(Noise) correlations in optical lattices

Transcription

1 (Noise) correlations in optical lattices Dries van Oosten WA QUANTUM mainz.de/bec

2 The Teams The Fermions: Christoph Clausen Thorsten Best Ulrich Schneider Sebastian Will Lucia Hackermüller Dries van Oosten Tim Rom Martin Zwierlein The Bosons: Simon Fölling Stefan Trotzky Ute Schnorrberger Patrick Cheinet Michael Feld Theory: Belen Paredes Immanuel Bloch Artur Widera Olaf Mandel Fabrice Gerbier funding by DFG, EU Marie Curie Excellence Grant, Max Planck Gesellschaft $ AFOSR WA QUANTUM mainz.de/bec

3 getting atoms into the lattice time of flight imaging bosonic Mott isolator brillouin zone mapping fermionic band isolator noise correlations (anti)bunching superlattice tunneling dynamics outline

4 laser cooling red detuned laser beam v v doppler shift photon scattering atom "at rest": 100μK pretty cold!

5 laser setup setup laser laser cooling: (amplified) diode lasers 780nm for Rb & 767nm for K two species MOT a few K (fermion) a few Rb (boson)

6 the vacuum system MOT chamber: pretty good vacuum transport coils glas cell: very good vacuum

7 QUIC trap: sympathetic cooling of 40K with 87Rb QUIC trap: ωradial = 2π x 144Hz ωaxial = 2π x 22Hz for Rb (F=2, mf=2) pressure < mbar trap atoms using a magnetic trap use rf field to cut away the fastest Rb atoms let collisions re thermalise the atoms for ffinal = 2 MHz: NRb = NK =4.105 T = 2 µk very cold! source:

8 The optical dipole force Energy of a dipole in an electric field: U dip An electric field induces a dipole moment: r r =-d E r r d =ae U dip r - a (w) I (r ) Red detuning: Blue detuning: Atoms are trapped in the intensity maxima Atoms are repelled from the intensity maxima See R. Grimm et al., Adv. At. Mol. Opt. Phys. 42, (2000). Pioneering work by Steven Chu

9 crossed dipole trap 2 x 150 µm beam profile in trap center 1030nm, aspect ratio 1:4 Strongly anisotropic trap: ωvertical = 2π x 150Hz ωin plane = 2π x 25Hz for Rb (hyperfine state independent) Protects against differential sag "Homogeneous in plane"

10 crossed dipole trap: final cooling simultaneous quantum degeneracy!

11 how did we make these image? absorption imaging

12 what about the optical lattice 1) far red detuned crossed dipole trap: 2) blue detuned lattice: large homogeneous system (horizontal) small differential sag (vertical) 2 x 150 µm Independent control of lattice depth and external confinement controling relative mobility (tunneling t) of K and Rb magic wavelength 755 nm using K as localised random defects for Rb less spontaneous scattering, deep lattice blue lattice is anti confining

13 the band structure fast switch off: reveals momentum p distribution of atoms in the latice adiabatic ramp down: band population is conserved and crystal momentum q is mapped to free particle momentum p

14 superfluid to Mott insulator transition (bosons) phase coherence can be restored by ramping back to shallow lattice

15 band insulator (fermions) 4 Er deep lattice, increasing dipole power see also: M. Köhl et al., PRL 94, (2005)

16 Noise correlations: are all Gaussian clouds alike? TOF image of bosonic Mott insulator after sudden release TOF image of fermionic band insulator after sudden release no long range phase correlation filled band no structure in TOF no density modulation no structure in TOF

17 noise correlation measurement TOF image of fermionic band insulator after sudden release atoms on 100 x 100 pixels 10 atoms per pixel envelope is determined by on site single particle wave function (Wannier function) what is the source of the noise? atomic shot noise:

18 Hanbury Brown Twiss effect for atoms indistinguishable particles click click

19 Hanbury Brown Twiss effect for atoms alat indistinguishable particles there is another way click click d 2 Φ: relative phase accumulated when propagating from source to detector

20 Hanbury Brown Twiss effect for atoms alat indistinguishable particles d 2 Φ: relative phase accumulated when propagating from source to detector

21 Hanbury Brown Twiss effect for atoms Bosonic 87Rb TOF image correlation function! experiment: S. Fölling et al., Nature 434, 481 (2005) theory: E. Altman, E. Demler & M. Lukin, PRA 70, (2004).

22 Hanbury Brown Twiss effect for atoms indistinguishable particles d 2 Φ: relative phase accumulated when propagating from source to detector

23 fermionic anti bunching with atoms Rom et. al Nature (2007) time of flight correlation function first observation of anti bunching with neutral atoms!

24 how to make a superlattice 1530 nm & 765 nm L For a real L=0.25m: 500MHz freq change

25 how to make a superlattice +250 MHz 250 MHz

26 patterned loading of the short lattice Mott Insulator in 1530 lattice Increase 765 lattice Switch off 1530 lattice Release?

27 2ħk840 noise correlations with patterned loading 2ħk765 2ħk1530

28 An array of double wells t=0 t = h / 2J No Interference Interference Max. Contrast Few atom BEC in a double well potential: M. Albiez et al., PRL 95, (2005) Controlled atom dynamics in a double-well lattice: M. Anderlini et al., JPB 39, , (

29 Single Atom tunneling Two Mode Model with Tunnelcoupling: φ = π 2J 2J sign sin C = abs sin 2 t t Phase Visibility t (ms)

30 Two atom tunneling Atom pair is shifted by U First order tunneling of a single atom is detuned Second order tunneling of the atom pair still resonant Correlated tunneling of the atom pair due to the repulsive interaction resonant J U 2 U detuned J 2 +U 2 Repulsively bound pairs in an optical lattice: K. Winkler et al., Nature 441, (2006)

31 Atom Pair Tunneling: J/U = 0.25 Population Imbalance Phase Visibility Time (ms)

32 Switching the tunneling: Tilted Doublewells E By tilting the double wells single atom tunneling can be made resonant again

33 Measuring population imbalance directly Transferring R to higher vibrational bands, leaving L in the ground state Adiabatic mapping of the Brillouin zones Preparing and probing atomic number states with an atom interferome J. Sebby-Strabley et al., arxiv:quant-ph/ v1, (2007)

34 conclusion and outlook noise correlations: bunching and anti bunching patterned loading using a superlattice interference images: reveals momentum determine phase coherence study tunneling dynamics brillouin zone mapping: reveals quasi momentum determine band population study excitations