fluctuations in strongly interacting fermi gases christian sanner, jonathon gillen, wujie huang,...
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Fluctuations in Strongly Interacting Fermi Gases
Christian Sanner, Jonathon Gillen, Wujie Huang, Aviv Keshet,Edward Su, Wolfgang Ketterle
Center for Ultracold AtomsMIT
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 gasesis relevant.The fluctuations around the average can contain very usefulinformation that is not accessible via the mean values.
Fluctuations in a system atthermal equilibrium
Fluctuation-Dissipation Theorem
Response of the system toapplied perturbations
e.g. for number fluctuations in the grand canonical ensemble:
TB
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)(1
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Suppression of fluctuations in an ideal Fermi Gas
1)( 2
N
N
TNk
V
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FT E
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3)(
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Classical ideal gas:
Ideal Fermi gas:
Sub-Poissonian fluctuations
Poissonian fluctuations
Suppression of density fluctuations in an ideal Fermi Gas
Suppression of fluctuations in an ideal Fermi Gas
momenta allover integrated )1( variancebinomial kk nn
harmonicconfinement
Measuring the fluctuations1. Photon shot noise
In bright field observation the spatial distribution of detectedphotons is going to show the typical projection noise
NN
more photons reduced relative noiseN
Nt
Two divided framesat low intensity:
Two divided framesat high intensity:
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 andvery short acquisition times (a few 100µs betweenatom and reference shot, vibrations!) and operatingat sufficient light levels we obtain images that arephoton shot noise limited in the atom free regions.
Measuring the fluctuations3. Noise due to nonlinear effects
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
imprinted structurein the atomic cloud
flat background (very good fringe cancellation)
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
0/~ 0/~ FEn 2/30
FnE2/30
~2
3)]([ 2
21FT
TnNN ~
2
3)]([ 2
21FT
TnNN
Measuring Susceptibility and Compressibility
Suppression of spin fluctuations in a paired Fermi Gas
single image noise profile
790G paired
790G unpaired
527G at 0.14 TF
790G at 0.19 TF
830G at 0.19 TF
915G at 0.13 TF
1000G 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).....