1. 1 Trey Porto Joint Quantum Institute NIST / University of Maryland Open quantum systems: Decoherence and Control ITAMP Nov. 20-22 2008 Coherent Control of Atoms in a Double-Well Optical Lattice

2. Desire: Coherent Control Vibrational Control (external) Spin Control (internal) Our system: optically tapped cold neutral atoms

3. Desire: Coherent Control Vibrational Control Spin Control MergingMoving Auxiliary state control qubit state control

4. Control Testbed: 2D Double Well ‘ ’ ‘  ’ Two different period lattices with adjustable - intensities - positions += AB 2 control parameters

5. + = /2 nodes  BEC Mirror Folded retro-reflection is phase stable Polarization Controlled 2-period Lattice Sebby-Strabley et al., PRA 73 033605 (2006)

6. Vibrational control of atoms in a double-well lattice Sub-lattice addressing (sub-wavelength optical MRI) Controlled spin-exchange 2-neutral atom interactions Testbed Demonstrations

7. Controlled 2-atom spin-exchange

8. Onsite exchange -> fast 140  s swap time ~700  s total manipulation time Population coherence preserved for >10 ms. ( despite 150  s T 2 *! ) Anderlini et al. Nature 448 452 (2007)

9. Toward 2-qubit gate - Initial Mott state preparation (~30% holes) - Imperfect vibrational motion ~85% - Imperfect projection onto T 0, S ~95% - Sub-lattice spin control >95% - Field stability T 2 ~300  s Global exchange interaction current limitations:

10. Toward 2-qubit gate - Initial Mott state preparation (~30% holes) - Imperfect vibrational motion ~85% - Imperfect projection onto T 0, S ~95% - Sub-lattice spin control >95% - Field stability T 2 ~300  s Filtering/state preparation Coherent quantum control Move to clock states T 2 *= 60 ms, T 2 > 300ms Coherent Hyperfine control Global exchange interaction current limitations:

11. Outline I.Vibrational Control II.Spin Control

12. ~0.5 ms transfer time fidelity limited by vibrational energy scale competes with spin-coherence times. mapped at t 0 from ‘ ’ lattice mapped at t f from ‘ /2’ lattice Adiabatic vibrational transfer

13. For the spin-exchange, we compromised: with vibrational fidelity F ~0.80 to 0.85 Improve spin-coherence and vibrational control

14. coherent quantum control techniques improve both speed and fidelity Coherent Quantum Control Step 1: reasonable model of the system Measured populations as a function of tilt during merge

15. Coherent Quantum Control Step 1: reasonable model of the system With G. De Chiara and T. Calarco Measured populations as a function of merge time

16. Optimized Control Step 2: optimize the control theoretically Gate control parameters Un-optimized left well projections Unwanted excitation unoptimized optimized Ask for 150  s optimization time With G. De Chiara and T. Calarco

17. Quantum control techniques unoptimized optimized Optimized at very short merge time and only for vibrational motion! (Longer times and full optimization should be better.) Step 2: optimize the control theoretically Gate control parameters With G. De Chiara and T. Calarco

18. Quantum control techniques unoptimized optimized Experimental consideration: band width of feedback Step 2: optimize the control theoretically Gate control parameters With G. De Chiara and T. Calarco

19. Quantum control techniques Step 3: Implement optimization

20. Outline I.Vibrational Control II.Spin Control

21. Sub-Wavelength Addressing State dependent light shift looks like local B-field Polarization modulation in an optical lattice Polarization modulation in a focused beam

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

23. Sub-lattice addressing in a double-well Left sites Right sites ≈ 1kGauss/cm ! Lee et al., PRL 99 020402 (2007)

24. optical 87 Rb Choices for qubit states Field sensitive states 0 1 0 2 At high field, quadratic Zeeman isolates two of the F=1 states 1 m F = -2 m F = -1 Easily controlled with RF Optical MRI works

25. optical 87 Rb Choices for qubit states Field sensitive states 0 1 0 2 At high field, quadratic Zeeman isolates two of the F=1 states 1 m F = -2 m F = -1 Easily controlled with RF Optical MRI works Problems: - field sensitive states = very bad qubit - Optical MRI field affects neighboring qubit states T * 2 = 120  s

26. optical 87 Rb Other Choices for qubit States Field insensitive states at B=0 0 1 0 2 1 m F = -2 m F = -1

27. optical 87 Rb Other Choices for qubit States 0 1 0 2 1 m F = -2 m F = -1 Field insensitive states at B=3.2 Gauss

28. Clock States Improve coherence time by moving to clock states Switch to clock states: Field insensitive  wave control Optical MRI addressing does not directly work on clock states

