Raman lattice configuration to generate the 1D SOC. There are two orthogonal 1D SOCs, which exist in the positive and negative directions of the magnetic quantization axis respectively. This case is compared with 2D SOC based on the nonchiral 2D optical Raman lattice scheme for studying the topological energy band. This paper broadens the horizon for understanding chiral physics and simulating topological quantum systems.
The recent experimental realization of spin-orbit (SO) coupling for ultracold bosons and fermions opens an exciting avenue for engineering quantum matter that may be challenging to realize in solid-state materials such as SO-coupled pseudospin-1 fermions. While one-dimensional SO coupling for spin-1 bosons has been experimentally realized, the generation of two-dimensional (2D) SO coupling and its topological properties are largely unexplored. Here we propose an experimental scheme for realizing a 2D Rashba-type SO coupling in a square lattice for pseudospin-1 Fermi gases. Because of the extended spin degree of freedom, many interesting topological phases could exist without relying on lattice point group symmetries that are crucial in solid-state materials. These exotic phases include triply degenerate points, quadratic band touching, a large Chern number (C=5C=5C=5) superfluid with five Majorana modes, triple-Weyl fermions, and so on. Our scheme can be generalized to larger spins and provides a distinctive route for engineering topological quantum matter by utilizing large spin degrees of freedom, instead of specific lattice symmetries.