Optically induced spin-Hall effect in atoms

Topological spin-orbit-coupled fermions beyond rotating wave approximation

The realization of spin-orbit-coupled ultracold gases has driven a wide range of research and is typically based on the rotating wave approximation (RWA). By neglecting the counter-rotating terms, RWA characterizes a single near-resonant spin-orbit (SO) coupling in a two-level system. Here, we propose and experimentally realize a new scheme for achieving a pair of two-dimensional (2D) SO couplings for ultracold fermions beyond RWA. This work not only realizes the first anomalous Floquet topological Fermi gas beyond RWA, but also significantly improves the lifetime of the 2D-SO-coupled Fermi gas. Based on pump-probe quench measurements, we observe a deterministic phase relation between two sets of SO couplings, which is characteristic of our beyond-RWA scheme and enables the two SO couplings to be simultaneously tuned to the optimum 2D configurations. We observe intriguing band topology by measuring two-ring band-inversion surfaces, quantitatively consistent with a Floquet topological Fermi gas in the regime of high Chern numbers. Our study can open an avenue to explore exotic SO physics and anomalous topological states based on long-lived SO-coupled ultracold fermions.

Vortex and symmetric radiation character of nonlinear Thomson scattering in Laguerre-Gaussian circularly polarized laser pulses

The radiation character of nonlinear Thomson scattering is investigated in the interaction of Lagueree-Gaussian circularly polarized laser pulses with a single electron in the angular plane. With theoretical analysis and numerical calculation, it is shown that the angular radiation distributions have annular structures with great fourfold or plane symmetry in pulses characterized by comparatively lower laser intensity (a₀ < 6), prolonged pulse duration (τ > 50fs)or wide beam waist (b₀ > 5μm). In other circumstances, a vortex radiation pattern is found for the first time on the basis of the electron dynamics. Further, by increasing the initial phase of laser pulse, the overall angular radiation has an interesting counter-clockwise rotating trend with a cycle of Δξ₀ = 2π. These results would help the understanding of nonlinear Thomson scattering and push forward the research of twisted X/γ-ray generation in optical laboratory.

Highly Controllable and Robust 2D Spin-Orbit Coupling for Quantum Gases

We report the realization of a robust and highly controllable two-dimensional (2D) spin-orbit (SO) coupling with a topological nontrivial band structure. By applying a retro-reflected 2D optical lattice, phase tunable Raman couplings are formed into the antisymmetric Raman lattice structure, and generate the 2D SO coupling with precise inversion and C_{4} symmetries, leading to considerably enlarged topological regions. The lifetime of the 2D SO coupled Bose-Einstein condensate reaches several seconds, which enables exploring fine-tuning interaction effects. These essential advantages of the present new realization open the door to explore exotic quantum many-body effects and nonequilibrium dynamics with novel topology.

Angular Momentum of Twisted Radiation from an Electron in Spiral Motion

We theoretically demonstrate for the first time that a single free electron in circular or spiral motion emits twisted photons carrying well-defined orbital angular momentum along the axis of the electron circulation, in adding to spin angular momentum. We show that, when the electron velocity is relativistic, the radiation field contains harmonic components and the photons of lth harmonic carry lℏ total angular momentum for each. This work indicates that twisted photons are naturally emitted by free electrons and are more ubiquitous in laboratories and in nature than ever thought.

Controlling and probing non-abelian emergent gauge potentials in spinor Bose-Fermi mixtures

Gauge fields, typified by the electromagnetic field, often appear as emergent phenomena due to geometrical properties of a curved Hilbert subspace, and provide a key mechanism for understanding such exotic phenomena as the anomalous and topological Hall effects. Non-abelian gauge potentials serve as a source of non-singular magnetic monopoles. Here we show that unlike conventional solid materials, the non-abelianness of emergent gauge potentials in spinor Bose-Fermi atomic mixtures can be continuously varied by changing the relative particle-number densities of bosons and fermions. The non-abelian feature is captured by an explicit dependence of the measurable spin current density of fermions in the mixture on the variable coupling constant. Spinor mixtures also provide us with a method to coherently and spontaneously generate a pure spin current without relying on the spin Hall effect. Such a spin current is expected to have potential applications in the new generation of atomtronic devices.

Abelian and non-abelian emergent gauge fields govern the physics of many topological phenomena, such as Hall effects. Here the authors show theoretically that in a spinor Bose-Fermi mixture the non-abelianness of the gauge potential can be tuned, offering the chance to study the abelian-non-abelian crossover.

