Erwin Schr ödinger’s Cat (1935)

1. efficient detector radioactive particle cyanide capsule after one half life:  =  cat is simultaneously dead and alive! state of cat is “entangled” with radioactive particle particlecat Erwin Schrödinger’s Cat (1935) sealed box

2. Deterministic entanglement of trapped atomic ions I NIST, Boulder, Ion Storage group: Other ion groups pursuing entanglement: Aarhus Garching (MPQ) Hamburg Innsbruck LANL London (Imperial) Michigan Ontario (McMaster) Oxford Teddington (NPL) M. Barrett (postdoc, Georgia Tech.)† J. C. Bergquist (NIST) B. Blakestad (student, CU) J. J. Bollinger (NIST) J. Britton (student, U. Colorado) J. Chiaverini (postdoc, Stanford) B. DeMarco (postdoc, U. Colorado) ‡ W. Itano (NIST) B. Jelenković (guest, Blegrade) ¶ M. Jensen (U. Colorado) J. Jost (student, U. Colorado) E. Knill (NIST, computation Div.) C. Langer (student, U. Colorado) D. Leibfried (NIST) W. Oskay (postdoc, U. Texas) R. Ozeri (postdoc, Weizmann) T. Rosenband (U. Colorado) T. Schätz (postdoc, MPQ) P. Schmidt (postdoc, Stuttgart) D. J. Wineland (NIST) †Present address: Otago University, NZ ‡ Present address: U. Illinois ¶ Present address: J.P.L.

3. Deterministic entanglement of trapped atomic ions I • Summary: •  basic ion trapology and entangling •  is it useful? maybe • - quantum computers • baby steps with ions • - cats and metrology (next lecture) • future NIST, Boulder, Ion Storage group: Other ion groups pursuing entanglement: Aarhus Garching (MPQ) Hamburg Innsbruck LANL London (Imperial) Michigan Ontario (McMaster) Oxford Teddington (NPL) M. Barrett (postdoc, Georgia Tech.)† J. C. Bergquist (NIST) B. Blakestad (student, CU) J. J. Bollinger (NIST) J. Britton (student, U. Colorado) J. Chiaverini (postdoc, Stanford) B. DeMarco (postdoc, U. Colorado) ‡ W. Itano (NIST) B. Jelenković (guest, Blegrade) ¶ M. Jensen (U. Colorado) J. Jost (student, U. Colorado) E. Knill (NIST, computation Div.) C. Langer (student, U. Colorado) D. Leibfried (NIST) W. Oskay (postdoc, U. Texas) R. Ozeri (postdoc, Weizmann) T. Rosenband (U. Colorado) T. Schätz (postdoc, MPQ) P. Schmidt (postdoc, Stuttgart) D. J. Wineland (NIST) Caveat: • many body quantum statistics not inherent, must be “engineered” †Present address: Otago University, NZ ‡ Present address: U. Illinois ¶ Present address: J.P.L.

4. • end view Ion trapping, particular case: “linear” RF trap (quadrupole mass filter plugged on-axis with static fields) V0cos Tt Uo Uc ~2R (Get ’s and  numerically) more trap details: http://www.lkb.ens.fr/recherche/qedcav/houches/houches79.html

5. • end view Ion trapping, particular case: “linear” RF trap (quadrupole mass filter plugged on-axis with static fields) V0cos Tt Uo Uc ~2R Neglecting “RF micromotion,” (at T) trap looks like 3-D harmonic well. For linear trap:

6. 2 0 0 m m 3 1 4 2 I O N S 3 ' 4 ' 1 ' 2 ' Fast (entangling) gates: Speed  x,y (dimensions)-2 Idealized trap: (RF quadrupole mass analyzer with trapping zones) RF electrodes control electrodes Approximation: gold-coated alumina wafers

7. Chris Myatt et al. 0.2 mm “linear” Paul (RF) trap V0 ~ 500 V T/2 ~ 50 – 250 MHz x,y/2 10 - 20 MHz

8. z B0 y x Quantum mechanically: y = y0(a + a†), (y0 = zero-point amplitude) resonant interaction = a+ + a† - entangles spin and motion Motion/spin entanglement: e.g., electron g – 2 experiment Dehmelt, Van Dyck, et al. electron cyclotron orbit resonant term flips spin details about laser couplings: http://www.lkb.ens.fr/recherche/qedcav/houches/houches79.html

9. Trapped ions (or neutral atoms) Cavity-QED quantized oscillator = mode ofmotion quantized oscillator = mode ofelectromagnetic field

