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

kT G

(

x l

,

x l

' )   (

x l

,

x l

' ) e.g. for number fluctuations in the grand canonical ensemble:

V N

2 1

k B T

( 

N

) 2  

T

Suppression of fluctuations in an ideal Fermi Gas V N

2 Classical ideal gas: 1

k B T

( 

N

) 2  

T



T



V Nk B T

 ( 

N

) 2

N

 1 Poissonian fluctuations Ideal Fermi gas: 

T

 3

V

2

NE F



T

 ( 

N

) 2

N

 3 2

k B T E F

Sub-Poissonian fluctuations

Suppression of density fluctuations in an ideal Fermi Gas

Suppression of fluctuations in an ideal Fermi Gas

harmonic confinement binomial variance

n k

( 1 

n k

) integrated over all 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 reduced relative noise 

t

 

N N

Two divided frames at low intensity: Two divided frames at high intensity:

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 one photon momentum) (Li6: Doppler shift of 0.15 MHz for 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/q Fermi = 1.1  m quantum fluctuations…..

0.23 ± .01 T F 0.33 ± .02 T F 0.60 ± .02 T F

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

[  (

N

1    /  0

N

2 )] 2  0  3

n T

2

T F

 3

n

/ 2

E F

[  (

N

1 

N

2 )] 2   /  0  0  3

n T

2

T F

 3 / 2

nE F

Suppression of spin fluctuations in a paired Fermi Gas

790G paired single image 790G unpaired noise profile

527G at 0.14 T F 830G at 0.19 T F 790G at 0.19 T F 1000G at 0.13 T 915G at 0.13 T F F

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 = E F

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) .....