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arXiv:0707.0675 · Physical Review Letters

Disorder-Induced Order in Two-Component Bose-Einstein Condensates

Armand Niederberger, T. Schulte, Jan Wehr, Maciej Lewenstein, Laurent Sanchez-Palencia, Krzysztof Sacha

Published Jan 24, 2008• 54 citations
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Abstract

We propose and analyze a general mechanism of disorder-induced order in two-component Bose-Einstein condensates, analogous to corresponding effects established for XY spin models. We show that a random Raman coupling induces a relative phase of pi/2 between the two BECs and that the effect is robust. We demonstrate it in one, two, and three dimensions at T=0 and present evidence that it persists at small T>0. Applications to phase control in ultracold spinor condensates are discussed.

DOI
10.1103/physrevlett.100.030403

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•Jan 1, 2010•0 citations
We propose and analyze a general mechanism of disorder-induced order in two-component Bose-Einstein condensates, analogous to corresponding effects established for XY spin models. We show that a random Raman coupling induces a relative phase of pi/2 between the two BECs and that the effect is robust. We demonstrate it in one, two, and three dimensions at T=0 and present evidence that it persists at small T>0. Applications to phase control in ultracold spinor condensates are discussed.
We study spatial spin and density self-ordering of a two-component Bose-Einstein condensate via collective Raman scattering into a linear cavity mode. The onset of the Dicke superradiance phase transition is marked by a simultaneous appearance of a crystalline density order and a spin-wave order. The latter spontaneously breaks the discrete Z_{2} symmetry between even and odd sites of the cavity optical potential. Moreover, in the superradiant state the continuous U(1) symmetry of the relative phase of the two condensate wave functions is explicitly broken by the cavity-induced position-dependent Raman coupling with a zero spatial average. Thus, the spatially averaged relative condensate phase is locked at either π/2 or -π/2. This continuous symmetry breaking and relative condensate phase locking by a zero-average Raman field can be considered as a generic order-by-disorder process similar to the random-field-induced order in the two-dimensional classical ferromagnetic XY spin model. However, the seed of the random field in our model stems from quantum fluctuations in the cavity field and is a dynamical entity affected by self-ordering. The spectra of elementary excitations exhibit the typical mode softening at the superradiance threshold.
We consider a mixture of a superfluid Fermi gas of ultracold atoms and a Bose-Einstein condensate of molecules possessing a continuous U (1) (relative phase) symmetry. We study the effects of a spatially random photo-associative–dissociative symmetry-breaking coupling of the systems. Such coupling allows one to control the relative phase between a superfluid order parameter of the Fermi system and the condensate wave function of molecules for temperatures below the Bardeen-Cooper-Schriefer critical temperature. The presented mechanism of phase control belongs to the general class of phenomena in which disorder interacts with continuous symmetry. Our results show the robustness and wide range of applicability of disorder-induced order and are valid for both disordered and regular couplings. Here, the effect is studied in the case of interacting fermionic and bosonic gases in the superfluid phase.
We propose a general mechanism of disorder-induced order by studying a particular case of classical ferromagnetic XY model in a random uniaxial field which breaks the continuous symmetry of the model. We prove rigorously that the system has spontaneous magnetization at temperature T=0, and we present strong evidence that this is also the case for small T>0. We discuss generalizations of this mechanism to various classical spin models and quantum systems. We propose a realization of this phenomenon with ultracold atoms in an optical lattice.
The authors consider a random magnetic model which is related to Bose condensation in the presence of a random potential. It is an XY model with a random z field. The classical model always has an ordered ground state. The nature of the ground state is unusual: the main contribution to the spontaneous magnetisation comes from a dilute set of weakly interacting pairs of spins. Within each pair the spins are strongly coupled, so for low-energy dynamics only the motion of the total spin of the pair is relevant. This allows the construction of an effective Hamiltonian only involving the pairs' total spins. When this is semi-classically quantised via a 1/S expansion, they find that the zero-point spin wave motion destroys the magnetised ground state if either the number of spin states is sufficiently small (for fixed strength of disorder), or for sufficiently large disorder (for fixed number of spin states). Finally they discuss the relation of the model to the problem of Bose condensation in a random potential, where the interaction strength is related to the number of spin states in the spin model.
In this paper, we study the effect of a random quenched external field for spin order and also multiple Bose–Einstein condensation (BEC). This system is realized by the cold atomic gases in an optical lattice. In particular, we are interested in the strong-repulsion region of the two-component gases for which the bosonic t-J model is a good effective model. In the bosonic t-J model, a long-range order of the pseudo-spin and also BEC of atoms appear quite naturally as in the fermion t-J model for the high-temperature superconducting materials. Random Raman scattering between two internal states of a single atom plays a role of the random external field, and we study its effects on the pseudo-spin order and the BEC by means of quantum Monte-Carlo simulations. The random external field breaks a continuous U(1) symmetry existing in the original bosonic t-J model and it induces new orders, named random-field-induced order (RFIO). We show a phase diagram of the bosonic t-J model with the random external magnetic field and study the robustness of the RFIO states. We also study topological excitations like vortices and the domain wall in the RFIO state. Finally, we point out the possibility of a quantum bit by the RFIO.
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).