1. Long coherence times with dense trapped atoms collisional narrowing and dynamical decoupling Nir Davidson Yoav Sagi, Ido Almog, Rami Pugatch, Miri Brook (Kurizki group, Michael Aizenman) Weizmann Institute of Science, Israel

2. Efficiency of quantum memories depends on optical depth Strong nonlinearity per photon Collective coupling to SC circuits Unique model system! Why dense atomic ensembles?

3. Quantum memories 2010 - : Us, Kuzmich, Porto, Rosenbusch, Bloch ….

4. Experimental setup Magneto optical trapping Sisyphus cooling Raman sideband cooling Evaporative cooling

5. Experimental setup Magneto optical trapping Sisyphus cooling Raman sideband cooling Evaporative cooling

6. Experimental setup Magneto optical trapping Sisyphus cooling Raman sideband cooling Evaporative cooling

7. Experimental setup Magneto optical trapping Sisyphus cooling Raman sideband cooling Evaporative cooling

8. Collisional narrowing Spectrum with discrete fluctuations Motional broadening Dynamical decoupling Bath spectral characterization Outline

9. Motional narrowing “ ”

11. Collisional narrowing Gaussian Exponent

12. Experimental results Collisional narrowed decay time Inhomogeneous decay time Y. Sagi, I. Almog and N. Davidson, Phys. Rev. Lett. 105, 093001 (2010)

13. Experimental results Data collapse! Y. Sagi, I. Almog and N. Davidson, Phys. Rev. Lett. 105, 093001 (2010)

15. Mott insulator suppresses collisions Mott-Insulator with exactly one atom per site ~80 Hz EIT lines ~250 msec storage time for light U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, PRL 2010

16. Discrete Vs continuous fluctuations Kubo-Anderson model Y. Sagi, R. Pugatch, I. Almog and N. Davidson, Phys. Rev. Lett. 104, 253003 (2010)

17. Discrete Vs continuous fluctuations Cold collisions in atomic ensembles Kubo-Anderson model Y. Sagi, R. Pugatch, I. Almog and N. Davidson, Phys. Rev. Lett. 104, 253003 (2010)

18. Telegraph noise in semiconductors Single molecule spectroscopy Discrete fluctuations

19. Solution of the discrete model Without collisions: With collisions: A. Brissaud and U. Frisch, J. Math. Phys. 15, 524 (1974).

20. Atoms in 3D harmonic trap Density of states for 3D harmonic trap Boltzmann factor

21. How do we measure the parameters?  1 is measured in low density with

22.  is measured by inducing oscillations in the waist of the atomic cloud and observing their decay:

23. Comparing theory to experiment Y. Sagi, R. Pugatch, I. Almog and N. Davidson, Phys. Rev. Lett. 104, 253003 (2010 )

24. Comparison to Kubo’s model Bloembergen et al, PRA 1984

25. Can fluctuations broaden the spectrum ? Example: Student’s t-distribution Motional narrowing A. Burnstein, Chem. Phys. Lett. 83, 335 (1981).

26. Can fluctuations broaden the spectrum ? Example: Student’s t-distribution Motional narrowing Motional broadening A. Burnstein, Chem. Phys. Lett. 83, 335 (1981).

27. Can fluctuations broaden the spectrum ? Y. Sagi, I. Almog, R. Pugatch, M. Aizenman and N. Davidson, PRA, in press (2011)

28. Mathematical proof for stable distributions α - characteristic exponent of a stable distribution Gaussian: α=2, Cauchy: α=1, Levi: α=1/2 Y. Sagi, I. Almog, R. Pugatch, M. Aizenman and N. Davidson, PRA, in press (2011) where

29. Motional broadening: exponential decay Y. Sagi, I. Almog, R. Pugatch, M. Aizenman and N. Davidson, PRA, in press (2011)

30. Effect of cutoff Motional broadening persists until cutoff is sampled

31. Relation to Zeno and anti Zeno Y. Sagi, I. Almog, R. Pugatch, M. Aizenman and N. Davidson, PRA, in press (2011)

32. Suppression of collisional decoherence by dynamical decoupling

33. Echo fails at high densities

34. Dynamical Decoupling Y. Sagi, I. Almog and N. Davidson, Phys. Rev. Lett. 105, 093001 (2010)

35. Process tomography of DD Y. Sagi, I. Almog and N. Davidson, Phys. Rev. Lett. 105, 093001 (2010)

36. Process tomography of non-linear Hamiltonian “twist” of the Bloch sphere Rubidium 87: a 11 +a 22 -2*a 12 = 0.3% of a 11 and a 22

37. Continuous Rabi pulse Measuring the bath spectrum S(  ) F(  t)   The decay rate is G. Gordon et. al., J. Phys. B: At. Mol. Opt. Phys. 42, 223001 (2009)

38. Measured collisional bath spectrum Trap oscillation frequency Lorentzian I. Almog et. al., submitted (2011)

39. Measured decay vs predictions from bath spectrum I. Almog et. al., submitted (2011)

40. Anomalous diffusion of atoms in a 1D dissipative lattice

41. Motional broadening in real space Q=1.0 Q=1.57

42. Measurements of 1D anomalous diffusion Ballistic Diffusion

43. Self similarity

44. Collisional narrowing PRL 105 093001 (2010) Discrete fluctuations PRL 104, 253003 (2010) Dynamical decoupling PRL 105 053201 (2010) Collisional broadening PRA, in press (2011) Bath characterization submitted (2011) Anomalous diffusion in preparation (2011) Summary

45. Collisional narrowing Y. Sagi, I. Almog and ND, PRL 105 093001 (2010) Spectrum with discrete fluctuations Y. Sagi, I. Almog, R. Pugatch and ND, PRL 104, 253003 (2010) Motional broadening Y. Sagi, I. Almog, R. Pugatch, M. Aizenman and ND, submitted (2010) Dynamical decoupling Y.Sagi, I. Almog and ND, PRL 105 053201 (2010) Bath spectral charecterization I. Almog et. al., submitted (2011) Outline

46. How to create a Power-law velocity distribution? Don’t be in thermal equilibrium ! Sisyphus cooling scheme: Y. Castin, J. Dalibrad, C. Cohen-Tannoudji (1990)

47. Measurements of 1D anomalous diffusion Ballistic Diffusion

48. Measurements of 1D anomalous diffusion It is possible to measure both the spatial atomic distribution and the velocity distribution (by a time of flight method).

49. Direct observation of anomalous diffusion

50. 1D anomalous diffusion Ballistic Normal diffusion

51. Self similarity in the experiment

52. Self similarity in the experiment (2)

53. Effect of cutoff Motional broadening persists until cutoff is sampled

54. Optimal DD sequence for a Lorentzian bath G. S. Uhrig, Phys. Rev. Lett. 98, 100504 (2007).

55. Process tomography of non-linear Hamiltonian

56. Mott insulator suppresses collisions Mott-Insulator with exactly one atom per site ~80 Hz EIT lines ~250 msec storage time for light U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, PRL 2010

57. Measured collisional bath spectrum Axial oscillation frequency Radial oscillation frequency Lorentzian part

58. An ensemble of oscillators with a distribution of resonant frequencies. If is a Gaussian process, the dephasing is given in terms of the correlation function by: For a Poissonian fluctuations, we obtain: Gaussian theory: Kubo’s model

59. The solution of the model Without collisions: With collisions: Where the tilde stands for the Laplace transform. The spectrum can be calculated by:

62. Measuring the bath spectrum

63. B

64. Dephasing of optically trapped atoms In our experiment For Gaussian phase distribution