Disordered-induced order with ultra-cold atoms

Abstract

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).