1. 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

2. 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…

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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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,…

10. 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

11. 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=

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

13. 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

14. 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)

15. 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)

16. 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))

17. 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

18. 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

19. 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

20. 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

21. 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)

22. 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)

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

24. Comparison of loss widths Attractive interactionsRepulsive interactions

25. Comparison of loss widths Attractive interactionsRepulsive interactions

26. Comparison of loss widths Attractive interactionsRepulsive interactions Γ3Γ3

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

28. Ongoing work Start with one-atom Mott insulator…

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

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

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

32. Thank you!