Creating the Toolbox of Mesoscopic Physics for Quantum Gases

Transcription

1 Creating the Toolbox of Mesoscopic Physics for Quantum Gases Tilman Esslinger ETH Zürich Funding: ETH, EU (ERC, NameQuam, Scala), NCCR QSIT, MaNEP, SNF

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3 Superconductivity Resistance Temperature Kamerlingh-Onnes 1911

4 Superconductivity BCS-Theory

5 Hamiltonian Access Many-Body Physics

6 Open questions: H?" Novel models, devices, surprises?

7 Fermi-Hubbard (U>0) H = t cˆ cˆ + U nˆ nˆ { i j},, σ i, σ j, σ i, i, i

8 Fermi-Hubbard (U>0) H = t cˆ cˆ + U nˆ nˆ { i j},, σ i, σ j, σ i, i, i

9 Fermi-Hubbard (U>0) H = t cˆ cˆ + U nˆ nˆ { i j},, σ i, σ j, σ i, i, i d-wave superconductor Scalapino, Phys. Rep. 250, 329 (1995) Hofstetter et al., Phys. Rev. Lett. 89, (2002)

10 Fermi-Hubbard (U>0) H = t cˆ cˆ + U nˆ nˆ { i j},, σ i, σ j, σ i, i, i d-wave superconductor Scalapino, Phys. Rep. 250, 329 (1995) Hofstetter et al., Phys. Rev. Lett. 89, (2002)

11 Let s Quantum build the Hubbard Simulator Model + Quantum Gases ( 40 K) Optical Lattices See also: Mainz/Munich, Hamburg, MIT, Houston,

12 potential consists of a lattice + confining potential distance between lattice sites: 500 nm quantum gas populates more than 100,000 lattice sites

13 Measuring I

14 tight-binding weak potentials free atoms /2 /2 /2 /2 /2 /2

15 Measuring I

16 Measuring II

17 Measuring II Metal Mott-Insulator

18 Measuring Double Occupancy m F =-9/2 m F =-7/2 m F =-5/2

19 Suppression of double occupancy U/(6J)=0 U/(6J)=4.8 R. Jördens, N. Strohmaier, K. Günter, H. Moritz, T. Esslinger, Nature 455, 204 (2008). See also: U. Schneider et al., Science 322, 1520 (2008).

20 Quantitative comparison depletion of band insulator depletion of Mott insulator R. Jördens, L. Tarruell,D. Greif, T. Uehlinger, N. Strohmaier, H. Moritz,T. Esslinger, L. De Leo, C. Kollath, A. Georges, V. Scarola, L. Pollet, E. Burovski, E. Kozik, and M. Troyer Phys. Rev. Lett. 104, (2010)

21 Magnetic order? Mean field: Heisenberg (QMC): s Néel = ln2 s Néel =0.338(5) ln2/2

22 Quantum Magnetism

23 Temperature challenge Metal Current temperature U Mott insulator Exchange: J=4t 2 /U Spin ordering

24 Approaches to Magnetism removing of entropy in the trap Proposal: J.-S. Bernier, C. Kollath, A. Georges, L. D. Leo, F. Gerbier, C. Salomon, and M. Köhl, Phys. Rev. A 79, (R) (2009) Experiment: effective model for Ising spin chain: J. Simon et al. Nature 472, 307 (2011) Experiment: frustrated classical magnetism, J. Struck, et al. Science 333, 996 (2011)

25 The Tool

26 The Tool X and Y + X and Y V(x,y) =V X cos 2 (kx + θ / 2)+V X cos 2 (kx)+v Y cos 2 (ky)+ 2α V X V Y cos(kx)cos(ky)

27 Tunable geometry optical lattice Chequerboard Dimer 1D chains V X V =0 X Triangular Honeycomb Square Non-standard lattices: Phillips, Bloch, Sengstock, Weitz, Hemmerich, Samper-Kurn,

28 The Idea

29 The Idea J T J s Dimerized lattice

30 The Idea J T J s Dimerized lattice Anisotropic lattice

31 Detection Observable: neighboring sites T J s Triplet T Singlet S (, > +, > ) (, > -, > ) N S > N T

32 Detecting magnetic correlations 2. Induce singlet-triplet 1. Suppress Merge Detection tunneling sites Rabi oscillations Measure number of singlets, triplets and singlet-triplet imbalance See: S. Trotzky et al., Phys. Rev. Lett. 105, (2010)

33 Detecting magnetic correlations D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, and T. Esslinger, arxiv: , Science Express 23 May 2013

34 Detecting magnetic correlations D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, and T. Esslinger, arxiv: , Science Express 23 May 2013

35 Detecting magnetic correlations t d /t=20 D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, and T. Esslinger, arxiv: , Science Express 23 May 2013

36 Detecting magnetic correlations

37 Detecting magnetic correlations

38 Anisotropic lattice

39 Detecting magnetic correlations D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, and T. Esslinger, arxiv: , Science Express 23 May 2013

40 Detecting magnetic correlations D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, and T. Esslinger, arxiv: , Science Express 23 May 2013

