Cold Atomic Gases in Optical Lattices with Disorder
T. Schulte, S. Drenkelforth, J. Kruse, Wolfgang A. Ertmer, J. Arlt, Adrian Kantian, Laurent Sanchez-Palencia, Luis Santos, Anna Sanpera, Krzysztof Sacha, P. Zoller, Maciej Lewenstein, Jakub Zakrzewski
Cold atomic gases placed in optical lattices enable studies of simple condensed matter theory models with parameters that may be tuned relatively easily.When the optical potential is randomized (e.g. using laser speckle to create a random intensity distribution) one may be able to observe Anderson localization of matter waves for non-interacting bosons, the so-called Bose glass in the presence of interactions, as well as the Fermi glass or quantum spin glass for mixtures of fermions and bosons.
Cold atomic gases placed in optical lattices enable studies of simple condensed matter theory models with parameters that may be tuned relatively easily.When the optical potential is randomized (e.g. using laser speckle to create a random intensity distribution) one may be able to observe Anderson localization of matter waves for non-interacting bosons, the so-called Bose glass in the presence of interactions, as well as the Fermi glass or quantum spin glass for mixtures of fermions and bosons.
Cold atomic gases placed in optical lattices enable studies of simple con- densed matter theory models with parameters that may be tuned relatively easily. When the optical potential is randomized (e.g. using laser speckle to create a random intensity distribution) one may be able to observe Anderson localization of matter waves for non-interacting bosons, the so-called Bose glass in the presence of interactions, as well as the Fermi glass or quantum spin glass for mixtures of fermions and bosons.
An ultracold atomic Bose gas in an optical lattice is shown to provide an ideal system for the controlled analysis of disordered Bose lattice gases. This goal may be easily achieved under the current experimental conditions by introducing a pseudorandom potential created by a second additional lattice or, alternatively, by placing a speckle pattern on the main lattice. We show that, for a noncommensurable filling factor, in the strong-interaction limit, a controlled growing of the disorder drives a dynamical transition from superfluid to Bose-glass phase. Similarly, in the weak interaction limit, a dynamical transition from superfluid to Anderson-glass phase may be observed. In both regimes, we show that even very low-intensity disorder-inducing lasers cause large modifications of the superfluid fraction of the system.
We present a review of properties of ultracold atomic Fermi-Bose mixtures in inhomogeneous and random optical lattices. In the strong interacting limit and at very low temperatures, fermions form, together with bosons or bosonic holes, composite fermions. Composite fermions behave as a spinless interacting Fermi gas, and in the presence of local disorder they interact via random couplings and feel effective random local potential. This opens a wide variety of possibilities of realizing various kinds of ultracold quantum disordered systems. In this paper we review these possibilities, discuss the accessible quantum disordered phases, and methods for their detection. The discussed quantum phases include Fermi glasses, quantum spin glasses, ``dirty'' superfluids, disordered metallic phases, and phases involving quantum percolation.
This chapter starts with an introduction to disordered systems, with an emphasis on disorder in condensed matter, and discusses such phenomena as the Anderson localization, and quantum phases such as with Bose glass. It then turns to various experimental realizations of disorder in ultracold atomic gases. The chapter focuses on disordered Bose-Einstein condensates and the phenomenon of Anderson localization in speckle or quasi-periodic, quasi-random potential. It moves on to disordered ultracold fermionic systems, and disordered ultracold Bose–Fermi (B–F) and Bose–Bose (B–B) mixtures. Finally, the chapter examines spin glasses (providing a brief presentation of the mean field theory of Parisi, and the droplet model) and disorder induced order.
