“Characterizing many-body systems by observing density fluctuations”

Wolfgang KetterleMassachusetts Institute of Technology

MIT-Harvard Center for Ultracold Atoms

8/7/2010

QFS 2010 Satellite WorkshopGrenoble

Next challengeMagnetic 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 phasesdensity fluctuations to determine compressibility, spin susceptibilityand temperature

• New cooling schemespin 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,Garchingpreprint, June 2010

Not only the mean of the density distribution of ultracold gasesis relevant.The fluctuations around the average can contain very usefulInformation.

New methods to detect interesting new phases of matter

Density fluctuations

fluctuation-dissipation theoremn atomic densityN atom number in probe volume VT 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 theoremn atomic densityN atom number in probe volume VT isothermal compressibility

ideal classical gas

Poissonian fluctuations

non-interacting Fermi gassub-PoissonianPauli suppressionof fluctuations

New methods to detect interesting new phases of matter

FT nE2

3

Spin fluctuations: relative density fluctuations

fluctuation-dissipation theoremM magnetization –N)V probe volume

spin susceptiblity

Crossover or phase transitions, signature in :For a paired or antiferromagnetic system, , For a ferromagnetic system, diverges.

(∆𝑀 )2=𝜒 (𝑘¿¿𝐵𝑇𝑉 )¿

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).

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

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 structurein the atomic cloud

flat background (very good fringe cancellation)

for the very light Li atoms, the recoil induced detuning is thedominant nonlinear effect

6 photons/atom

transmission

optical density

noise

OD variance

variance due to photonshot noise

atom number variance

variance for Poissonian statistics

Noise thermometry

T/TF = 0.23 (1) T/TF = 0.33 (2) T/TF = 0.60 (2)

Shot noisehot

cold

Counting N atoms m times:Poissonian variance: NTwo standard deviations of the variance: mN 22

“Pauli suppression” in Fermi gases

• two particle effects, at any temperature (but cold helps)Hanbury-Brown Twiss effect, antibunching

electrons: Basel, Stanford 1999neutral 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 fluctuationsMIT (2010)

suppression of light scattering (requires EF>Erecoil)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 mixture

<<

Paired mixture

Using dispersion to measure relative density

|2>=-1/2, =0

|1>=-1/2, =1

|e>=-3/2, =-1,0,1

20 40 60 80 100 120 140

20

40

60

80

100

120

140

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 IIUltracold fermions:Latticedensity fluct.Christian SannerAviv KeshetEd SuWujie HuangJonathon Gillen

BEC IIINa-LiFerromagnetismCaleb ChristensenYe-ryoung LeeJae ChoiTout WangGregory LauD.E. Pritchard

BEC IVRb BEC in optical latticesPatrick MedleyDavid WeldHiro MiyakeD.E. Pritchard$$

NSFONRMURI-AFOSRDARPA