Degenerate quantum gases with spin-orbit coupling: a review

This review focuses on recent developments in synthetic spin-orbit (SO) coupling in ultracold atomic gases. Two types of SO coupling are discussed. One is Raman process induced coupling between spin and motion along one of the spatial directions and the other is Rashba SO coupling. We emphasize their common features in both single-particle and two-body physics and the consequences of both in many-body physics. For instance, single particle ground state degeneracy leads to novel features of superfluidity and a richer phase diagram; increased low-energy density-of-state enhances interaction effects; the absence of Galilean invariance and spin-momentum locking gives rise to intriguing behaviours of superfluid critical velocity and novel quantum dynamics; and the mixing of two-body singlet and triplet states yields a novel fermion pairing structure and topological superfluids. With these examples, we show that investigating SO coupling in cold atom systems can, enrich our understanding of basic phenomena such as superfluidity, provide a good platform for simulating condensed matter states such as topological superfluids and more importantly, result in novel quantum systems such as SO coupled unitary Fermi gas and high spin quantum gases. Finally we also point out major challenges and some possible future directions.

Light-induced gauge fields for ultracold atoms

Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our Universe is ruled by gravity, whose gauge structure suggests the existence of a particle-the graviton-that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms 'feeling' laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials-both Abelian and non-Abelian-in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms.

Spin-orbit coupling and quantum spin Hall effect for neutral atoms without spin flips

We propose a scheme which realizes spin-orbit coupling and the quantum spin Hall effect for neutral atoms in optical lattices without relying on near resonant laser light to couple different spin states. The spin-orbit coupling is created by modifying the motion of atoms in a spin-dependent way by laser recoil. The spin selectivity is provided by Zeeman shifts created with a magnetic field gradient. Alternatively, a quantum spin Hall Hamiltonian can be created by all-optical means using a period-tripling, spin-dependent superlattice.

Detecting topological phases in cold atoms

Chern insulators are band insulators which exhibit a gap in the bulk and gapless excitations in the edge. Detection of Chern insulators is a serious challenge in cold atoms since the Hall transport measurements are technically unrealistic for neutral atoms. By establishing a natural correspondence between the time-reversal invariant topological insulator and the quantum anomalous Hall system, we show for a class of Chern insulators that the topology can be determined by only measuring Bloch eigenstates at highly symmetric points of the Brillouin zone. Furthermore, we introduce two experimental schemes, including the spin-resolved Bloch oscillation, to carry out the measurement. These schemes are highly feasible under realistic experimental conditions. Our results may provide a powerful tool to detect topological phases in cold atoms.

The spin Hall effect in a quantum gas

Electronic properties such as current flow are generally independent of the electron's spin angular momentum, an internal degree of freedom possessed by quantum particles. The spin Hall effect, first proposed 40 years ago, is an unusual class of phenomena in which flowing particles experience orthogonally directed, spin-dependent forces--analogous to the conventional Lorentz force that gives the Hall effect, but opposite in sign for two spin states. Spin Hall effects have been observed for electrons flowing in spin-orbit-coupled materials such as GaAs and InGaAs (refs 2, 3) and for laser light traversing dielectric junctions. Here we observe the spin Hall effect in a quantum-degenerate Bose gas, and use the resulting spin-dependent Lorentz forces to realize a cold-atom spin transistor. By engineering a spatially inhomogeneous spin-orbit coupling field for our quantum gas, we explicitly introduce and measure the requisite spin-dependent Lorentz forces, finding them to be in excellent agreement with our calculations. This 'atomtronic' transistor behaves as a type of velocity-insensitive adiabatic spin selector, with potential application in devices such as magnetic or inertial sensors. In addition, such techniques for creating and measuring the spin Hall effect are clear prerequisites for engineering topological insulators and detecting their associated quantized spin Hall effects in quantum gases. As implemented, our system realizes a laser-actuated analogue to the archetypal semiconductor spintronic device, the Datta-Das spin transistor.

Manipulating topological edge spins in a one-dimensional optical lattice

We propose to observe and manipulate topological edge spins in a one-dimensional optical lattice based on currently available experimental platforms. Coupling the atomic spin states to a laser-induced periodic Zeeman field, the lattice system can be driven into a symmetry protected topological (SPT) phase, which belongs to the chiral unitary (AIII) class protected by particle number conservation and chiral symmetries. In the free-fermion case the SPT phase is classified by a Z invariant which reduces to Z(4) with interactions. The zero edge modes of the SPT phase are spin polarized, with left and right edge spins polarized to opposite directions and forming a topological spin qubit (TSQ). We demonstrate a novel scheme to manipulate the zero modes and realize single spin control in an optical lattice. The manipulation of TSQs has potential applications to quantum computation.

Spin-orbit-coupled dipolar Bose-Einstein condensates

We propose an experimental scheme to create spin-orbit coupling in spin-3 Cr atoms using Raman processes. By employing the linear Zeeman effect and optical Stark shift, two spin states within the ground electronic manifold are selected, which results in a pseudospin-1/2 model. We further study the ground state structures of a spin-orbit-coupled Cr condensate. We show that, in addition to the stripe structures induced by the spin-orbit coupling, the magnetic dipole-dipole interaction gives rise to the vortex phase, in which a spontaneous spin vortex is formed.

Mean-field dynamics of spin-orbit coupled Bose-Einstein condensates

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.

