1. 1 Trey Porto Joint Quantum Institute NIST / University of Maryland LASSP Seminar Cornell Oct. 30 2007 Controlled exchange interactions between pairs of atoms in an optical lattice

2. Quantum information processing w/ neutral atoms Correlated many-body physics w/ neutral atoms Engineering new optical trapping and control techniques Research Directions

3. This Talk Sub-lattice RF addressing in a lattice -independent Bloch-sphere control of atoms in sub-lattices Controlled exchange-mediated interactions -using exchange to get spin-dependent entangling (SWAP)

4. Outline -Description of the lattice - Demonstrations of tools double well splitting, controlled motion, sub-lattice spin addressing -Putting it all together: controlled two-atom exchange swapping

5. Outline -Description of the lattice - Demonstrations of tools double well splitting, controlled motion, sub-lattice spin addressing -Putting it all together: controlled two-atom exchange swapping

6. Motivation for the double-well lattice: Isolate pairs of atoms in controllable potential, to test - demonstrate addressing ideas - controlled interactions, at 2-atom level Provide new possibilities for cold atom lattice physics Double-Well Lattice

7. Phase Stable 2D Double Well ‘ ’ ‘  ’ Basic idea: Combine two different period lattices with adjustable - intensities - positions Mott insulator single atom/site += AB

8. + = /2 nodes  BEC Mirror Folded retro-reflection is phase stable Polarization Controlled 2-period Lattice Sebby-Strabley et al., PRA 73 033605 (2006)

9. Add an independent, deep vertical lattice Provides an independent array of 2D systems Polarization Controlled 2-period Lattice

10. Light Shifts Scalar Vector ee h gg  Intensity and state dependent light shift Pure scalar, Intensity lattice Intensity + polarization Effective B field, with -scale spatial structure Flexibility to tune scalar vs. vector component Red detuning attractive Blue detuningrepulsive Optical standing wave

11. Vector Light Shifts x y z Example: lin || lin no elipticity, intensity modulation Example: lin lin no intensity modulation, alternating circular polarization Position dependent effective magnetic field

12. Vector light shift + bias B-field: controllable state-dependent barriers state-dependent tilts Use for site-dependent RF addressing State Dependent Potential For the demonstrations shown here, we use these 2 states in 87 Rb We use the quadratic Zeeman shift to isolate a pseudo spin-1/2 ~34 MHz ~34.3 MHz ~50 gauss

13. X-Y directions coupled - Checkerboard topology - Not sinusoidal (in all directions) e.g., leads to very different tunneling - spin-dependence in sub-lattice - blue-detuned lattice is different - interesting Band-structure Lattice Features

14. Outline -Description of the lattice - Demonstrations of tools double well splitting, controlled motion, sub-lattice spin addressing -Putting it all together: controlled two-atom exchange swapping

15. q E x Lattice can be turned on/off in different time scales Sudden: (<< 100  s) (“pulsing” lattice) Eigenstate projection Intermediate: Fast compared to interaction/tunneling, Slow compared to non-interacting band “Map” band distribution Slow compared to all times: (>> few ms) complete adiabaticity (“adiabatic”) Dynamic Lattice Amplitude Control Time of flight imaging

16. pypy pxpx Reciprocal Lattices and Brillouin Zones ‘ ’ lattice ‘ /2’ lattice Band-adiabatic load in 500  s, snap off 300 ms 500  s Brillouin Zone mapping phase incoherent 500  s 20  s

17. Double Slit Diffraction Slowly load mostly- lattice, snap off Coherently split single well Single slit diffraction load in ~300 ms phase scrambled split in ~200  s coherent split Double slit diffraction

18. Time dependence of diffraction time Load and hold

19. Time dependence of diffraction time Contrast collapse: Not factorizable into a product state split + +

20. Time dependence of diffraction time No interaction, no collapse split +

21. Time dependence of diffraction time N > 1 N =1 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Time (ms) In 3D lattice, see: Greiner et al. Nature, 419 (2002) Sebby-strabley, PRL 98, 200405 (2007)

22. Loading (Slowly) One Atom Per Site Step 1: (for most experiments) Start with a Bose-Einstein condensate, slowly turn on the lattice Load one atom per site using the Mott-Insulator transition or Well “fermionized”, but some holes

23. Probe: Selective Removal of Sites Load right well expel left Load left well expel left band map

24. “Expelling” as a left/right probe  dump left  dump left  dump left

25. “Expelling” as a left/right probe Scan the relative phase between lattices Relative phase  =0

26. ~ ms transfer time atoms can be put on the same site, (but different vibrational level), allowed to interact, and then separated adiabatically mapped at t 0 from ‘ ’ lattice mapped at t f from ‘ /2’ lattice Adiabatic transfer “excitation”

27. State Dependent Potential 34 MHz Zeeman ~ 150 kHz Lattice

28. Start with atoms in m=-1 Apply RF to spin flip to m=0 “Evaporate” m=0 atoms Measure m=-1 occupation in the left or right well. sub-lattice addressing by light shift gradient Sub-Lattice Addressing RF Left sites Right sites

29. Start with atoms in m=-1 Apply RF to spin flip to m=0 “Evaporate” m=0 atoms Measure m=-1 occupation in the left or right well. Sub-Lattice Addressing Right well Left well Lee et al., PRL 99, 020402 (2007)

