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. Fluctuations in a system at thermal equilibrium Fluctuation-Dissipation Theorem 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: Ideal Fermi gas: Sub-Poissonian fluctuations 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 fluctuations 1. 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 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.

10. Measuring the fluctuations 3. 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 structure in the atomic cloud flat background (very good fringe cancellation) for the very light Li atoms, the recoil induced detuning is the dominant nonlinear effect

12. transmission optical density noise

15. expanded cloud 1/q Fermi = 1.1  m quantum fluctuations…..

16. 0.23 ±.01 T F 0.33 ±.02 T F 0.60 ±.02 T F

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

23. Suppression of spin fluctuations in a paired Fermi Gas

24. single imagenoise profile 790G paired 790G unpaired

26. 527G at 0.14 T F 790G at 0.19 T F 830G at 0.19 T F 915G at 0.13 T F 1000G at 0.13 T F

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 = E F

36. Decay of the unbound atom population

37. 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.

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