10. QUANTUM COMPUTERS: UNIVERSAL LOGIC GATE SETS DiVincenzo, PRA 51, 1015 (’95) Barenco et al. PRA 52, 3457 (’95) Classical: 1-bit NOT 2-bit AND 00 → 0 01 → 0 10 → 0 11 → 1 0 → 1 1 → 0 π-phase gate U1,2() Quantum: rotation 1 0102 0102 0112 i0112 1102 i1102 1112  |1112 R(θ,φ) 2 π entanglement! general ref: Quantum Computation and Quantum Information Michael Nielsen and Isaac Chuang (Cambridge University Press, Cambridge, 2000) (“Mike and Ike”)

11. Quantum Computer algorithm to efficiently factorize large numbers Peter Shor (AT&T, ~1995): N-qubits: i001….101001…..101 measure qubits Ci = 2-N/2 i Process all possible inputs simultaneously Ci = 0 for most i (quantum interference) bit no. 0 1 2 3 use measured “i” in classical algorithm to determine factors U = Ur,s() Up,q() ……Rk(θ,φ) Ui,j() e.g., factorize 150 digit decimal #  ~ 109 ops N

12. Quantum Computer algorithm to efficiently factorize large numbers At some intermediate time: “live cat” “dead cat” Peter Shor (AT&T, ~1995): N-qubits: i001….101001…..101 measure qubits Ci = 2-N/2 i Process all possible inputs simultaneously Ci = 0 for most i (quantum interference) bit no. 0 1 2 3 use measured “i” in classical algorithm to determine factors U = Ur,s() Up,q() ……Rk(θ,φ) Ui,j() e.g., factorize 150 digit decimal #  ~ 109 ops N

13. Motion “data bus” (e.g., center-of-mass mode) • • • • n=3 n=2 n=1 n=0 Internal-state qubit Motion qubit states Atomic ion entanglement factory: Basic Idea for ion quantum computer: Cirac and Zoller, PRL74, 4091 (1995) SPIN  MOTION MAP SPIN  MOTION GATE  typically, optical transition (Innsbruck) or hyperfine transition

14. 2P3/2 2P1/2 Mapping: [ + ]0[0 + 1] two-photon stimulated-Raman transitions  laser beams  addressability  laser beams  strong gradient  transition frequency  RF modulator  Example (NIST): 9Be+ (2S1/2 electronic ground state) F = 2, mF = -2 F = 1,mF = -1 details about Raman transitions: http://www.lkb.ens.fr/recherche/qedcav/houches/houches79.html

15. Entanglement: 0[cos(/2)0 + sin(/2)1]  Example (NIST): 9Be+ (2S1/2 electronic ground state) F = 2, mF = -2 F = 1,mF = -1

16. 9Be+ (2S1/2 electronic ground state) F = 2, mF = -2 F = 1,mF = -1 R(,): n cos(/2) n + eisin(/2)n n -e-isin(/2) n + cos(/2)n superposition coherence times 1, 2 > 10 min observed

17. 1  0 1 1 aux  0 0 Gates, example 1: • conditional dynamics: • gates!  phase shift, 1  - 1 Chris Monroe et al., PRL 75, 4714 (1995) (complete Cirac Zoller gate: Schmidt-Kaler et al., Nature422, 408 (2003))

18. phase-space diagram for (mode of axial) motion p   ei  enclosed area x Gates, example 2: Geometrical phase gate: (Didi Leibfried et al.) • use optical dipole forces to implement displacement make displacement • state-dependent special case of more general formalism by: Milburn, Schneider, James, Forschr. Physik 48, 801 (2000) Sørensen & Mølmer, PRA62, 02231 ( 2000)

19. center-of-mass mode C.O.M stretch mode stretch= 3½C.O.M. walking-wave polarization gradient diff stretch Optical-dipole (Stark shift) force, F = -2F AC version of neutral-atom displacement gates (e.g., exps of Bloch, Greiner et al.)

20. p  ei/2 = i  ei/2 = i  x state vector rotation  phase gate C 1 1 1 C ei/2 ei/2 1 = U = C 1 ei/2 ei/2 ei e-i 1 C ,  no displacement ,  Phase space for two-ion stretch mode

21. /2, 3/2 Ramsey interferometer input  output 37 s  /2 /2  phase 3/2 GATE measure parity (Cass Sackett et al. Nature, ’01) (spin echo) C.O.M. /2 = 4.64 MHz Fidelity of Bell states made with gate: F½{ + i}{ - i}  0.97 Didi Leibfried et al., Nature422, 412 (2003)

22. Scale up?

23. axial modes, N = 4 ions a (C.O.M.) b (stretch) c (Egyptian) d (stretch-2) () “carrier” 60 d b+c c b c-a 2b,a+c a+b b-a 2a c-a b-a b+c 2b,a+c a a+b Fluorescence counts 40 2a N-ion spectrum: d a b carrier axial modes only c 20 -15 -10 -5 0 5 10 15 Raman Detuning dR (MHz) Many ions in one trap? Four-ion excitation spectrum: (Chris Monroe et al., Atomic Physics 17, 2001)

