“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 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 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 theorem
n 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 theorem
n 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 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.
(∆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, antibunchingelectrons: 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 II
Ultracold fermions:Latticedensity fluct.Christian SannerAviv KeshetEd SuWujie HuangJonathon Gillen
BEC III
Na-LiFerromagnetismCaleb ChristensenYe-ryoung LeeJae ChoiTout WangGregory LauD.E. Pritchard
BEC IV
Rb BEC in optical latticesPatrick MedleyDavid WeldHiro MiyakeD.E. Pritchard
$$NSFONRMURI-AFOSRDARPA
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