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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

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

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Characterizing many body systems by observing density fluctuations wolfgang ketterle

“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


Characterizing many body systems by observing density fluctuations wolfgang ketterle

Next challenge

Magnetic ordering - quantum magnetism

(ferromagnetism, antiferromagnetism, spin liquid, …)

Dominant entropy: spin entropy


Characterizing many body systems by observing density fluctuations wolfgang ketterle

Bosonic or fermionic Hubbard Hamiltonian

is equivalent to spin Hamiltonian (for localized particles)

Duan, Demler, Lukin (2003)


Characterizing many body systems by observing density fluctuations wolfgang ketterle

Magnetic Ground States

Z-Ferromagnet:

XY-Ferromagnet:

Antiferromagnet:


Characterizing many body systems by observing density fluctuations wolfgang ketterle

  • Towards quantum magnetism

  • Characterization of new quantum phases

  • density fluctuations to determine compressibility, spin susceptibilityand temperature

  • New cooling scheme

  • spin gradient demagnetization cooling


Characterizing many body systems by observing density fluctuations wolfgang ketterle

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


Characterizing many body systems by observing density fluctuations wolfgang ketterle

Not only the mean of the density distribution of ultracold gases

is relevant.

The fluctuations around the average can contain very useful

Information.


Characterizing many body systems by observing density fluctuations wolfgang ketterle

New methods to detect interesting new phases of matter

Density fluctuations

fluctuation-dissipation theorem

natomic density

Natom 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


Characterizing many body systems by observing density fluctuations wolfgang ketterle

New methods to detect interesting new phases of matter

Density fluctuations

fluctuation-dissipation theorem

natomic density

Natom number in probe volume V

Tisothermal compressibility

  • ideal classical gas

Poissonian fluctuations

  • non-interacting Fermi gas

sub-Poissonian

Pauli suppressionof fluctuations


Characterizing many body systems by observing density fluctuations wolfgang ketterle

Spin fluctuations: relative density fluctuations

fluctuation-dissipation theorem

Mmagnetization –N)

Vprobe volume

spin susceptiblity

Crossover or phase transitions, signature in :

For a paired or antiferromagnetic system, ,

For a ferromagnetic system, diverges.


Characterizing many body systems by observing density fluctuations wolfgang ketterle

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).


Characterizing many body systems by observing density fluctuations wolfgang ketterle

  • 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

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


Characterizing many body systems by observing density fluctuations wolfgang ketterle

6 photons/atom


Characterizing many body systems by observing density fluctuations wolfgang ketterle

transmission

optical density

noise


Characterizing many body systems by observing density fluctuations wolfgang ketterle

OD variance

variance for Poissonian statistics

variance due to photonshot noise

atom number variance


Characterizing many body systems by observing density fluctuations wolfgang ketterle

Noise thermometry

T/TF = 0.23 (1)

T/TF = 0.33 (2)

T/TF = 0.60 (2)


Characterizing many body systems by observing density fluctuations wolfgang ketterle

Shot noise

hot

cold


Characterizing many body systems by observing density fluctuations wolfgang ketterle

Counting N atoms m times:

Poissonian variance: N

Two standard deviations of the variance:


Characterizing many body systems by observing density fluctuations wolfgang ketterle

  • “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


Characterizing many body systems by observing density fluctuations wolfgang ketterle

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.


Characterizing many body systems by observing density fluctuations wolfgang ketterle

Noninteracting mixture

Paired mixture

<<

=


Characterizing many body systems by observing density fluctuations wolfgang ketterle

Using dispersion to measure relative density

|e>

=-3/2, =-1,0,1

|2>

=-1/2, =0

|1>

=-1/2, =1


Characterizing many body systems by observing density fluctuations wolfgang ketterle

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


Characterizing many body systems by observing density fluctuations wolfgang ketterle

0

527G 790G 915G

a<0

a>0

a=0

preliminary data


Characterizing many body systems by observing density fluctuations wolfgang ketterle

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


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