“characterizing many-body systems by observing density fluctuations” wolfgang ketterle
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“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 - PowerPoint PPT PresentationTRANSCRIPT
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“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
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Next challengeMagnetic ordering - quantum magnetism(ferromagnetism, antiferromagnetism, spin liquid, …)
Dominant entropy: spin entropy
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Bosonic or fermionic Hubbard Hamiltonian
is equivalent to spin Hamiltonian (for localized particles)
Duan, Demler, Lukin (2003)
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Z-Ferromagnet:
XY-Ferromagnet:
Antiferromagnet:
Magnetic Ground States
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Towards quantum magnetism
• Characterization of new quantum phasesdensity fluctuations to determine compressibility, spin susceptibilityand temperature
• New cooling schemespin gradient demagnetization cooling
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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
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Not only the mean of the density distribution of ultracold gasesis relevant.The fluctuations around the average can contain very usefulInformation.
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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
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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
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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 )¿
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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).
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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
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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
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6 photons/atom
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transmission
optical density
noise
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OD variance
variance due to photonshot noise
atom number variance
variance for Poissonian statistics
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Noise thermometry
T/TF = 0.23 (1) T/TF = 0.33 (2) T/TF = 0.60 (2)
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Shot noisehot
cold
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Counting N atoms m times:Poissonian variance: NTwo standard deviations of the variance: mN 22
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“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
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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
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=
Noninteracting mixture
<<
Paired mixture
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Using dispersion to measure relative density
|2>=-1/2, =0
|1>=-1/2, =1
|e>=-3/2, =-1,0,1
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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
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527G 790G 915G
0
a=0 a>0 a<0
preliminary data
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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