Session J2: Vector Potentials in Cold Gases

Realizing artificial magnetic fields via optical lattice immersion

Ultracold atoms in optical lattices are one of the top candidates for performing direct quantum simulations of fundamental condensed matter phenomena such as the quantum Hall effect. While numerous proposals have been made for how to simulate the effect of a magnetic field on trapped neutral atoms, these typically have very stringent experimental requirements in order to access relevant parameter regimes. Here we describe an alternative scheme in which atoms trapped in a static optical lattice are immersed into a rotating Bose-Einstein condensate (BEC). We show that the interaction with a rotating BEC induces a controllable phase twist on the hopping term for the impurity atoms in the lattice. Crucially this scheme does not require any careful balancing of the centrifugal term in contrast to directly rotating the lattice. For a 1D ring-shaped setup we examine analytically the dependence of this phase twist on BEC's angular velocity and the coupling of impurity atoms to BEC phonons. These findings are further generalized to a 2D lattice submerged in a 2D BEC which is moderately rotating and harmonically confined. In this case the artificial magnetic field is inhomogeneous and we discuss how its spatial dependence can be controlled by varying the trapping potential of the BEC. In earlier work on static immersions we showed that the coupling of the impurity atoms to BEC phonons leads to a cross-over from coherent to incoherent transport of the impurity atoms and to an attractive interaction between impurity atoms causing clustering effects. We discuss some preliminary work investigating how the nature of these effects change in a rotating setup.   

Cold atoms in a rotating optical lattice

We have demonstrated a novel experimental arrangement which can rotate a two-dimensional optical lattice at frequencies up to several kilohertz. Our arrangement also allows the periodicity of the optical lattice to be varied dynamically, producing a 2D ``accordion lattice'' [1]. The angles of the laser beams are controlled by acousto-optic deflectors and this allows smooth changes with little heating of the trapped cold (rubidium) atoms. We have loaded a BEC into lattices with periodicities ranging from 1.8$\mu$m to 18$\mu$m, observing the collapse and revival of the diffraction orders of the condensate over a large range of lattice parameters as recently reported by a group in NIST [2]. We have also imaged atoms in situ in a 2D lattice over a range of lattice periodicities. Ultracold atoms in a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields, i.e. the Hamiltonian of the atoms in the rotating frame resembles that of a charged particle in a strong magnetic field. In the future, we plan to use this to investigate a range of phenomena such as the analogue of the fractional quantum Hall effect. \\[4pt] [1] R. A. Williams, J. D. Pillet, S. Al-Assam, B. Fletcher, M. Shotter, and C. J. Foot, ``Dynamic optical lattices: two-dimensional rotating and accordion lattices for ultracold atoms,'' Opt. Express 16, 16977-16983 (2008) \\[0pt] [2] J. H. Huckans, I. B. Spielman, B. Laburthe Tolra, W. D. Phillips, and J. V. Porto, Quantum and Classical Dynamics of a BEC in a Large-Period Optical Lattice, arXiv:0901.1386v1   

Vortex configurations of ultracold bosons in rotating optical lattices

Atomic clouds in rotating optical lattices are at the intellectual intersection of several major paradigms of condensed matter physics. An optical lattice simulates the periodic potential ubiquitous in solid state physics, while rotation probes the superfluid character of these cold atomic gases by driving the formation of quantized vortices. Here we concentrate on our own work investigating the vortex configurations that emerge in a trapped Bose-Einstein condensate in a rotating optical lattice. We investigate this system in two separate regimes. First, we find that close proximity to the Mott state dramatically affects the vortex configurations. To illustrate we give examples in which the vortices: (i) all sit at a fixed distance from the center of the trap, forming a ring, or (ii) coalesce at the center of the trap, forming a giant vortex. Second, we investigate the regime far from the Mott phases, where the competition between vortex-vortex interactions and pinning to the optical lattice results in a complicated energy landscape, leading to hysteresis. The qualitative structure of the vortex configurations depends on the ratio between the vortex density and the site density -- with regular lattices forming when these quantities are commensurate. In both regimes we simulate absorption images after time-of-flight expansion, and thus show how these states could be observed in the laboratory.   

Creating effective vector potentials with light

Ultra cold atoms are remarkable systems with a truly unprecedented level of experimental control and one application of this control is engineering the systems hamiltonian. To date this has focused mostly on the real-space potential that the atoms experience for example, multiple-well traps or optical lattice potentials. Here we present our experimental work which tailors the energy-momentum dispersion of the cold atoms. We couple different internal states of rubidium 87 via a momentum-selective Raman transition and load our system into the resulting adiabatic eigenstates. Using this technique we show the controlled modification of the energy-momentum dispersion leads to an effective vector potential. This work was performed in collaboration with Y.-J. Lin, R.~L.~Compton, A.~R.~Perry, W.~D.~Phillips and J.~V.~Porto.