Novel Probes for Fermionic Gases

1. Novel Probes for Fermionic Gases J. Meineke, T. Müller, B. Zimmermann, D. Stadler J.-P. Brantut, H. Moritz, T. Esslinger ETH Zürich

2. Experimental setup Microscope objectives 6Li atoms

3. Microscope setup

4. Microscope setup • High-resolution imaging system: • resolution: 660nm (FWHM) for =671nm • NA = 0.53, magnification factor: 54

5. Microscopic manipulation flexible micro-tweezers

6. Atoms in micro-traps Square lattice Ring lattice a=2.5 mm  6.9 mm B. Zimmermann, T. Müller, J. Meineke, T. Esslinger, H. Moritz, New Journal of Physics 13, 043007 (2011)

7. Imaging through the microscope high resolution imaging “standard” imaging 20μm 500mm • Information on • correlations, quantum statistics? • temperature, susceptibilities? • entanglement?

8. Microscopic probing … … of in-situ density fluctuations

9. Quantum statistics and fluctuations thermal quantum degenerate probe volume Suppressed density fluctuations in a degenerate Fermi gas due to Pauli principle! thermal higher order quantum correction For 1D Bose gases: J. Esteve et al., PRL 96,130403 (2006) & J. Armijo et al., PRL 105, 230402 (2010) For 2D Bose gases: C.-L. Hung, X. Zhang, Na. Gemelke, C. Chin, Nature 470, 236 (2011)

10. Measurement of density fluctuations different realizations absorption imaging • Calculate mean and variance over many realizations • Account for photon shot noise and imaging effects Fluctuation in gas on a pixel Effect of imaging resolution

11. Manifestation of antibunching Indication for the level of local quantum degeneracy Our work at ETH Zürich: PRL 105, 040401 (2010) Similar work at MIT in TOF: PRL 105, 040402 (2010)

12. Thermodynamic properties local density approximation Compressibility κ Fluctuation-dissipation theorem: density fluctuations model independent measurement of temperature Q. Zhou and T. L. Ho, arXiv: 0908.3015, to appear in PRL; κin SF-MI: N. Gemelke, X. Zhang, C.-L. Hung, C. Chin, Nature 460, 995 (2009).

13. Fluctuation-based thermometry Temperature: Conventional Fluctuation-based degenerate 20530nK 14531nK thermal 1,6 0.2 K 1,1 0.06 K T. Müller , B. Zimmermann, J. Meineke, J.-P. Brantut, T. Esslinger, H. Moritz, Phys. Rev. Lett. 105, 040401 (2010)

15. Local Spin-Fluctuations Two-component quantum gas

16. Atom-Light Interface Atoms Light Hammerer et al., Rev. Mod. Phys. 82, 1041 (2010)

17. Atom-Light Interface Bruun et al., PRL 102, 030401 (2009)

18. Measuring Spin-Polarization

19. Measuring Spin-Polarization Phase Spin-polarization Speckle: Sanner et al., PRL 106, 010402 (2011)

20. The Interferometer

21. The Interferometer

22. Performance Single component: Phase-shift proportional to atomic density

23. Performance Photon shot-noise limited

24. Results

25. Distribution of Spin-Polarization Weakly interacting gas

26. Distribution of Spin-Polarization Weakly interacting gas

27. Distribution of Spin-Polarization Weakly interacting gas

28. Distribution of Spin-Polarization Strong repulsive interactions

29. Suppression of Spin-Fluctuations 9.2dB • Relative suppression • Agrees with theory for noninteracting Fermions • Analogous to suppression of density-fluctutations due to antibunching

30. Spin-Susceptibility spin-susceptibility Measurements of spin-susceptibility: Salomon, Zwierlein, Ketterle

31. Spin-Susceptibility spin-susceptibility

32. Entanglement

33. Entanglement Wiesniak et al., NJP 7, 258 (2005); Toth et al., PRA 79, 042334 (2009)

34. Entanglement Adm2 (μm-2) Wiesniak et al., NJP 7, 258 (2005); Toth et al., PRA 79, 042334 (2009)

35. NovelProbes Microscopicaccess mesoscopic systems thermodynamic properties fluctuations correlations

36. Teamwork Henning Moritz Jakob Meineke David Stadler Torben Müller Sebastian Krinner Jean-Philippe Brantut Tilman Esslinger

38. Data Processing

39. Novel Probes for Fermionic Gases J. Meineke, T. Müller, B. Zimmermann, D. Stadler J.-P. Brantut, H. Moritz, T. Esslinger ETH Zürich