30. Atoms at sub- spacing -focused beam sees several sites Example: Addressable One-qubit gates 

31. Example: Addressable One-qubit gates Atoms at sub- spacing -focused beam sees several sites - state dependent shifts effective field gradients

32. Example: Addressable One-qubit gates Atoms at sub- spacing -focused beam sees several sites - state dependent shifts effective field gradients RF,  wave or Raman

33. Example: Addressable One-qubit gates Atoms at sub- spacing -focused beam sees several sites - state dependent shifts effective field gradients - frequency addressing

34. State selective motion/splitting Start with either m=-1 or m=0 Selectively and coherently split wavefunction m=0 on left m=-1 on right or

35. Outline -Description of the lattice - Demonstrations of tools double well splitting, controlled motion, sub-lattice spin addressing -Putting it all together: controlled two-atom exchange swapping

36. Putting it all together: a swap gate Step 1: load single atoms into sites Step 2: spin flip atoms on right Step 3: combine wells into same site Step 4: wait for time T Step 5: measure state occupation (vibrational + internal) 1) 2) 3) 4)

37. Exchange Gate: exchange split by energy U projection triplet singlet

38. Exchange Gate: exchange split by energy U projection triplet singlet r 1 = r 2

39. Exchange Gate: exchange split by energy U projection triplet singlet

40. Controlled Exchange Interactions

41. Basis Measurements Stern-Gerlach + “Band-mapping”

42. Swap Oscillations Onsite exchange -> fast 140  s swap time ~700  s total manipulation time Population coherence preserved for >10 ms. ( despite 150  s T2*! ) Anderlini, Nature 448 452 (2007)

43. Coherent Evolution First  /2Second  /2 RF

44. - Initial Mott state preparatio (30% holes -> 50% bad pairs) - Imperfect vibrational motion ~ 85% - Imperfect projection onto T 0, S ~ 95% - Sub-lattice spin control >95% - Field stability move to clock states (state-dependent control through intermediate states) Current (Improvable) Limitations

45. Coherent collisional gates Neighboring atoms are -spatially isolated or -in “activated” states Example: Two-qubit control

46. Optical tweezer adiabatically brings neighboring atoms together. Coherent collisional shift Coherent collisional gates Neighboring atoms are -spatially isolated or -in “activated” states Example: Two-qubit control

47. Optical tweezer adiabatically brings neighboring atoms together. Atoms are separated after an interaction time. Coherent collisional shift Coherent collisional gates Neighboring atoms are -spatially isolated or -in “activated” states Example: Two-qubit control

48. Toward “Scalable” Quantum Computing Test bed for addressable two qubit ideas Test and extend ideas to addressing add tweezers registration is essential

49. Using Parallelism Quantum Cellular Automata limited addressability (e.g. on the edges) distinct entangling, nearest neighbor rules Formally equivalent to circuit Qcomp Individually address only the edge atoms B-rules A-rules

50. Using Parallelism Measurement Based or “One way” or “Cluster State” Qcomp -Create a parallel-entangled cluster state -measurements + 1-qubit rotations Entangled with each of its neighbors

51. Tools for lattice systems State preparation, e.g. - ‘filter’ cooling - constructing anti-ferromagnetic state. Diagnostics, e.g. - number distributions (including holes) - neighboring spin correlations Realizing lattice Hamiltonians, e.g. - band structure engineering - ‘stroboscopic’ techniques - coupled 1D-lattice “ladder” systems - RVB physics...

52. Postdocs Jenni Sebby-Strabley Marco Anderlini Ben Brown Patty Lee Nathan Lundblad John Obrecht BenJenni Marco Patty People Lasercooling Group I. Spielman K. Helmerson P. Lett T. Porto W. Phillips

53. The End

54. Different tunneling Different J but similar U and vibrational spacing Same input power

55. Red Blue Different band structure, Different Wannier functions

56. Interesting band structure e.g. 1/2 filling looks like dimerized hexagonal lattice

57. 2D Mott-insulator Spielman, Phillips, TP PRL 98, 080404 (2007) z 2D systems y x

58. 2D Mott-insulator Quite good comparison to a homogeneous theory (no free parameters) Sengupta and Dupuis, PRA 71, 033629 Momentum distribution

59. 2D Mott-insulator Bimodal fit disappears quite sharply position agrees with theory (no fit distinction between thermal/depletion)

60. (non-)adiabatically dressed latttices RF coupling

61. Wannier function control Two band Hubbard model state-dependent control of: t/U,  /U, position of -lattice t  Ian Spielman

62. Characterizing Holes In a fixed period lattice, difficult to measure “holes” Isolated holes in /2 Combine holes with neighbors

63. Can be coupled with perpendicular DC or RF fields couples spin to Bloch state motion Purely vector part of with no coupling (large Zeeman splitting) lin Coupling spin and motion

64. local effective field alternating plaquettes

65. Connection between single-particle base states and correlated physics when you put in interactions. Designing Bose-Hubbard Hamiltonians

66. State selective motion/splitting Start with either m=-1 or m=0 Selectively split sites Tilt dependence of transfer efficiency or

67. Coherent State-Dependent “Splitting” Site specific RF excitation Double-slit diffraction  /2 pulse (Actually, folded into a spin-echo sequence) Lee et al., PRL 99, 020402 (2007)

68. Constructing n=2 Shell n=1 shell, Normally available n=2 and n=1 shells n=2 core, n=2 shell, Adiabatically purify n=2 shell n=1 shell, /2n=2 shell, PRL 98, 200405 (2007)