41 Quantum Simulation of the Fermi-Hubbard Model Lower temperature d-wave Quantum Magnetism Phase diagram Mott-insulator Quantum degeneracy Control create system determine phases quantitative understanding microscopic access

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45 Transport in cold atoms

46 Transport in cold atoms

47 Conduction

48 Conduction I V ases transitions, superconductivity, ballistic/diffusive conduction, quantized conductances, insulating phases, superc

49 Non-equilibrium steady-state V µ R I µ - ev

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52 300 µm 30 µm Left Reservoir NL Right Reservoir NR

53 Conduction is transmission from one reservoir to another µ L µ R Landauer ( ) Finite resistance without scattering + Büttiker

54 Inducing a chemical potential bias Symmetric position Shift trap (slow) Evaporative cooling Shift trap back (fast)

55 Fermi battery reservoir channel reservoir N L N R

56 Battery discharge ΔN/N time (s) G: conductance C: compressibility N µ

57 Ohm s law Current (10 3 /s) Confinements: 3.9 khz and 3.2 khz Number imbalance (10 3 ) J.-P. Brantut, J. Meineke, D. Stadler, S. Krinner, T. Esslinger, Science 337, 1069 (2012)

58 Landauer formula G = N c h N c Ratio of conductances: G(3.2) G(3.9) =0.76(10) 0.82 N c : number of channels

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60 In-situ observation reservoir channel reservoir 1 px 600 nm

61 Density difference with/without current reservoir channel reservoir 1 px 600 nm

62 Density difference with/without current contact contact channel reservoir channel reservoir

63 Diffusive Channel See also: Aspect, Inguscio, Hulet, DeMarco

64 Diffusive Channel channel J.-P. Brantut, J. Meineke, D. Stadler, S. Krinner, T. Esslinger, Science 337, 1069 (2012)

65 Diffusive Channel channel J.-P. Brantut, J. Meineke, D. Stadler, S. Krinner, T. Esslinger, Science 337, 1069 (2012)

66 And a Superfluid?

67 Superfluid Flow

68 Superfluid Flow See also: Superfluid two-dimensional Bose gas, R. Desbuquois et al., Nature Physics 8, 645 (2012).

69 Superfluid Flow Finite resistance! Gate potential U (µk) r = τ ω y 1 = RCω y

70 Superfluid Flow

71 Looking in-situ Intrinsic transport property Dri0 velocity Thermodynamic scale Ω( U)= n col ( V) dv U Ku et al., Science 335, (2012) Horikoshi et al. Science 327, 442 (2010) Nascimbène et al., Nature 463, (2010)

72 Superfluid Flow David Stadler, Sebastian Krinner, Jakob Meineke, Jean-Philippe Brantut, Nature 491, 736 (2012).

73 Drift velocity Ω Ω 0 Pressure of 2D idael Fermi gas: Ω 0 = π 2 2 n col m

74 Drop of resistance Normalized Resistance Normalized Pressure

75 Disorder and strongly interaction superfluid Molecular BEC Molecular BEC See also: Aspect, Inguscio, Hulet, DeMarco

76 Length Scales Correlation length of disorder: =300 nm Size of the molecules: 200 nm Healing length: 250 nm

77 Disorder and strongly interaction superfluid Correlation energy 2 mσ 2 Classical percolation threshold

78 Disorder and strongly interaction superfluid B = R BEC R WIF = Κ τ BEC τ WIF : ratio of the reservoir compressibility Percolation plays important role

79 Disorder and strongly interaction superfluid T=0 TF-approx in random pot. (Bourdel et al. PRA 86, ) Finite density Finite compressibility! 2 m dn dµ = n d2 d 2 x 2 m 2 ω x 2

80 Outlook

81 Thanks! Funding: ETH, SNF (QSIT, MaNEP), EU (NameQuam), ERCadv Quantum Gases in Optical Lattices Leticia Tarruell Daniel Greif Thomas Uehlinger Gregor Jotzu Martin Lebrat Lithium Microscope Jakob Meineke David Stadler Jean-Philippe Brantut Sebastian Krinner Dominik Husmann BEC and Cavity Ferdinand Brennecke Rafael Mottl Tobias Donner Renate Landig Impact experiment Tobias Donner Julian Leonard Laura Corman Moonjoo Lee Leigh Martin Christian Zosel Electronics Alexander Frank Administration Veronica Bürgisser Former Members: Torben Müller, Kristian Baumann (Stanford), Silvan Leinss, Robert Jördens (NIST), Bruno Zimmermann, Henning Moritz (Hamburg), Christine Guerlin (Thales), Niels Strohmaier (Hamburg),Thomas Bourdel (Palaiseou), Kenneth Günter, Michael Köhl (Cambrigde), Anton Öttl, Stephan Ritter (MPQ), Thilo Stöferle (IBM), Yosuke Takasu (U Kyoto) Theory discussions: Ehud Altmann, Gianni Blatter, Georg Bruun, Eugene Demler, Antoine Georges, Thierry Giamarchi, Gian Michele Graf, Sebastian Huber, Corinna Kollath, Dario Poletti, Christian Rüegg, Manfred Sigrist, Wilhelm Zwerger,