1. Quantum state manipulation of trapped ions D. J. Wineland, NIST, Boulder, Colorado

2. Time magazine Article about D-Wave quantum computer February 17, 2014

3. Summary:  ion qubits  Spectroscopy & atomic clocks  quantum limited measurements & quantum information  elements of quantum computing  quantum simulation  Mostly NIST examples, but many people & many groups worldwide

4. 199 Hg + 1 mm “trap” electrodes = 282 nm Mercury ion “qubit”, 1981 → | 2 S 1/2   |0  | 2 D 5/2   |1  (   0.1 s) superpositions  |0  +  |1  ultraviolet light

5. 1 mm   0  +   1  |1  |0  Qubit measurement 2 P 1/2 (   2 ns)

6. 1 mm 2 P 1/2 194 nm Hg + photomultiplier   0  +   1    0  |1  |0 

7. 1 mm 2 P 1/2 194 nm Hg + photomultiplier |1  |0    0  +   1    1 

8.  trapping  first-order Doppler shift  0  laser cooling  time dilation small  trapping in high vacuum at 4 K  small environmental perturbations (collisions, black body shifts, etc.) Single 199 Hg + ions for (optical) clocks: J. C. Bergquist et al., (NIST)1981   first clock with systematic uncertainly (7x10 -17 ) below Cesium - W. H. Oskay et al., Phys. Rev. Lett. 97, 020801 (2006) Jim Bergquist 2 S 1/2 2 D 5/2 2 P 1/2 Hg +

9.  trapping  first-order Doppler shift  0  laser cooling  time dilation small  trapping in high vacuum at 4 K  environmental perturbations (collisions, black body shifts, etc.) small Jim Bergquist  first clock with systematic uncertainly (7x10 -17 ) below Cesium - W. H. Oskay et al., Phys. Rev. Lett. 97, 020801 (2006) 2 S 1/2 2 D 5/2 2 P 1/2 Hg + Single 199 Hg + ions for (optical) clocks: J. C. Bergquist et al., (NIST)1981  Plus several other ion species: 88 Sr +, 171 Yb +, 27 Al +, 40 Ca +, 115 In + review: P. Gill, Phil. Trans. R. Soc. A 369, 4109 (2011) 229 Th 3+ (PTB, UCLA Kuzmich group)

10. 199 Hg + 1 mm 2 S 1/2 = |0  2 D 5/2 = |1  2 S 1/2 2 D 5/2 … m=0 m=2 m=1 … m=0 m=2 m=1 motion quantum states fine-scale energy structure: Transition frequency  1 x 10 15 Hz  m = 1 transition Frequency  10 6 – 10 7 Hz

11. Prob. (S 1/2 )  J. C. Bergquist, W. M. Itano, D. J. Wineland, Phys. Rev. A36, 428 (1987). 2 S 1/2 2 D 5/2 2 P 1/2 Hg + 282 nm alternately apply Single-ion spectroscopy: 2 S 1/2 2 D 5/2 … m=0 m=2 m=1 … m=0 m=2 m=1  m = 0

12. Prob. (S 1/2 )  J. C. Bergquist, W. M. Itano, D. J. Wineland, Phys. Rev. A36, 428 (1987). 2 S 1/2 2 D 5/2 … m=0 m=2 m=1 … m=0 m=2 m=1  m = -1 2 S 1/2 2 D 5/2 … m=0 m=2 m=1 … m=0 m=2 m=1  m = +1 2 S 1/2 2 D 5/2 2 P 1/2 Hg + 282 nm alternately apply

13. Prob. (S 1/2 )  F. Diedrich et al., PRL 62, 403 (1989) 2 S 1/2 2 D 5/2 … m=0 m=2 m=1 … m=0 m=2 m=1  m = -1  m = 0 2 S 1/2 2 D 5/2 … m=0 m=2 m=1 … m=0 m=2 m=1  m = -1  m = 0 2 S 1/2 2 D 5/2 … m=0 m=2 m=1 … m=0 m=2 m=1  m = -1 Ground-state cooling (put atom in m=0 motion state)

14. INTERNAL STATE “SPIN” QUBIT MOTION “DATA BUS” (e.g., center-of-mass mode) Motion qubit states |m = 3  |m = 2  |m = 1  |m = 0  Atomic ion quantum computation: J. I. Cirac, P. Zoller, Phys. Rev. Lett. 74, 4091 (1995) (emerged from 1994 ICAP, Boulder, CO) 2. SPIN  MOTION MAP 3. SPIN  MOTION GATE Ignacio Cirac Peter Zoller |  |  “m” for motion 1. START MOTION IN GROUND STATE

15. SPIN  MOTION MAP “  - pulse” ● ● ● ● ● ● quantized motion levels m = 0 m = 3 m = 1 m = 2 m = 4 m = 0 m = 3 m = 1 m = 2 m = 4 |1  |0  (  |0  +  |1  ) |m=0  |0  (  |m=0  +  |m=1  ) initial state transfer information onto motion

