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Hanns-Christoph Nägerl Institut für Experimentalphysik, Universität Innsbruck Atoms with tunable interactions in optical lattice confinement 1700 m Firenze, May 21 st 2012: New quantum states of matter in and out of equilibrium

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theory support (Strasbourg/Innsbruck/Pittsburgh): Guido Pupillo / Marcello Dalmonte / Andrew Daley new phd and master students: Nobie Redmon Florian Meinert Philipp Meinmann Michael Gröbner P. Schmelcher (Hamburg) V. Melezhik (Dubna) H. Ritsch (Innsbruck) N. Bouloufa (Orsay) O. Dulieu (Orsay) collaborators: T. Bergeman (Stony Brook) H.-P. Büchler (Stuttgart) J. Aldegunde (Durham) J. Hutson (Durham) P. S. Julienne (NIST) Elmar Haller (now to Glasgow) Johann Danzl (now to Göttingen) Katharina Lauber Manfred Mark B. Rutschmann CsIII-Team CsIII-Project Team Members & Collaborators…

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Bose-Hubbard Physics U<0 and U=U(n) n = particle number at the lattice sites Motivation: Bosons in lattices and confined dimensions

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Feshbach resonance two atoms B E molecule B aSaS a bg B0B0 ¢ = coupling scattering length a S = a S ( B ) Tuning of interactions: Feshbach resonances

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scattering length for 2 atoms in hyperfine states (F,m F )= (3,3) magnetic field B (Gauss) 0 10 scattering length a S (1000 a 0 ) -10 5 -5 this talk… (lets zoom in) s s broad s-resonances calculations by P. Julienne et al., NIST

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Tuning of interactions: Feshbach resonances 0 5050 100 150 0 d d d g g g g magnetic field B (Gauss) scattering length a S (1000 a 0 ) 1 2 -2 zero crossing …or here make mols here… make BEC here g tune here narrower d-resonances very narrow g-resonances scattering length for 2 atoms in hyperfine states (F,m F )= (3,3) calculations by P.Julienne et al., NIST

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Tuning of interactions: three-body loss Kraemer et al., Nature 440, 315 (2006) scattering length a S (1000 a 0 ) recombination length ½ 3 (1000 a 0 ) ½ 3 / K 3 1/4 K 3 = three-body loss rate coefficient K 3 / a 4 Efimov resonance

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Basic concepts of lattice physics The standard Bose-Hubbard model Tunneling matrix element On-site interaction energy External energy shift External potential ε Tunneling J Interaction U Approximations Bloch bands Higher Bloch bands omitted U No nearest neighbor interaction Interactions Tunneling No next nearest neighbor tunneling J Interaction potential Simple non-regularized pseudopotential

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Properties of the Bose-Hubbard (BH) model Groundstates at T=0 Superfluid J»U Delocalized particles Coherent phase No excitation gap Phase diagram J/U µ/U insulator n=2 insulator n=1 superfluid Mott insulator J«U Localized particles No phase coherence Excitation gap Experiment External confinement wedding cake structure Exps: Bloch, Esslinger, Greiner,…

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Probing the phase transition Experimental setup Tunneling J Interaction U External potential ε Lattice depth Scattering length Dipole trap Probe coherence by ToF measurements Measurement method µ/U insulator n=1 superfluid J/U superfluidMott insulator Lattice depth time

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Probing the phase transition Mark et al. Phys. Rev. Lett. 107, 175301 (2011) FWHM Observable Kink in FWHM Results 212 a 0 320 a 0 427 a 0 J/U µ/U Phase transition point aS=aS=

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Measuring the excitation spectrum MI excitation spectrum Elementary MI excitations U 2UU Measurement method Amplitude modulation time Lattice depth Experimental sequence

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Measuring the excitation spectrum Results U2U a S =212 a 0 Mark et al. Phys. Rev. Lett. 107, 175301 (2011) U 2UU 320 a 0 Resonance splitting near U-peak 427 a 0 Density dependence

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Beyond the standard BH model Approximations Bloch bands Interaction potential Invalid for strong interactions Three particles 3x two-particle interactions Effective interactions Johnson et al. New J. Phys. 11, 093022 (2009) Efimov physics dimer Efimov trimer +1/a Energy -1/a Two particles Busch et al. Found. of Physics 28, 549 (1998) Schneider et al. Phys. Rev. A 80, 013404 (2009) Büchler et al. Phys. Rev. Lett. 104, 090402 (2010) +a Energy -a Kraemer et al. Nature 440, 315 (2006)

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Beyond the standard BH model Expectation U(2) 3U(3)- U(2) 3U(3)- 2U(2) Double occupancyThree-body loss 427 a 0 Mark et al. Phys. Rev. Lett. 107, 175301 (2011) 3xU U 3xU(3) U(2) Density dependence High density Intermediate Low density 427 a 0 Measurement 3U(3)-2U(2) U(2)

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Theory and Experiment 2U BH U BH 3U(3)-U(2) 3U(3)-2U(2) U(2) Mark et al. Phys. Rev. Lett. 107, 175301 (2011) 2U BH U BH 3U(3)-U(2) 3U(3)-2U(2) U(2) (see also work by I. Blochs group, S. Will et al., Nature 465, 197 (2010))

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Attractive interactions BH model with negative U Three-body loss Γ3Γ3 Superfluid J»|U| Γ3Γ3 Mott insulator J«|U| Γ3Γ3 Mott insulator J«|U| Metastable Highly excited state of the system

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Preparation of the attractive MI state Lattice loading Repulsive Mott insulator Switch to attractive a Γ3Γ3 Wait / modulate Switch to repulsive a Observe overall heating depth 20 E R

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Stability of the attractive MI state Varying interactions Mark et al., to appear in PRL (2012) hold time = 50 ms blue areas: narrow Feshbach resonances zero crossing

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Stability of the attractive MI state Varying interactions Mark et al., to appear in PRL (2012) hold time = 50 ms Varying the hold time -2000 a 0 -240 a 0 +220 a 0

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De-excitation spectrum U BH 3U(3)-2U(2) U(2) U*(2) U(2) 3U(3)- 2U(2) U*(2) Excitation resonances U(2) 3U(3) - 2U(2) -306 a 0 ? Mark et al., to appear in PRL (2012)

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Three-body loss resonance Fast broadening of the resonance Rate of three-body loss without lattice Kraemer et al., Nature 440, 315 (2006) Three-body loss rate Γ3Γ3 Γ3Γ3 Three-body loss Mark et al., to appear in PRL (2012)

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Suppressed three-body loss: Quantum Zeno effect Analogy Large three-body loss stabilizes! :

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Comparison of loss widths Attractive interactionsRepulsive interactions

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Comparison of loss widths Attractive interactionsRepulsive interactions

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Comparison of loss widths Attractive interactionsRepulsive interactions Γ3Γ3

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Comparison of loss widths Attractive interactionsRepulsive interactions superfluid of dimers? (Theroy: A. Daley et al., PRL 2009)

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Ongoing work Start with one-atom Mott insulator…

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Ongoing work Then apply lattice tilt and create doublons… see Greiner group quantum magnetism

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Ongoing work: Doublon creation (very preliminary) in an array of 1D-tubes so far: 75% doublon creation so far: 75% doublon creation

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Ongoing work … and then watch dynamics as the lattice depth is lowered…

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Thank you!

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