of 20/20
Commensurate-Incommensurate phase transition in cold atomic gases Commensurate-Incommensurate phase transition in cold atomic gases 05/03/2010 SISSA, Trieste Marcello Dalmonte, Dipartimento di Fisica, Alma Mater Studiorum- Università di Bologna e Sezione INFN, Bologna

Commensurate-Incommensurate phase transition in cold ... · Commensurate-Incommensurate phase transition in cold atomic gases Commensurate-Incommensurate phase transition in cold

  • View
    3

  • Download
    0

Embed Size (px)

Text of Commensurate-Incommensurate phase transition in cold ... · Commensurate-Incommensurate phase...

  • Commensurate-Incommensurate phase transition in cold atomic gases

    Commensurate-Incommensurate phase transition in cold atomic gases

    05/03/2010SISSA, Trieste

    Marcello Dalmonte,Dipartimento di Fisica, Alma Mater Studiorum-

    Università di Bologna e Sezione INFN, Bologna

  • Journal club on...Journal club on...

    And complementary information and experiments:●W. Zwerger, arXiv:cond-mat/0211314v2;●T. Stöferle et al., Phys. Rev. Lett. 92, 130403 (2004);●D. Clément et al., Phys. Rev. Lett. 102, 155301 (2009).

  • Cold atoms in 1 DCold atoms in 1 D1D gas of bosons with contact interactions

    with dimensionless interaction strength:

    +optical lattice

  • Cold atoms and optical lattices: the deep lattice case

    Cold atoms and optical lattices: the deep lattice case

    D. Jaksch et al., PRL98D. Jaksch et al., PRL98

    When , atoms occupy the lowest vibrational level in each well

    Bose-Hubbard model

    SF

    MI

    Phase transition point:

  • Weak optical lattice: what happens?Weak optical lattice: what happens?

    Treat the lattice as a perturbation if the system is strongly interacting!

    Lieb-Liniger model + perturbation

    + optical lattice

  • Lieb-Liniger modelLieb-Liniger model

    T. Kinoshita et al., Science(2004); B. Paredes et al., Nature(2004).T. Kinoshita et al., Science(2004); B. Paredes et al., Nature(2004).

    Quasi-condensate

    Tonks gas,Fermionic limit

    More sensitive to perturbations!

  • Effective hydrodynamic approachEffective hydrodynamic approach

    F. D. M. Haldane, PRL 81 F. D. M. Haldane, PRL 81

    Density and phase felds with commutation relation:

    Depends on interactions, canbe determined via Bethe ansatz

  • Luttinger liquid pictureLuttinger liquid pictureRecasting the previous Hamiltonian in the Luttinger-liquid form:

    Only K determines the long-distance decay of correlation functions:

  • Weak lattice as a perturbationWeak lattice as a perturbation

    +

    =

    Close to one particle per site

  • Physical meaning of QPhysical meaning of Q

    Describes competition between two-lenghtscales!

    Inverse inter-particle distance Inverse lattice spacing

    Strong repulsion wants to maximise interparticle distance

    Background potential wants to pin particles at potential mimima

  • Sine-Gordon physics: Q=0Sine-Gordon physics: Q=0Commensurate case: the only relevant length-scale is the lattice spacing:

    BKT equations to evaluate a phase transition between superfuid and insulator

  • Sine-Gordon physics: Q=0Sine-Gordon physics: Q=0

    If , a vanishingly small optical lattice can pin all particles!

  • Non-commensurate case: Pokrovsky-Talapov model Non-commensurate case: Pokrovsky-Talapov model

    Rescaling the density:

    Leads to:

    Effective chemical potential for density

    excitations!

  • Energy competitionEnergy competitionCosine term: any excitation over

    the “commensurate” confguration cost an energy contribution

    proportional to the gap

    Chemical potential: excitations are favored for large enough Q

  • Effect of a trapping potentialEffect of a trapping potential

    True potential is inhomogeneous due to the trap

    Coexistence of insulator and superfuid regions!

    Density profle:

  • Add-ons: experimental setupAdd-ons: experimental setup

    E. Haller et al., arXiv:1002.3795E. Haller et al., arXiv:1002.3795

    1)Mott insulator of Cs atoms: the optical lattice is deep and 3D2)Lower down the lattice in one direction3)Tune the interaction between atoms with a resonance

  • Add-ons: experimental resultsAdd-ons: experimental results

    E. Haller et al., in preparationE. Haller et al., in preparation

    In excellent agreementwith BKT predictions

    even at V=2

    Confrms BH numerical predictions

  • Add-ons: spectrum and gap scalingAdd-ons: spectrum and gap scaling

    lattice depth0.7 Er1.0 Er1.4 Er2.1 Er

    Very good accordancewith Zamolodchikov

    formula for V

  • Open questions and suggestionsOpen questions and suggestionsWhat happens when both

    models break down?Gap scaling away from

    weak coupling?

    ●Dynamical properties of the sine-Gordon and PT models●Thermalization properties●Commensurate-incommensurate transition in 2D and 3D●Finite-size effects?

  • LabLab

    ElmarHaller

    Johann Danzl

    RussellHart

    Manfred Mark

    Mattias Gustavsson

    Hanns-Christoph Nägerl Lukas

    Reichsöllner

    OliverKriegelsteiner

    AndreasKlinger

    Guido Pupillo