Trapped two-dimensional condensates with synthetic spin-orbit coupling

We study trapped 2D atomic Bose-Einstein condensates with spin-independent interactions in the presence of an isotropic spin-orbit coupling, showing that a rich physics results from the nontrivial interplay between spin-orbit coupling, confinement and interatomic interactions. For low interactions two types of half-vortex solutions with different winding occur, whereas strong-enough repulsive interactions result in a stripe-phase similar to that predicted for homogeneous condensates. Intermediate interaction regimes are characterized for large enough spin-orbit coupling by an hexagonally-symmetric phase with a triangular lattice of density minima similar to that observed in rapidly rotating condensates.

The quantum anomalous Hall effect in kagomé lattices

The quantum anomalous Hall (QAH) effect in kagomé lattices is investigated in the presence of both Rashba spin-orbit coupling and an exchange field. In addition to the gap at the Dirac points as found in graphene, a new topological energy gap is opened at the Γ point. With the Fermi energy lying in the first gap, the Chern number = 2 as in graphene, whereas with it lying in the second one, = 1. The distribution of Berry curvature is obtained to reveal the nontrivial topological properties in momentum space. For stripes with 'armchair' and 'zigzag' edges, the topological characteristics of gapless edge states on the genus g = 2 Riemann surface are studied. The obtained nonzero winding numbers also demonstrate the QAH effe

Probing non-abelian statistics of Majorana fermions in ultracold atomic superfluid

We propose an experiment to directly probe the non-abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show that different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark-state subspace.

Spin-orbit coupled spinor Bose-Einstein condensates

An effective spin-orbit coupling can be generated in a cold atom system by engineering atom-light interactions. In this Letter we study spin-1/2 and spin-1 Bose-Einstein condensates with Rashba spin-orbit coupling, and find that the condensate wave function will develop nontrivial structures. From numerical simulation we have identified two different phases. In one phase the ground state is a single plane wave, and often we find the system splits into domains and an array of vortices plays the role of a domain wall. In this phase, time-reversal symmetry is broken. In the other phase the condensate wave function is a standing wave, and it forms a spin stripe. The transition between them is driven by interactions between bosons. We also provide an analytical understanding of these results and determine the transition point between the two phases.

Delocalization of relativistic dirac particles in disordered one-dimensional systems and its implementation with cold atoms

We study theoretically the localization of relativistic particles in disordered one-dimensional chains. It is found that the relativistic particles tend to delocalization in comparison with the nonrelativistic particles with the same disorder strength. More intriguingly, we reveal that the massless Dirac particles are entirely delocalized for any energy due to the inherent chiral symmetry, leading to a well-known result that particles are always localized in one-dimensional systems for arbitrary weak disorders to break down. Furthermore, we propose a feasible scheme to detect the delocalization feature of the Dirac particles with cold atoms in a light-induced gauge field.

Non-Abelian magnetic monopole in a Bose-Einstein condensate

Recently, an effective non-Abelian magnetic field with a topology of a monopole was shown to emerge from the adiabatic motion of multilevel atoms in spatially varying laser fields [J. Ruseckas, Phys. Rev. Lett. 95, 010404 (2005)10.1103/PhysRevLett.95.010404]. We study this monopole in a Bose-Einstein condensate of degenerate dressed states and find that the topological charge of the pseudospin cancels the monopole charge resulting in a vanishing gauge invariant charge. As a function of the laser wavelength, different stationary states are classified in terms of their effect to the monopole part of the magnetic field and a crossover to vortex ground state is observed.

Effect of induced spin-orbit coupling for atoms via laser fields

We propose an experimental scheme to observe spin-orbit coupling effects of a two-dimensional Fermi atomic gas cloud by coupling its internal electronic states (pseudospins) to radiation in a Lambda configuration. The induced spin-orbit coupling can be of the Dresselhaus and Rashba type with a Zeeman term. We show that the optically induced spin-orbit coupling can lead to a spin-dependent effective mass under appropriate conditions with one of them able to be tuned between positive and negative effective masses. As a direct observable we show that in the expansion dynamics of the atomic cloud the initial atomic cloud splits into two clouds for the positive effective mass case regime, and into four clouds for the negative effective mass regime.

Generalized Stern-Gerlach effect for chiral molecules

The Stern-Gerlach effect is well known as spin-dependent splitting of a beam of atoms with magnetic moments by a magnetic-field gradient. Here, we show that an induced gauge potential may lead to a similar effect for chiral molecules. In the presence of three inhomogeneous light fields, the center of mass of a three-level chiral molecule is subject to an optically induced gauge potential, and the internal dynamics of the molecule can be described as an adiabatic evolution in the reduced pseudospin subspace of the two lowest energy levels. We demonstrate numerically that such an induced gauge potential can lead to observable pseudospin-dependent and chirality-dependent generalized Stern-Gerlach effects for mixed left- and right-handed chiral molecules under realistic conditions.