Quantum degenerate atomic gases offer a unique platform for the exploration of a wide variety of interacting many-body systems in a pristine environment, based on a set of powerful tools for the coherent control of the atoms' internal and external degrees of freedom. Here, we present experimental studies of strongly interacting bosonic mixtures in one-dimensional (1D) systems, in which the mobilities of the two species are independently controlled with a state-selective optical lattice. In a first experiment, we freeze out the tunneling of one species from a binary mixture, and study the formation of ``quantum emulsion'' states, where immobile atoms serve as a static, random disorder for a more mobile species. We investigate the 1D superfluid-to-insulator transition in the presence of this disorder, and make comparisons to the effects of quasi-disorder from an incommensurate optical lattice. We observe enhanced localization in the more random potential, highlighting the important role of correlations in disordered systems. Through a combined measurement of transport, localization, and excitation spectra, we are able to obtain strong evidence for observation of a disordered, insulating quantum phase, the 1D Bose glass. In a second experiment, we introduce a new experimental technique for the characterization of ultracold gases held in optical lattices. In analogy to neutron diffraction from solids, we use atomic de Broglie waves to non-destructively probe the spatial structure of 1D Mott insulators through elastic Bragg diffraction, and to probe inelastic band-structure excitations of more weakly interacting 1D Bose gases. Furthermore, we use the diffraction of matter waves to detect the formation of forced-antiferromagnetic ordering in a crystalline atomic spin mixture. Lastly, we study the dynamical response of matter waves to a periodically pulsed, incommensurate optical lattice, a situation that realizes a system of two coupled kicked quantum rotors. We observe that the coupling induces a suppression of energy growth at quantum resonances, and a localization-to-delocalization transition in momentum space for off-resonant driving. Our observations confirm a long-standing theoretical prediction for the two-rotor system, and illustrate how classical behavior can emerge from the evolution of a simple quantum system. | 193 pages
Ultra-cold atomic gases by themselves and in combination with disorder are a highly active and innovative field of research. Since the first expenmental realization of Bose.-Elnstein condensation in 1995, ultra-cold quantum gases have become a powerful tool to study condensed matter, quantum optics, and quantum Infonnation problems. Disordered systems are been extremely difficult to study, but recent advances of ultra-cold experiments have brought about new tools and approaches to tackle these problems as well. In particular, urtra-cold quantum gases can be subject to controlled spatially disordered potentials. Breakthroughts like the seminal observation of Anderson localization in 2008 illustrate the powerful experimental control of quantum systems. There are currently two main approaches to realizing controlled disordered potentials for ultra-cold atomi gases: incommensurate '!lulti-chromatic lattices and speckle radiation. Altematlve approaches using holographic masks, rapidly oscillating laser beams and secondary lattices xJng scatterers in space are currently being studied by several groups. The sum of these innovative techniques that aim at realizing controlled disorder l'uels studies on disordered ultra-cold systems - In particular, the between interactions and disorder in non-interacting Bose- and Fenni systems, and the creation of glass states together with associated quantum phase transitions are currently attracting a lot of attention this thesis reports on the applicability and robustness of a related phenomenon called disorder-induced order. In essence, it is the process by which certain systems order when a specific type of controlled disorder is applied. In absence of disorder, the systems we consider present a contlnuous vvymmetry, e.g. a rotational U(1) symmetry as In the ferromagnetic XV model. If we apply a homogenous magnetic field along a given direction of the X I lane, all spins will align roughly in this direction. If we replace this homogenous field by a spatially randomly oscillating field in the same direction at low temperature, the system tends to avoid this external field and orders in a direction orthogonal to the field, inside the XV plane. The effect turns out to be robust enough to occur with regularly oscillating fields (e.g. staggered fields, sinuSOlda1ty oscillating fields), pseudo-random fields (realizable by uperposlng optical lattices), and random fields (as created by speckle plates), However, we stress that these disordered fields must not be dlstnbuted according to the continuous symmetry of the system but restricted to a subspace e.g. in the XV model, the spins can orient in any direction of the XV plane - and, if the disordered field is oriented WIth random angles, the system WIll not magnetize. The effect only occurs if the disorder is always along a given direction with random orientation. We study several configurations of disorder-induced order numerically and analytically, and present possible expenmental realizations for the classical XY system as an illustration of the basic Intuition of the effect IPRB 74 224448 (2006)], a system of two Raman-coupled Bose-Elnstein condensates, where disorder allows to control the relative phase of the two condensates IPRl 10030403 (2008)) superfluid BCS pairs in presence of a diatomic reservoir, where disorder fixes the complex phase of the painng function IEPl 86 26004 (2009)], and the quantum XY spin chain, where disorder leads to spontaneous magnetization in the direction orthogonat to the disordered fietd [PRA, accepted] Other systems in which we expect disorder-induced order to occur, not discussed in thiS thesis, are spinor condensates and possibly systems with synthetic gauge fields. Finally, there are reports of randomness-induced XV Ofdering in a graphene quantum Hall ferromagnet (PRl 98 156801 (2007) as well as disorder-induced ordering of superfluid 3HE-A in aerogel [JETPl84 455 (2006), Jl TP 150453 (2008).