“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
(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)
Magnetic Ground States
Z-Ferromagnet:
XY-Ferromagnet:
Antiferromagnet:
Towards quantum magnetism
• Characterization of new quantum phases
density fluctuations to determine compressibility, spin susceptibility
and 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 mean 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
Density fluctuations
fluctuation-dissipation theorem
n
N
T
atomic density
atom number in probe volume V
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
New methods to detect interesting new phases of matter
Density fluctuations
fluctuation-dissipation theorem
n
N
T
atomic density
atom number in probe volume V
isothermal compressibility
 ideal classical gas
Poissonian fluctuations
 non-interacting Fermi gas
3
T 
2nEF
sub-Poissonian
Pauli suppression
of fluctuations
Spin fluctuations: relative density fluctuations
fluctuation-dissipation theorem
M
magnetization (N –N)
V
probe volume
(∆𝑀)2 = 𝜒(𝑘𝐵 𝑇𝑉)
𝜕𝑚
𝜒
spin susceptiblity
𝜕𝐻
Crossover or phase transitions, signature in 𝜒 :
For a paired or antiferromagnetic system, 𝜒 = 0,
For a ferromagnetic system, 𝜒 diverges.
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).
Advantages:
Expansion:
 more
magnifies
spatial
spatial
resolution
scale elements than for in-trap imaging
 adjustment
locally preserves
of optimum
Fermi-Dirac
opticaldistribution
density through
with same
ballistic
T/Texpansion
F
 no
same
high
fluctuations
magnification
as innecessary
situ
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)
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
transmission
optical density
noise
OD variance
variance for Poissonian statistics
variance due to photon
shot noise
atom number variance
Noise thermometry
T/TF = 0.23 (1)
T/TF = 0.33 (2)
T/TF = 0.60 (2)
Shot noise
hot
cold
Counting N atoms m times:
Poissonian variance: N
Two standard deviations of the variance:
2N 2 m
“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
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.
Noninteracting mixture
2
(∆(N−N)) = (∆(N+N))
2
Paired mixture
2
(∆(N−N)) << (∆(N+N))
2
Using dispersion to measure relative density
|e>
𝑚𝐽 =-3/2, 𝑚𝐼 =-1,0,1
|2>
𝑚𝐽 =-1/2, 𝑚𝐼 =0
|1>
𝑚𝐽 =-1/2, 𝑚𝐼 =1
𝜑 ∝ 𝑁1 − 𝑁2
𝜑 ∝ 𝑁1 +
1
𝑁
3 2
Absorption imaging of dispersive speckle
Propagation after a phase grating:
a phase oscillation becomes an
amplitude oscillation
20
40
Phase fluctuations lead to
amplitude fluctuations after
spatial propagation
60
80
100
120
140
20
40
60
80
100
120
140
0
527G
790G
a=0
a>0
preliminary data
915G
a<0
BEC II
Ultracold
fermions:
Lattice
density fluct.
Christian Sanner
Aviv Keshet
Ed Su
Wujie Huang
Jonathon Gillen
$$
NSF
ONR
MURI-AFOSR
DARPA
BEC III
Na-Li
Ferromagnetism
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