Dense Atomic Ensembles and Collisional Narrowing for Quantum Memories

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

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

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

9. Motional narrowing “ ”

11. Collisional narrowing Exponent Gaussian

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

18. Discrete fluctuations • Telegraph noise in semiconductors • Single molecule spectroscopy

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? • t1 is measured in low density with

22. G 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 where 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)

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 collisionaldecoherence 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: a11+a22-2*a12 = 0.3% of a11 and a22

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

38. Measured collisional bath spectrum Lorentzian Trap oscillation frequency 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. Summary 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)

45. Outline • 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)

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