A scheme for realizing an omnidirectional spin Hall effect is proposed with ultracold atomic systems, where the induced spin current and its polarization are perpendicular to the applied external field, and can have arbitrary directions depending on the orientation of the external field.
We propose an optical means to realize the spin-Hall effect (SHE) in a neutral atomic system by coupling the internal spin states of atoms to radiation. The interaction between the external optical fields and the atoms creates effective magnetic fields that act in opposite directions on "electrically" neutral atoms with opposite spin polarizations. This effect leads to a Landau level structure for each spin orientation in direct analogy with the familiar SHE in semiconductors. The conservation and topological properties of the spin current, and the creation of a pure spin current are discussed.
Using the sensitivity of atomic transitions on the polarizations of pump fields in multi-Zeeman-sublevel atomic systems, we show the polarization-direction-dependent anisotropic susceptibility of atoms that yields the strong coupling between the spin and the transverse momentum of light, i.e., spin–orbit interaction (SOI). Moreover, we also show that the spin-Hall effect of light can be obtained due to SOI. It can be controlled via the orientation of the anisotropy and frequency of light, and substantially enhanced up to several micrometers, which could be easily observed in experiment.
Ultracold atoms in optical lattices serve as a tool to model different physical phenomena appearing originally in condensed matter. To study magnetic phenomena one needs to engineer synthetic fields as atoms are neutral. Appropriately shaped optical potentials force atoms to mimic charged particles moving in a given field. We present the realization of artificial gauge fields for the observation of anomalous Hall effect. Two species of attractively interacting ultracold fermions are considered to be trapped in a shaken two dimensional triangular lattice. A combination of interaction induced tunneling and shaking can result in an emergent Dice lattice. In such a lattice the staggered synthetic magnetic flux appears and it can be controlled with external parameters. The obtained synthetic fields are non-Abelian. Depending on the tuning of the staggered flux we can obtain either anomalous Hall effect or its quantized version. Our results are reminiscent of Anomalous Hall conductivity in spin-orbit coupled ferromagnets.
We propose a scheme to create an effective magnetic field for ultracold atoms in a planar geometry. The setup allows the experimental study of classical and quantum Hall effects in close analogy to solid-state systems including the possibility of finite currents. The present scheme is an extention of the proposal in Phys. Rev. Lett. 93, 033602 (2004), where the effective magnetic field is now induced for three-level $\ensuremath{\Lambda}$-type atoms by two counterpropagating laser beams with shifted spatial profiles. Under conditions of electromagnetically induced transparency the atom-light interaction has a space-dependent dark state, and the adiabatic center-of-mass motion of atoms in this state experiences effective vector and scalar potentials. The associated magnetic field is oriented perpendicular to the propagation direction of the laser beams. The field strength achievable is one flux quantum over an area given by the transverse beam separation and the laser wavelength. For a sufficiently dilute gas the field is strong enough to reach the lowest Landau level regime.
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.
Measurement techniques based upon the Hall effect are invaluable tools in condensed-matter physics. When an electric current flows perpendicular to a magnetic field, a Hall voltage develops in the direction transverse to both the current and the field. In semiconductors, this behavior is routinely used to measure the density and charge of the current carriers (electrons in conduction bands or holes in valence bands)--internal properties of the system that are not accessible from measurements of the conventional resistance. For strongly interacting electron systems, whose behavior can be very different from the free electron gas, the Hall effect's sensitivity to internal properties makes it a powerful tool; indeed, the quantum Hall effects are named after the tool by which they are most distinctly measured instead of the physics from which the phenomena originate. Here we report the first observation of a Hall effect in an ultracold gas of neutral atoms, revealed by measuring a Bose-Einstein condensate's transport properties perpendicular to a synthetic magnetic field. Our observations in this vortex-free superfluid are in good agreement with hydrodynamic predictions, demonstrating that the system's global irrotationality influences this superfluid Hall signal.