29. Clock State Coherence T 2 ~ 300 ms (prev. 300  s) Improve coherence time by moving to clock states 3.2 Gauss

30. Clock State Coherence T * 2 ~ 20 ms (prev. 150  s) Improve coherence time by moving to clock states T * 2 ~ 60 ms (prev. 150  s) 3.2 Gauss Time (ms) Contrast

31. Optical Addressing of Clock States Need a technique to address clock states Transitions between clock states are MRI-addressable Develop techniques to addressably map qubit states Field sensitive transitions Field insensitive Field sensitive

32. Hyperfine Manifold Control Develop techniques for robust Hyperfine manifold control qubit mapping not entirely trivial - near degeneracies - quadratic shifts Theory input from I. Deutsch Symmetry breaking  wave Field insensitive Field sensitive

33. Example: single-site qubit addressing Memory qubits are distinct from “activated” qubits Goal: arbitrary qubit rotation on a single site Field & position insensitive

34. Example: single-site qubit addressing Goal: arbitrary qubit rotation on a single site qubit mapping is position sensitive Memory qubits are distinct from “activated” qubits

35. Example: single-site qubit addressing Goal: arbitrary qubit rotation on a single site Isolated qubit control Memory qubits are distinct from “activated” qubits

36. Example: single-site qubit addressing Goal: arbitrary qubit rotation on a single site Reverse process Memory qubits are distinct from “activated” qubits

37. Example: single-site qubit addressing Memory qubits are distinct from “activated” qubits Goal: arbitrary qubit rotation on a single site

38. Attractive approach: - field insensitive states = good qubit - No cross-talk Optical MRI field does not affect neighboring sites - Optical MRI mapping is a simple  -pulse: very amenable to robust pulse control “Activated” Qubit Mapping

39. Sub-Lattice Qubit Mapping Demonstrate these techniques in our double-well lattice

40. Mapped Ramsey Step 1: verify clean Ramsey fringe on clock Phase /  Open and close 2-pulse Ramsey sequence on Population

41. Mapped Ramsey Step 2: Ramsey fringe preserved with OMRI field -Open Ramsey on, -add left/right field gradient, -close Ramsey sequence on

42. Mapped Ramsey Step 2: Ramsey fringe preserved with OMRI field Phase Population Left Right Left sites Right sites -Open Ramsey on, -add left/right field gradient, -close Ramsey sequence on

43. Mapped Ramsey Step 2b: determine optical field strength Left sites Right sites

44. Mapped Ramsey Step 3: Map qubit on left, maintaining coherence -Open Ramsey on, -add left/right field gradient, map to, only on left -close Ramsey sequence right: left:

45. Mapped Ramsey Step 3: Map qubit on left, maintaining coherence Left sites Right sites -Open Ramsey on, -add left/right field gradient, map to, only on left -close Ramsey sequence right: left:

46. Mapped Ramsey Step 3: Map qubit on left, maintaining coherence Left sites Right sites -Open Ramsey on, -add left/right field gradient, map to, only on left -close Ramsey sequence right: left: Use quadratic Zeeman effect to avoid leakage

47. Mapped Ramsey Step 3: Map qubit on left, maintaining coherence -Open Ramsey on, -add left/right field gradient, map to, only on left -close Ramsey sequence right: left: LEFT RIGHT

48. Mapped Ramsey Sequence !! Step 3: Map qubit on left, maintaining coherence -Open Ramsey on, -add left/right field gradient, map to, only on left -close Ramsey sequence right: left: LEFT RIGHT

49. Mapped Ramsey Sequence !! Step 3: Map qubit on left, maintaining coherence -Open Ramsey on, -add left/right field gradient, map to, only on left -close Ramsey sequence right: left: LEFT RIGHT Should be improvable with robust (composite) pulse techniques

50. Example Composite Pulse Improvements  -pulse CORPSE pulse detuning insensitivity

51. Example Composite Pulse Improvements  -pulse CORPSE pulse detuning insensitivity Want arbitrary Unitary control + Insensitivity to errors

52. Future Direction Collaboration with Inst. d’Optique BEC production transport atom cloud Separate chamber Comercial aspheres

53. Postdocs John Obrecht Nathan Lundblad Double-well Team Patty Nathan John Former postdocs/students Bruno Laburthe Chad Fertig Jenni Sebby-Strabley Marco Anderlini Ben BrownPatty Lee Ken O’Hara Johnny Huckans

54. The End

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

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

57. Lattice Brillioun Zone Mapping

58. Example: Addressable One-qubit gates  Optical Magnetic Resonance Imaging

59. Example: Addressable One-qubit gates Optical Magnetic Resonance Imaging

60. Example: Addressable One-qubit gates RF,  wave or Raman Optical Magnetic Resonance Imaging

61. Example: Addressable One-qubit gates Zhang, Rolston Das Sarma, PRA, 74 042316 (2006) Optical Magnetic Resonance Imaging