“Characterizing many-body systems by observing density fluctuations” Wolfgang Ketterle Massachusetts Institute of Technology MIT-Harvard Center for Ultracold Atoms 8/7/2010 QFS 2010 Satellite Workshop Grenoble

Next challenge Magnetic ordering - quantum magnetism (ferromagnetism, antiferromagnetism, spin liquid, …) Dominant entropy: spin entropy

Bosonic or fermionic Hubbard Hamiltonian is equivalent to spin Hamiltonian (for localized particles) Duan, Demler, Lukin (2003)

Z-Ferromagnet: XY-Ferromagnet: Antiferromagnet: Magnetic Ground States

Towards quantum magnetism Characterization of new quantum phases density fluctuations to determine compressibility, spin susceptibility and temperature New cooling scheme spin gradient demagnetization cooling

Greiner labs (Harvard) Science, 6/17/2010 Single site resolution in a 2D lattice across the superfluid to Mott insulator transition Bloch group, Garching preprint, June 2010

Not only the mean of the density distribution of ultracold gases is relevant. The fluctuations around the average can contain very useful Information.

New methods to detect interesting new phases of matter Density fluctuations fluctuation-dissipation theorem natomic density Natom number in probe volume V  T isothermal compressibility Crossover or phase transitions, signature in  T : Mott insulator, band insulator are incompressible Sub-shot noise counting of (small number of) bosons: Raizen, Oberthaler, Chin, Greiner, Spreeuw, Bloch, Steinhauer

Density fluctuations fluctuation-dissipation theorem natomic density Natom number in probe volume V  T isothermal compressibility  ideal classical gas Poissonian fluctuations  non-interacting Fermi gas sub-Poissonian Pauli suppression of fluctuations New methods to detect interesting new phases of matter

Spin fluctuations: relative density fluctuations fluctuation-dissipation theorem

C. Sanner, E.J. Su, A. Keshet, R. Gommers, Y. Shin, W. Huang, and W. Ketterle: Phys. Rev. Lett. 105, (2010). related work: Esslinger group, PRL 105, (2010).

Expansion:  magnifies spatial scale  locally preserves Fermi-Dirac distribution with same T/T F  same fluctuations as in situ Advantages:  more spatial resolution elements than for in-trap imaging  adjustment of optimum optical density through ballistic expansion  no high magnification necessary

You want to scatter many photons to lower the photon shot noise, but …. IMPRINT MECHANISMS -Intensities close to the atomic saturation intensity -Recoil induced detuning (Li-6: Doppler shift of 0.15 MHz for one photon momentum) -Optical pumping into dark states imprinted structure in the atomic cloud flat background (very good fringe cancellation) for the very light Li atoms, the recoil induced detuning is the dominant nonlinear effect

6 photons/atom

transmission optical density noise

OD variance variance due to photon shot noise atom number variance variance for Poissonian statistics

Noise thermometry T/T F = 0.23 (1)T/T F = 0.33 (2)T/T F = 0.60 (2)

Shot noise hot cold

Counting N atoms m times: Poissonian variance: N Two standard deviations of the variance:

“Pauli suppression” in Fermi gases two particle effects, at any temperature (but cold helps) Hanbury-Brown Twiss effect, antibunching electrons: Basel, Stanford 1999 neutral atoms: Mainz (2006), Orsay (2007) two particle effects, at low temperature (but not degenerate) freezing out of collisions (when db <range of interactions): elastic collisions JILA (1997) clock shifts MIT (2003) many-body effects, requires T << T F freezing out of collisions (between two kinds of fermions) JILA (2001) suppression of density fluctuations MIT (2010) suppression of light scattering (requires E F >E recoil ) not yet observed

so far not observed For 20 years: Suggestions to observe suppression of light scattering (Helmerson, Pritchard, Anglin, Cirac, Zoller, Javanainen, Jin, Hulet, You, Lewenstein, Ketterle, Masalas, Gardiner, Minguzzi, Tosi) But: Light scattering d  /dq  S(q) is proportional to density fluctuations which have now been directly observed. Note: For our parameters, only scattering of light by small angles is suppressed. Total suppression is only 0.3 % - does not affect absorption imaging. Suppression of light scattering in Fermi gases

Noninteracting mixturePaired mixture

Using dispersion to measure relative density

Propagation after a phase grating: a phase oscillation becomes an amplitude oscillation Phase fluctuations lead to amplitude fluctuations after spatial propagation Absorption imaging of dispersive speckle

527G 790G 915G 0 a=0 a>0 a<0 preliminary data

BEC II Ultracold fermions: Lattice density fluct. Christian Sanner Aviv Keshet Ed Su Wujie Huang Jonathon Gillen BEC III Na-Li Ferromagnetism Caleb Christensen Ye-ryoung Lee Jae Choi Tout Wang Gregory Lau D.E. Pritchard BEC IV Rb BEC in optical lattices Patrick Medley David Weld Hiro Miyake D.E. Pritchard $$ NSF ONR MURI-AFOSR DARPA