16.  aux   m=1   m=0  11  m=1   m=0   m=1   m=0  SPIN-MOTION GATE: (Chris Monroe et al. PRL, ’95) |0|0

17. Atomic ion experimental groups pursuing QIP: MIT NIST Northwestern NPL Osaka Oxford Paris (Université Paris) Pretoria, S. Africa PTB Saarland Sandia National Lab Siegen Simon Fraser Singapore SK Telecom, S. Korea Sussex Sydney U. Washington Weizmann Institute Aarhus Amherst The Citadel Tsinghua (Bejing) U.C. Berkeley U.C.L.A. Duke ETH (Zürich) Freiburg Garching (MPQ) Georgia Tech Griffiths Hannover Innsbruck JQI (U. Maryland) Lincoln Labs Imperial (London) Mainz + many other platforms: neutral atoms, Josephson junctions, quantum dots, NV centers in diamond, single photons, …

18. ● small electrodes: use lithographic techniques ● move ions in multi-zone arrays for scaling 1 mm Jason Amini et al. (NIST) microfab at: GTRI, Sandia, NIST, Berkeley, Innsbruck, Mainz, …. Scale up qubit numbers? Optically entangle remote ions (Monroe et al.)

19. Joint qubit states More robust entangling operations & logic gates: use state-dependent optical dipole forces e.g., laser beam standing waves Early proposals: Milburn, Schneider, James (1999) Sørensen & Mølmer (1999, 2000) Solano, de Matos Filho, Zagury (1999) |   |0 , |   |1 

20. Joint qubit states

23. E1E1 E2E2

24. E1E1 E2E2 AC Versions: moving standing wave excites motion near mode frequency ● D. Leibfried, et al, Nature 422, 412 (2003) ● ● C. J. Balance et al., (Oxford group), arXiv:1406.5473 error per gate 0.0011(7) world’s record! e..g., simulates spin-spin interaction

25. Center-of-mass)mode tilt mode transverse mode spectrum (9 ions) (  force >  COM ) vary  by varying detuning  = 0 - ~3 add magnetic field: Transverse Ising model Porras and Cirac, PRL 92, 207901 (2004) Porras and Cirac, PRL 96, 250501 (2006) Deng, Porras, Cirac, PRA 7782, 063407 (2005) Taylor and Calarco, PRA, 062331 (2008) Johanning et al., J. Phys. B 42, 154009 (2009) Schneider, Porras, Schätz, Rep. Prog. Phys. 75, 024401(2012) ● ● Exps: Shätz et al., Freiburg Monroe et al., U. Maryland Blatt et al., Innsbruck Bollinger et al., NIST (J i,j > 0, anti-ferromagnetic) Simulation: for  force   COM  GHZ states “moving standing wave” state- dependent forces

26. Chris Monroe Maryland P. Richerme et al., Nature 511, 198 (2014) Innsbruck P. Jurcevi et al., Nature 511, 202 (2014) Rainer BlattChristian Roos Entanglement propagation

27. 800700 transverse mode spectrum (modes out of plane) kHz COM potato chip tilt J. Britton et. al., Nature 484, 489 (2012); B. Sawyer et al., PRL 108, 213003 (2012); PRA 89, 033408 (2014) N  200  N > 100 spins  “self assembled” triangular lattice d 2-D array (Penning trap) Simulation in Wigner crystal top view John Bollinger, + J. Bohnet, J. Britton, B. Sawyer  Benchmarked Ising interactions with mean field theory To do: implement new trap & laser beams to increase J i,j relative to spontaneous emission

28. control electronics below surface trap VIAS Laser beams in plane with ions Chiaverini and Lybarger, PRA 77, 022324 (2008) Schmied, Wesenberg, Leibfried, PRL 102, 233002 (2009) Schmied, Wesenberg, Leibfried, New J. Phys. 13 115011 (2011) Engineered geometry for simulations A. Wilson, D. Leibfried et al. Building block: H I = ћg  x  x, g/2  = 450 Hz ions in separated wells (d = 30  m) (A. Wilson et al., Nature 512, 57 (2014). double well  Didi Leibfried Andrew Wilson

29. Ion heating: try to reduce with surface science techniques: collaboration with D. Hite, K. McKay, D. Pappas (NIST, Boulder) Ar + beam cleaning side view, surface-electrode trap D. A. Hite et al., PRL 109, 103001 (2012) (Ar + beam sputtering) x 100 heating reduction N. Daniilidis et al., (H äffner group) PRB 89, 245435 (2014): similar gain Cryo cooling helps too:  L. Deslauriers, S. Olmschenk, D. Stick, W. K. Hensinger, J. Sterk, and C. Monroe, Phys. Rev. Lett. 97, 103007 (2006).  J. Labaziewicz, Y. Ge, D. R. Leibrandt, S. X. Wang, R. Shewmon, and I. L. Chuang, Phys. Rev. Lett. 101, 180602 (2008).  J. Chiaverini and J. M. Sage, Phys. Rev. A 89, 012318 (2014). …… Review: M. Brownnutt, M. Kumph, P. Rabl, and R. Blatt, arXiv: 1409.6572

