Session M2: Focus Session: Synthetic Gauge Fields and Spin Orbit Coupling

Interactions engineered for spin-orbit coupled atomic gases

Ultracold gases of interacting spin-orbit coupled fermions are predicted to display exotic phenomena such as topological superfluidity and its associated Majorana fermions. Here, we experimentally demonstrate a route to strongly-interacting single-component atomic Fermi gases by combining an s-wave Feshbach resonance (giving strong interactions) and spin-orbit coupling (creating an effective p-wave channel). We identify the Feshbach resonance by its associated atomic loss feature and show that, in agreement with our single-channel scattering model, this feature is preserved and shifted as a function of the spin-orbit coupling parameters. With: R. A. Williams, M. C. Beeler, L. J. LeBlanc, and K. Jimenez-Garcia   

Synthetic gauge potentials for cold atoms by shaking

Ultracold atoms held in optical lattice potentials provide an almost ideal arena for the study of coherent quantum phenomena. We first explore the generation of synthetic gauges by controlling the switching conditions of the driving force. For two-dimensional optical lattices, we propose a powerful and flexible scheme which generates synthetic magnetic fields that couple only to the atom center-of-mass. We briefly outline some possible applications. \\[4pt] [1] ``Directed transport in driven optical lattices by gauge generation,'' C.E. Creffield and F. Sols, Phys. Rev. A 84, 023630 (2011).\\[0pt] [2] ``Comment on `Creating artificial magnetic fields for cold atoms by photon-assisted tunneling,'' C.E. Creffield and F. Sols, Europhysics Letters 101, 40001 (2013).   

Systematic Construction of tight-binding Hamiltonians for Topological Insulators and Superconductors

A remarkable discovery in recent years is that there exist various kinds of topological insulators and superconductors characterized by a periodic table according to the system symmetry and dimensionality. To physically realize these peculiar phases and study their properties using ultracold atoms in optical lattices, a critical step is to construct experimentally relevant Hamiltonians which support these topological phases. We propose a general and systematic method based on the quaternion algebra to construct the tight binding Hamiltonians for all the three-dimensional topological phases in the periodic table characterized by arbitrary integer topological invariants, which include the spin-singlet and the spin-triplet topological superconductors, the Hopf and the chiral topological insulators as particular examples. For each class, we calculate the corresponding topological invariants through both geometric analysis and numerical simulation. Our method can be straightforwardly generalized to one- and two-dimensions, and thus paves the way to implementation of various topological phases in optical lattices.   

Experimental investigation of spin-orbit coupled BECs

The generation of artificial gauge fields has emerged as a central tool to study condensed matter phenomena using ultracold quantum gases. In this context, the implementation of spin-orbit coupling is an advancement that is currently met with great interest, both theoretically and experimentally. In our lab we have implemented spin-orbit coupling by using a Raman dressing scheme and have studied the physics arising from a combination of spin-orbit coupling and an optical lattice. Since both spin-orbit coupling as well as an optical lattice strongly modify the dispersion relation, interesting bandstructures result from the combination of the two. We have probed such bandstructures by placing BECs into a moving spin-orbit coupled lattice while measuring atom loss rates due to modulational instability. Our experimental results are corroborated by a matching theoretical analysis. The current status of our ongoing investigations will be reported.   

Dipole-dipole interaction-induced spin-orbit coupling of polar molecules in optical lattices

Long-range dipole-dipole interactions between polar molecules in an optical lattice enable rotational excitations to move through the lattice even when the molecules themselves cannot, as has been directly observed in recent experiments [Yan {\it et al.}, Nature \textbf{501}, 521-525 (2013)]. We study the dynamics of rotational excitations in a 2D lattice of (bosonic or fermionic) polar molecules in the presence of electric dipole-dipole interactions which exchange rotational ``spin" angular momentum projection with orbital angular momentum, forming a cold molecule analog of the Einstein-de Haas effect. In particular, we present analytic results for the statics and dynamics of a dilute gas of rotational excitations in a unit-filed lattice. Prospects for observing such processes in near-term polar molecule experiments are discussed.   

Exotic Phases of Rashba Spin-Orbit Coupled Dipolar Bosons

We study the ground state phases of ultracold dipolar Bose gases in the presence of a Rashba spin-orbit coupling, which introduces a degenerate ring-like dispersion minimum for the atoms. Depending on the character of the dipolar interactions and the dimensionality of the system, we find that a number of topological and exotic spatially ordered states emerge, including merons and quantum quasicrystals. We provide an intuitive physical picture for the emergence of these phases, and discuss possible level schemes for atomic dysprosium.   

Superfluid-Mott insulator transition in spin-orbit coupled Bose-Hubbard Model

We consider a square optical lattice in two dimensions and study the effects of both the strength and symmetry of spin-orbit coupling (SOC) and Zeeman field on the ground-state, i.e., Mott insulator (MI) and superfluid (SF), phases and phase diagram, i.e., MI-SF phase transition boundary, of the two-component Bose-Hubbard model. In particular, based on a variational Gutzwiller ansatz, our numerical calculations show that the spin-orbit coupled SF phase is a nonuniform (twisted) one with its phase (but not the magnitude) of the order parameter modulating from site to site. Fully analytical insights into the numerical results are also given.