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Quantum Simulations with

Quantum Simulations with. Trapped Atomic Ions. Yb + crystal. ~5 m m. dc. dc. rf. rf. dc. dc. 3-layer geometry: single rf electrode scalable to larger structures, natural for junctions. dc. dc. rf. rf. dc. dc. 171 Yb + hyperfine spin. |  = |1,0 .

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Quantum Simulations with

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  1. Quantum Simulations with • Trapped Atomic Ions Yb+ crystal ~5 mm

  2. dc dc rf rf dc dc • 3-layer geometry: • single rf electrode • scalable to larger structures, natural for junctions dc dc rf rf dc dc

  3. 171Yb+hyperfine spin | = |1,0 wHF/2p = 12 642 812 118 + 311B2Hz 2S1/2 (600 Hz/G @ 1 G) | = |0,0

  4. 1 Probability 0 0 5 10 15 20 25 # photons collected in 800 ms 171Yb+ spin detection g/2p = 20 MHz 2P1/2 2.1 GHz |z 369 nm | wHF/2p = 12 642 812 118 + 311B2Hz 2S1/2 (600 Hz/G @ 1 G) |

  5. 1 >99% detection efficiency Probability 0 0 5 10 15 20 25 # photons collected in 500 ms 171Yb+ spin detection g/2p = 20 MHz 2P1/2 2.1 GHz |z  |z 369 nm | wHF/2p = 12 642 812 118 + 311B2Hz 2S1/2 (600 Hz/G @ 1 G) |

  6. 171Yb+ spin manipulation g/2p = 20 MHz 2P3/2 D = 33 THz 2P1/2 355 nm (10 psec @ 100 MHz) | wHF/2p = 12 642 812 118 + 311B2Hz 2S1/2 (600 Hz/G @ 1 G) |

  7. National Ignition Facility: 351nm (Livermore National Laboratory) Pavg ~ 5W at 355nm 10 psec pulses, 120 MHz rep rate 1 0 P(↑|↓) picosecond spin control 0 10 20 30 pulse energy (nJ) See talk by Jonathan Mizrahi (Sunday) J. Mizrahi, et al., ArXiv 1307.0557 (2013)

  8. Internal states of these ions entangled Trapped Ion Quantum Computer (Cirac-Zoller) Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995) CM, et al., Phys. Rev. Lett. 74, 4714 (1995) Q. Turchette, et al., Phys. Rev. Lett. 81, 3631 (1998) F. Schmidt-Kaler, et al., Nature 422, 408 (2003)

  9. Internal states of these ions entangled Trapped Ion Quantum Computer (Cirac-Zoller) Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995) CM, et al., Phys. Rev. Lett. 74, 4714 (1995) Q. Turchette, et al., Phys. Rev. Lett. 81, 3631 (1998) F. Schmidt-Kaler, et al., Nature 422, 408 (2003)

  10. Cirac-Zoller: number states of the QHO • extreme cooling: requires a pure motional state • not scalable: mode density problem 1 • Better: “spin-dependent displacements” • only requires cooling to the • Lamb-Dicke limit • “virtual” coupling to phonons • Possible • Mølmer & Sørensen (1999) • Solano, de Matos Filho, Zagury (1999) • Milburn, Schneider, James (2000) =

  11. F = F0|↑↑| - F0|↓↓| global spin-dependent force

  12. B ↑ ↓ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ | | ADD: Independent spin flips global spin-dependent force F = F0|↑↑| - F0|↓↓|

  13. spin-dependent force (171Yb+) B(x) 1,1 1,0 1,-1 Magnetic field gradient 2P1/2 0,0 1,1 1,0 1,-1 | 2S1/2 0,0 |

  14. spin-dependent force (171Yb+) s+ s+ 1,1 1,0 1,-1 Position-dependent AC Stark shift 2P1/2 0,0 D 369 nm g 1,1 1,0 1,-1 | 2S1/2 0,0 |

  15. spin-dependent force (171Yb+) Red+blue sideband applied simultaneously 1,1 1,0 1,-1 2P1/2 0,0 D 369 nm g g | g 1,0 1,1 1,-1 Lamb-Dicke parameter = 2S1/2 0,0 |

  16. global spin-dependent oscillating force simultaneous sidebands Lamb-Dicke approximation: normal mode decomposition † normal mode transformation matrix: ion i, mode k

  17. Aside: transverse Modes of an atom chain transverse modes . . . frequency transverse modes axial modes . . . . . . frequency S.-L. Zhu et al.,  Phys. Rev. Lett. 97, 050505 (2006) A. Serafini et al., New J. Phys. 11, 023007 (2009)

  18. Raman spectrum of N=9 ions fluorescence ~ N() (Dk nominally along x) transverse y axial z ZigZag COM COM transverse x ZigZag COM Raman beatnote (MHz)

  19. global spin-dependent oscillating force carrier lower sidebands upper sidebands Raman beatnotes: wHF±m wHF -m wHF+m frequency †

  20. † † evolution operator phonons interaction between qubits (entangling gates etc..)

  21. How to avoid phonon creation? (1) Pick detuning m and time t wisely “FAST MOLMER” for all modes k e.g.: m near single mode k only → (m-wk)t = 2pm m=1,2,… S.-L. Zhu, et al., Europhys Lett. 73 (4), 485 (2006).

  22. “FAST MOLMER” p x Rabi frequency Beatnote frequency

  23. How to avoid phonon creation? (1) Pick detuning m and time t wisely “FAST MOLMER” for all modes k e.g.: m near single mode k only → (m-wk)t = 2pm m=1,2,… S.-L. Zhu, et al., Europhys Lett. 73 (4), 485 (2006). (2) “Adiabatically eliminate” phonons: |m - wk| >> hW0“SLOW MOLMER”

  24. “SLOW MOLMER” p x Rabi frequency Beatnote frequency

  25. How to avoid phonon creation? (2) “Adiabatically eliminate” phonons: |m - wk| >> hW0“SLOW MOLMER”

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