30. Recipe: - Hydrogen loading of fiber (~ 100 atm, ~ 1 week) - “cure” with UV (transmitted beam) Input Output - 98% overlap with Gaussian TEM 00 mode Output Better laser beam control: UV Fibers?  better position stability  improve beam shape Preliminary:  z -  z phase gate with fibers: F > 0.995 Y. Colombe, D. H. Slichter, A. C. Wilson et al. Optics Express 22, 19783 (2014) Hollow core crystal fibers: F. Gebert, M. H. Frosz, T. Weiss, Y. Wan, A. Ermolov, N. Y. Joly, P. O. Schmidt, and P. St. J. Russell, Opt. Express, 22, 15388-15396 (2014).

31. 10  m gold on AlN substrate 25 Mg + ions trapped 30  m from surface U. Warring et al., PRA 87, 013437 (2013); PRL 110, 173002 (2013) C. Ospelkaus et al., Nature 476, 181 (2011). D. P. L. Aude et al., Appl. Phys. B 114, 3 (2014) (Oxford) current lead for  -wave hyperfine transitions Get rid of lasers?

32. 10  m gold on AlN substrate currents for sideband transitions F = 0.76(3) U. Warring et al., PRA 87, 013437 (2013); PRL 110, 173002 (2013) C. Ospelkaus et al., Nature 476, 181 (2011). Make B(t) =0, maximize B-field gradient  state-dependent magnetic forces

33. 10  m gold on AlN substrate currents for sideband transitions F = 0.76(3) U. Warring et al., PRA 87, 013437 (2013); PRL 110, 173002 (2013) C. Ospelkaus et al., Nature 476, 181 (2011). Make B(t) =0, maximize B-field gradient Potential benefits:  better control with RF/microwaves  “all electronic” integrated control  no spontaneous emission  ground state cooling not necessary  laser overhead vastly reduced

34. 10  m gold on AlN substrate currents for sideband transitions Make B(t) =0, maximize B-field gradient F = 0.76(3) U. Warring et al., PRA 87, 013437 (2013); PRL 110, 173002 (2013) C. Ospelkaus et al., Nature 476, 181 (2011). New apparatus (David Allcock, Daniel Slichter) - better optical access - shorter leads (lower RF and microwave loss) - separate loading zone - Ar+ cleaning - ability to cool (LN 2 ) - better thermal & electrical conductivity at 80K - new power amps

35. Al + “quantum-logic clock” (T. Rosenband, D. Lebrandt et al.) Coulomb interaction 2 P 3/2 2 S 1/2 (F=2, m F = -2) (F=3, m F = -3) 25 Mg + Al + 1S01S0 3P03P0 1P11P1 = 167 nm uncertainty = 8.0 x 10 -18 (time dilation shift) Till Rosenband  |  Al +  |  Al  motion superposition   |  Mg +  |  Mg David Leibrandt trap at ~ 300 K = 280 nm C. W. Chou et al., PRL 104, 070802 (2010)

36. Jun Ye’s group (JILA), Sr neutral atoms in optical lattice:  f/f 0 (systematic) = 6.4 x 10 -18 (B. J. Bloom et al., Nature 506, 71 (2014))  T  30 mK PTB, Braunschweig, Germany  f/f 0 (systematic) = 3.3 x 10 -18 (unpublished) weak (octupole) transition, laser Stark shifts, … H. Katori group (Riken) Sr neutral atoms in optical lattice  f/f 0 (systematic) = 7.2 x 10 -18 (arXiv:1405.4071) Moving target! 2.1

37. WE DO KNOW HOW IT WORKS …and why it doesn’t work FACTORING MACHINE probably decades away QUANTUM SIMULATION maybe within next decade?

38. Shlomi Kotler, Dustin Hite, Katie McCormick,Susanna Todaro, Leif Waldner, Yiheng Lin, Daniel Slichter, James Chou, David Allcock, Didi Leibfried, Jwo-Sy Chen, Sam Brewer, Kyle McKay David Hume Ting Rei Tan Jim Bergquist, John Bollinger, Joe Britton, Justin Bonet, Ryan Bowler, John Gaebler, Andrew Wilson, Dave Wineland, David Leibrandt, Peter Burns, Raghu Srinivas, Shon Cook, Robert Jordens Not pictured: Brian Sawyer, Till Rosenband, Wayne Itano, Dave Pappas, Bob Drullinger NIST “IONS” June 2014