1. 1 Trey Porto Joint Quantum Institute NIST / University of Maryland DAMOP 2008 Controlled interaction between pairs of atoms in a double-well optical lattice

2. Neutral atom quantum computing Well characterized qubits Ability to (re)initialize Decoherence times longer than operation times A universal set of gates 1) One-qubit 2) Two-qubit State specific readout All in a Scalable Architecture Minimal Requirements

3. Demonstrate controlled, coherent, 2-neutral atom interactions Provide a test bed for some scalable ideas e.g. sub-wavelength addressing Short Term Goal (also a potential platform for quantum information using global/parallel control)

4. Goal: demonstrate controlled, coherent, 2-neutral atom interactions Two individually trapped atoms Arrays of pairs of atoms in double-well lattice Neutral atom quantum processing This year: U. Wisc. Inst. dOptique This talk (Last year)

5. 2D Double Well Basic idea: Combine two different period lattices with adjustable - intensities - positions += AB 2 control parameters See also Folling et al. Nature 448 1029 (2007)

6. Add an independent, deep vertical lattice 3D lattice = independent array of 2D systems 3D confinement Mott insulator single atom per /2 site

7. Add an independent, deep vertical lattice 3D lattice = independent array of 2D systems 3D confinement Mott insulator single atom/ /2 site Many more details handled by the postdocs… Make BEC, load into lattice, Mott insulator, control over 8 angles … Sebby-Strabley, et al., PRA 73 033605 (2006) Sebby-Strabley, et al., PRL 98 200405 (2007)

8. 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 from red-detuned - non-trivial Band-structure Unique Lattice Features

9. This talk: Isolated a double-well sites Focus on a single double-well negligible coupling/tunneling between double-wells

10. Basis Measurements Release from lattice Allow for time-of flight (possibly with field gradient) Absorption Imaging gives momentum distribution

11. Basis Measurements Absorption Imaging give momentum distribution All atoms in an excited vibrational level

12. Basis Measurements Absorption Imaging give momentum distribution All atoms in ground vibrational level

13. Basis Measurements Absorption Imaging give momentum distribution Stern-Gerlach Spin measurement B-Field gradient

14. 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 from red-detuned - non-trivial Band-structure Unique Lattice Features Compare to recent work of Folling et al. Nature 448 1029 (2007)

15. Intensity modulation effective magnetic field Polarization modulation Scalar vs. Vector Light Shifts

16. Sub-lattice addressing in a double-well Make the lattice spin-dependent Apply RF resonant with local Zeeman shift

17. Sub-lattice addressing in a double-well Left sites Right sites 1kGauss/cm ! Lee et al., Phys. Rev. Lett. 99 020402 (2007)

18. Example: Addressable One-qubit gates

19. Example: Addressable One-qubit gates

20. RF, wave or Raman

21. Example: Addressable One-qubit gates Zhang, Rolston Das Sarma, PRA, 74 042316 (2006)

22. optical 87 Rb Choices for qubit states Field sensitive states 0 1 0 2 Work at high field, quadratic Zeeman isolates two of the F=1 states 1 m F = -2 m F = -1 Easily controlled with RF qubit states are sub-lattice addressable

23. optical 87 Rb Choices for qubit states Field insensitive states at B=0 0 1 0 2 1 m F = -2 m F = -1 controlled with wave qubit states are not sub-lattice addressable need auxiliary states

24. optical 87 Rb Choices for qubit states Field insensitive states at B=3.2 Gauss 0 1 0 2 1 m F = -2 m F = -1 controlled with wave qubit states are not sub-lattice addressable need auxiliary states

25. Dynamic vibrational control Merge pairs of atoms to control interactions Maintain separate orbital (vibrational) states: qubits are always labeled and distinct.

