Fluctuations in Strongly Interacting Fermi Gases

1
Fluctuations in Strongly Interacting Fermi Gases

Christian Sanner, Jonathon Gillen, Wujie Huang,
Aviv Keshet, Edward Su, Wolfgang Ketterle
Center for Ultracold Atoms MIT
2
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

3
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.
4
Fluctuation-Dissipation Theorem
Fluctuations in a system at thermal equilibrium
Response of the system to applied perturbations
e.g. for number fluctuations in the grand
canonical ensemble
5
Suppression of fluctuations in an ideal Fermi Gas
Classical ideal gas
Poissonian fluctuations
Ideal Fermi gas
Sub-Poissonian fluctuations
6
Suppression of density fluctuations in an ideal
Fermi Gas
7
Suppression of fluctuations in an ideal Fermi Gas
harmonic confinement
8
Measuring the fluctuations1. Photon shot noise
In bright field observation the spatial
distribution of detected photons is going to show
the typical projection noise
more photons reduced relative noise
Two divided frames at low intensity
Two divided frames at high intensity
9
Measuring the fluctuations2. 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.
10
Measuring the fluctuations3. 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
11
(No Transcript)
12
transmission
optical density
noise
13
(No Transcript)
14
(No Transcript)
15
expanded cloud 1/qFermi 1.1 ?m
quantum fluctuations..
16
0.23 .01 TF
0.33 .02 TF
0.60 .02 TF
17
(No Transcript)
18
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
19
Speckle imaging
20
Measuring Susceptibility and Compressibility
21
(No Transcript)
22
(No Transcript)
23
Suppression of spin fluctuations in a paired
Fermi Gas
24
790G paired
790G unpaired
single image
noise profile
25
(No Transcript)
26
527G at 0.14 TF
1000G at 0.13 TF
830G at 0.19 TF
915G at 0.13 TF
790G at 0.19 TF
27
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
28
Ferromagnetic instability and fluctuations in
repulsively interacting Fermi gases
critical opalescence in a binary mixture
29
figure adapted from L. Pricoupenko et al. (PRA
2004)
30
Previous work indirect signatures of
ferromagnetism

• Gyu-Boong Jo et al.
• Science 325, 1521

31

• 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

32
Two key improvements

•  

33
Spin fluctuations vs. magnetic field
34
Spin fluctuations vs. hold time at 830G
35
Decay of the unbound atom population
h 6.1kHz EF
36
Decay of the unbound atom population
37
Can a Fermi gas with short-range interactions be
a ferromagnet?

• We cant say for sure.
• But we looked really hard and we couldnt find
  any evidence that it can.
• Fully interpreting the results is challenging,
  but to us they suggest that it cant.

38
more details in PRL 105, 040402 (2010) PRL 106,
010402 (2011) .....