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

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 twodimensional 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-dimension 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. Spin-orbit coupling (SOC), the intrinsic interaction between a particle spin and its motion, plays a key role in many important phenomena, ranging from anomalous Hall effects [1] to topological insulators and superconductors [2][3][4]. Although SOC is ubiquitous in nature, the experimental control and observation of SOC induced effects are quite difficult. In this context, the recent experimental realization of synthetic SOC for cold atoms [5][6][7][8][9][10][11][12] provides a completely new and tunable platform for exploring SOC related physics. Early experiments only realized the 1D SOC (i.e., an equal sum of Rashba and Dresselhaus coupling, ∝ k x σ y ) using two counterpropagating Raman lasers [5][6][7][8][9][10][11][12]. Many theoretical proposals have explored the generation of 2D SOC (i.e., ∝ αk x σ y + βk y σ x ) [13][14][15][16][17][18][19][20] as well as their interesting physical properties in Bose and Fermi gases [21][22][23][24][25][26]. Recently, 2D SOC was also experimentally realized in ultracold 40 K Fermi gases [27] using three Raman lasers and the associated stable Dirac point on a 2D momentum plane was observed [27].The experimental generation of SOC is usually accompanied with a Zeeman field, which breaks various symmetries of the underlying system and induces interesting quantum phenomena. The accompanied Zeeman field can be in-plane (e.g., V σ y for SOC ∝ k x σ y ) or perpendicular (e.g., V σ z for SOC ∝ αk x σ y + βk y σ x ). The in-plane Zeeman field, while preserves the Dirac point, makes the band dispersion asymmetric, leading to new quantum states such as Fulde-Ferrell superfluids [28][29][30][31]. In contrast, the perpendicular Zeeman field can open a topological band gap at the Dirac point of the SOC, leading to many interesting topological transport [1] and superfluid phenomena, such as the long-sought Majorana [32,33] and Weyl [24,34,35] fermions. In cold atom experiments, although both in-plane and perpendicular Zeeman fields have been realized with 1D SOC, only inplane Zeeman field was realized with 2D SOC [27]. A perpendicular Zeeman field with 2D SOC is still lacked but highly...

Properties of spin–orbit-coupled Bose–Einstein condensates

“…This is in contrast to 1D SOC, which does not lead to topology. Motivated by the generation of topology and by the well-established studies of 2D SOC in condensed matter systems, there are strong theoretical [10,[172][173][174][175][176] and experimental efforts [30,35,36] in the cold atom community to prepare 2D SOC atomic systems. The phase diagram of a 2D SOC BEC possesses more features than the analogous 1D picture and the dynamics also differs, such as dipole oscillations [52].…”

“…They also developed a radio-frequency spectroscopy technique [33], and showed that molecules can be formed with the help of Feshbach resonances [34]. Very recently, they realized 2D SOC [35] for the first time in Fermi gases and observed the band-gap opening around the Dirac point by inducing a perpendicular Zeeman field [36]. 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].…”

Induced interactions in the BCS-BEC crossover of two-dimensional Fermi gases with Rashba spin-orbit coupling

“…Many proposals have been suggested for experimental realization of Rashba-only SOC [15][16][17][18][19][20][21]. Very recently, the realization of two-dimensional SOC which can be transformed into either Rashba or Dresselhaus SOC has been reported [22][23][24].…”

From a semimetal to a chiral Fulde-Ferrell superfluid

“…The findings are of significance in both experiment and fundamental theory. * Corresponding author: xiongjunliu@pku.edu.cn First, we propose that a new type of 2D SO coupled Dirac semimetal can be realized based on a scheme adopting only a single Raman transition and simpler than the recent experiments [1][2][3]. By readily breaking the inversion symmetry of the Dirac system, we find that the FF superfluid phase can be favored under an attractive interaction.…”

“…Furthermore, we show a fundamental theorem that the topology of a 2D chiral superfluid can be uniquely determined from the unpaired normal states, with which the topological chiral Fulde-Ferrell superfluid with a broad topological region is predicted for the present system. This generic theorem is also useful for condensed matter physics and material science in search for new topological superconductors.Introduction.-The recent experimental realization of two-dimensional (2D) spin-orbit (SO) coupling for ultracold atoms [1][2][3], which corresponds to synthetic nonAbelian gauge potentials [4][5][6], advances an essential step to explore novel topological quantum phases beyond natural conditions. Ultracold fermions with SO coupling can favor the realization of topological superfluids (TSFs) (similar as topological superconductors in solids [7][8][9][10][11][12][13]) based on an s-wave Feshbach resonance [14,15], which are highly-sought-after quantum phases for their ability to host non-Abelian Majorana zero modes and implement topological quantum computation [22][23][24][25].…”