26. Experimental requirements Step 1: load single atoms into sites Step 2: independently control spins Step 3: combine wells into same site, wait for time T Step 4: measure state occupation (orbital + spin) 1) 2) 3) 4)

27. Single particle states in a double-well 2 orbital states ( L, R ) 2 spin states (0,1) qubit label qubit 4 states( + other higher orbital states )

28. Single particle states in a double-well 2 orbital states ( g, e ) 2 spin states (0,1) qubit label qubit 4 states( other states = leakage )

29. Two particle states in a double-well Two (identical) particle states have - interactions - symmetry

30. Separated two qubit states single qubit energy L= left, R = right

31. Merged two qubit states single qubit energy Bosons must be symmetric under particle exchange e= excited, g = ground

32. + - Symmetrized, merged two qubit states interaction energy

33. + - Symmetrized, merged two qubit states Spin-triplet, Space-symmetric Spin-singlet, Space-Antisymmetric

34. + - Symmetrized, merged two qubit states Spin-triplet, Space-symmetric Spin-singlet, Space-Antisymmetric r 1 = r 2 See Hayes, Julliene and Deutsch, PRL 98 070501 (2007)

35. Exchange and the swap gate + - += Start in Turn on interactions spin-exchange dynamics Universal entangling operation

36. Basis Measurements Stern-Gerlach + Vibrational-mapping

37. 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 et al. Nature 448 452 (2007)

38. - Initial Mott state preparation (30% holes -> 50% bad pairs) - Imperfect vibrational motion ~ 85% - Imperfect projection onto T 0, S ~ 95% - Sub-lattice spin control >95% - Field stability Current (Improvable) Limitations

39. - Initial Mott state preparation (30% holes -> 50% bad pairs) - Imperfect vibrational motion - Imperfect projection onto T 0, S - Sub-lattice spin control - Field stability Current (Improvable) Limitations Filtering pairs Coherent quantum control Composite pulsing Clock States

40. Move to clock states 0 1 0 2 1 m F = -2 m F = -1 0 1 0 2 1 m F = -2 m F = -1 T 2 ~ 280 ms (prev. 300 s) OR Improved frequency resolution Improved coherence times

41. Move to clock states 0 1 0 2 1 m F = -2 m F = -1 0 1 0 2 1 m F = -2 m F = -1 OR Requires auxiliary states Plus wave/RF mapping between states e.g.

42. Two-body decay considerations 0 1 0 2 1 m F = -2 m F = -1 0 1 0 2 1 m F = -2 m F = -1 OR e.g. 2-body loss becomes important: p-wave loss dominant!

43. Quantum control techniques Example: optimized merge for exchange gate Gate control parameters unoptimized optimized

44. Quantum control techniques Example: optimized merge for exchange gate Gate control parameters unoptimized optimized Optimized at very short 150 s merge time and only for vib. motion! (Longer times and full optimization should be better.) De Chiara et al., PRA 77, 052333 (2008)

45. Faraday rotation: improved diagnostics polarization analyzer Real-time, single-shot spectroscopy Example: single-shot spectrogram of 10 MHz frequency sweep

46. Faraday rotation: improved diagnostics Left site s Righ t sites Single shot measurementMultiple-shot spectroscopy vs. More than 30 times less efficient quadratic Zeeman Sub-lattice spectroscopy

47. Future Longer term: -individual addressing lattice + tweezer - use strength of parallelism, e.g. quantum cellular automata

48. Postdocs Jenni Sebby-Strabley Marco Anderlini Ben Brown Patty Lee Nathan Lundblad John Obrecht BenJenni Marco Patty People Patty Nathan John Ian Spielman, Bill Phillips

49. The End

50. Coherent Evolution First /2Second /2 RF

51. Controlled Exchange Interactions

52. Sweep Low High Sweep High Low Faraday signals.

53. Outline - Demonstration of controlled Exchange oscillations -Intro to lattice - lattice. - state dependence. - qubit choice. -Demonstrations -Exchange oscillations -Theory of exchange - future directions with clock states. Better T2 and spin echo Considerations: filtering coherent quantum control dipolar loss detailed lattice characterization faraday