Fluctuations in Strongly Interacting
Fermi Gases
Christian Sanner, Jonathon Gillen, Wujie Huang, Aviv Keshet,
Edward Su, Wolfgang Ketterle
Center for Ultracold Atoms
MIT
1. Why is it interesting to measure fluctuations?
2. Fluctuations in an ideal Fermi gas
3. Speckle imaging and pair correlations along the
BEC-BCS crossover
4. Ferromagnetic instability and fluctuations in
repulsively interacting Fermi gases
Many layers of information in the
atomic density distribution
Not only the mean of the density distribution of ultracold gases
is relevant.
The fluctuations around the average can contain very useful
information that is not accessible via the mean values.
Fluctuation-Dissipation Theorem
Fluctuations in a system at
thermal equilibrium
Response of the system to
applied perturbations
1
G ( xl , xl ' )   ( xl , xl ' )
kT
e.g. for number fluctuations in the grand canonical ensemble:
V 1
2
(N )  T
2
N k BT
Suppression of fluctuations in an ideal
Fermi Gas
V 1
2
(

N
)
 T
2
N k BT
V
(N )
T 

1
Nk BT
N
2
Classical ideal gas:
Poissonian fluctuations
Ideal Fermi gas:
2
3V
(

N
)
3 k BT
T 0
T 



2 NEF
N
2 EF
Sub-Poissonian fluctuations
Suppression of density fluctuations in
an ideal Fermi Gas
Suppression of fluctuations in an ideal
Fermi Gas
harmonic
confinement
binomialvariancenk (1  nk ) integratedoverall momenta
Measuring the fluctuations
1. Photon shot noise
In bright field observation the spatial distribution of detected
photons is going to show the typical projection noise
N  N
more photons
Two divided frames
at low intensity:
Two divided frames
at high intensity:
N
reduced relative noise t 
N
Measuring the fluctuations
2. Technical noise
- fringes, fringes, fringes ... due to reflections, scattering, dust etc.
- Detector noise, CCD response fluctuations
By carefully choosing a detector with high QE and
very short acquisition times (a few 100µs between
atom and reference shot, vibrations!) and operating
at sufficient light levels we obtain images that are
photon shot noise limited in the atom free regions.
Measuring the fluctuations
3. Noise due to nonlinear effects
imprinted structure
in the atomic cloud
flat background (very
good fringe cancellation)
IMPRINT MECHANISMS
-Intensities close to the atomic saturation intensity
-Recoil induced detuning (Li6: 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
transmission
optical density
noise
expanded cloud 1/qFermi = 1.1 m
quantum fluctuations…..
0.23 ± .01 TF
0.33 ± .02 TF
0.60 ± .02 TF
1. Why is it interesting to measure fluctuations?
2. Fluctuations in an ideal Fermi gas
3. Speckle imaging and pair correlations along the
BEC-BCS crossover
4. Ferromagnetic instability and fluctuations in
repulsively interacting Fermi gases
Speckle imaging
Measuring Susceptibility and
Compressibility
3n T ~
[( N1  N 2 )] 

2 TF
~   / 0 0  3n / 2EF
2
3n T ~
[( N1  N 2 )] 

2 TF
~   /  0  0  3 / 2nEF
2
Suppression of spin fluctuations in a
paired Fermi Gas
790G paired
790G unpaired
single image
noise profile
527G at 0.14 TF
830G at 0.19 TF
790G at 0.19 TF
1000G at 0.13 TF
915G at 0.13 TF
1. Why is it interesting to measure fluctuations?
2. Fluctuations in an ideal Fermi gas
3. Speckle imaging and pair correlations along the
BEC-BCS crossover
4. Ferromagnetic instability and fluctuations in
repulsively interacting Fermi gases
Ferromagnetic instability and
fluctuations in repulsively interacting
Fermi gases
critical opalescence in a binary mixture
figure adapted from L. Pricoupenko et al. (PRA 2004)
Previous work: indirect signatures of
ferromagnetism
Gyu-Boong Jo et al.
Science 325, 1521
•
•
•
•
Conduit and Simons (2009): nonequilibrium dynamics
Zhai (2009): local anticorrelations
Pilati et al (2010): Quantum Monte Carlo
Pekker et al (2010): competition between magnetism
and pairing
• Zhang (2011): molecular formation and decay
• Barth and Zwerger (2011): Tan relations
• Zhou et al (2011): Scattering length approximation
and others…
Two key improvements
Spin fluctuations vs. magnetic field
Spin fluctuations vs. hold time at 830G
Decay of the unbound atom population
h 6.1kHz = EF
Decay of the unbound atom population
Can a Fermi gas with short-range
interactions be a ferromagnet?
We can’t say for sure.
But we looked really hard and we couldn’t
find any evidence that it can.
Fully interpreting the results is challenging,
but to us they suggest that it can’t.
more details in
PRL 105, 040402 (2010)
PRL 106, 010402 (2011)
.....