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

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

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### You want to scatter many photons to lower the photon shot noise, but ….

“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

Next challenge fluctuations”

Magnetic ordering - quantum magnetism

(ferromagnetism, antiferromagnetism, spin liquid, …)

Dominant entropy: spin entropy

Bosonic fluctuations” or fermionic Hubbard Hamiltonian

is equivalent to spin Hamiltonian (for localized particles)

Duan, Demler, Lukin (2003)

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

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

Not only the to Mott insulator transitionmean of the density distribution of ultracold gases

is relevant.

The fluctuations around the average can contain very useful

Information.

New methods to detect interesting new phases of matter to Mott insulator transition

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

New methods to detect interesting new phases of matter to Mott insulator transition

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

Spin fluctuations: relative density fluctuations to Mott insulator transition

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.

C. to Mott insulator transitionSanner, 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: to Mott insulator transition
- 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

imprinted structure to Mott insulator transition

in the atomic cloud

flat background (very good fringe cancellation)

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

6 photons/atom to Mott insulator transition

OD variance to Mott insulator transition

variance for Poissonian statistics

variance due to photonshot noise

atom number variance

Counting N atoms m times: to Mott insulator transition

Poissonian variance: N

Two standard deviations of the variance:

- “Pauli suppression” in Fermi gases to Mott insulator transition
- 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

Suppression of light scattering in Fermi gases to Mott insulator transition

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.

Using dispersion to measure relative density to Mott insulator transition

|e>

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

|2>

=-1/2, =0

|1>

=-1/2, =1

Absorption imaging of dispersive speckle to Mott insulator transition

Propagation after a phase grating:

a phase oscillation becomes an amplitude oscillation

Phase fluctuations lead to amplitude fluctuations after spatial propagation

BEC II to Mott insulator transition

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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