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

NTkN

V 22

)(1

),(),(1

'' llll xxxxGkT

Suppression of fluctuations in an ideal Fermi Gas

1)( 2

N

N

TNk

V

BT

F

BT

FT E

Tk

N

N

NE

V

2

3)(

2

3 20

TB

NTkN

V 22

)(1

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).....