“Characterizing many-body systems by observing density fluctuations” Wolfgang Ketterle

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

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

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

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

5. Towards quantum magnetism • Characterization of new quantum phases • density fluctuations to determine compressibility, spin susceptibilityand temperature • New cooling scheme • spin gradient demagnetization cooling

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

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

8. New methods to detect interesting new phases of matter Density fluctuations fluctuation-dissipation theorem n atomic density N atom number in probe volume V Tisothermal 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

9. New methods to detect interesting new phases of matter Density fluctuations fluctuation-dissipation theorem n atomic density N atom number in probe volume V Tisothermal compressibility • ideal classical gas Poissonian fluctuations • non-interacting Fermi gas sub-Poissonian Pauli suppressionof fluctuations

10. Spin fluctuations: relative density fluctuations fluctuation-dissipation theorem M magnetization –N) V probe volume spin susceptiblity Crossover or phase transitions, signature in : For a paired or antiferromagnetic system, , For a ferromagnetic system, diverges.

12. C. Sanner, E.J. Su, A. Keshet, R. Gommers, Y. Shin, W. Huang, and W. Ketterle: Phys. Rev. Lett. 105, 040402 (2010). related work: Esslinger group, PRL 105, 040401 (2010).

13. Expansion: • magnifies spatial scale • locally preserves Fermi-Dirac distribution with same T/TF • 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

14. imprinted structure in the atomic cloud flat background (very good fringe cancellation) 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 for the very light Li atoms, the recoil induced detuning is the dominant nonlinear effect

15. 6 photons/atom

16. transmission optical density noise

17. OD variance variance for Poissonian statistics variance due to photonshot noise atom number variance

18. Noise thermometry T/TF = 0.23 (1) T/TF = 0.33 (2) T/TF = 0.60 (2)

19. Shot noise hot cold

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

22. “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 << TF • freezing out of collisions (between two kinds of fermions) JILA (2001) • suppression of density fluctuations • MIT (2010) • suppression of light scattering (requires EF>Erecoil) • not yet observed

23. Suppression of light scattering in Fermi gases 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.

24. Noninteracting mixture Paired mixture << =

25. Using dispersion to measure relative density |e> =-3/2, =-1,0,1 |2> =-1/2, =0 |1> =-1/2, =1

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

27. 0 527G 790G 915G a<0 a>0 a=0 preliminary data

28. BEC II Ultracold fermions:Latticedensity fluct.Christian Sanner Aviv Keshet Ed Su WujieHuang Jonathon Gillen BEC III Na-LiFerromagnetism 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 ONRMURI-AFOSR DARPA