24. multiplexed trap architecture • 1. interconnected multi-zone structure •  subtraps decoupled • 2. move ions with electrode potentials • 3. logic ions sympathetically cooled • few normal modes to cool • weak cooling in memory zone 4. individual optical addressing • during gates not required •  gates in tight trap  fast • 5. readout, for error correction, • in (shielded) subtrap •  no decoherence from fluorescence • Wineland et al., J. Res. Nat. Inst. Stand. Technol. 103, 259 (1998); • Kielpinski et al., Nature 417, 709 (2002). • Other proposals: • Cirac et al., Phys. Rev. Lett. 78, 3221 (1997) • DeVoe, Phys. Rev. A 58, 910 (1998) • Cirac & Zoller, Nature 404, 579 ( 2000) • L.-M. Duan, et. al., quant-ph/0401020 (2004)

25. Modularity array N4N: ● no additional motional modes ● mode frequencies same “only” have to demonstrate basic module

26. Ion separation:

27. separation in six zone alumina/gold trap(Murray Barrett, Tobias Schaetz et al.) 200 m separation zone 100 m dc rf view along axis: dc rf

28. Boumeester et al. Nature, ’97 Furusawa et al. Science, ’98 Boshi et al. PRL, ’98 Kim et al. PRL, ’01 Bowen et al. PRA ’03 Zhang et al. PRA ‘03 PHOTONS: NMR: Nielsen et al. Nature ‘98 Quantum Teleportation (C. Bennett et al., PRL 1993) 2 bits of classical information Bob applies either I, x, y, or z to his bit to recover U Alice measures bits U and A, sends result to Bob Alice and Bob initially share one qubit of an entangled pair qubit inUnknown state

29. Teleportation protocol: A,B = AB - AB(normalization omitted) unknown  U = U +U rewrite  = A,B  unknown =4k=1 A,U,k  (Õkunknown)B A,U,k orthonormal & entangled (“Bell states”) (Õkunknown)B orthonormal Bob applies (Õk)-1 Bell states: - = AB - AB, + = AB + AB - = AB - AB, + = AB + AB

30. Quantum Teleportation with ions completes experiment initialization Create entangled state on outer ions |­ñ1|¯ñ2|¯ñ3 - |¯ñ1|¯ñ2|­ñ3 = |¯ñ2{|­ñ1|¯ñ3 - |¯ñ1|­ñ3} Alice prepares state to be teleported ( a|­ñ2 + b|¯ñ2 )( |­ñ1|¯ñ3 - |¯ñ1|­ñ3 ) 1 2 3 Alice performs Bell basis decoding using phase gate on ions 1 and 2 Bob performs conditional rotation dep. on meas. Bob recovers a|­ñ + b|¯ñon ion 3 and checks the state Prepare ions in state |¯¯¯ñ and motional ground state Alice measures ion 1 Alice measures ion 2 protocol in ~2.5 msec Barrett et al., Nature, June, ’04) (also demonstrated at Innsbruck with Ca+ ions, Nature, June ‘04)

31. Teleportation (and other experiments) require lots of spin-echos! DFS qubits:(Dave Kielpinski et al., Science, 291, (2001) ) immune to magnetic field fluctuations (but not gradients)

32. “field-independent” for B  0 “field-independent” at 119.5 gauss (Chris Langer) for B = 0.01 G, 2( = 1 rad)  0.52 s field- independent physical qubits? |F,mF |1,-1 |1,0 |1,+1 |2,+2 |2,+1 |2,0 |2,-1 |2,-2 9Be+ hyperfine energy for B = 0.01 G  |2,2 |1,1 2( = 1 rad)  7.5 s Previous demonstration (NIST) 2, 1 > 500 s (B = 0.82 T, 9Be+) B(gauss)  200 100 Bad news: Motional phase gate generally won’t work on field independent hyperfine transitions

33. Trapology: • Requirements: •  small (~ 10 - 400 m electrode separations) • no RF breakdown (~ 500 V, ~ 100 MHz between RF and “control” electrodes) •  small RF loss tangent of insulators • high vacuum compatibility (~ 10-11 Torr, room temp) •  bakeable (~ 300 C) •  CLEAN electrodes

34. Brian DeMarco, Amit Ben-Kish

35. B-Silicon Trap 1 cm side slot width 10um DC electrodes RF electrode central slot width 200um (Joe Britton, Dave Kielpinski) Anodic Bonding

36. Read neutral atom papers: planar geometry: (John Chiaverini) • fabrication steps • low loss substrate • deposit/pattern metal • control electrodes on outside (connections straightforward) • on-chip filtering Field lines:

37. Microfabricated surface ion trap Ground Control lead Trapping region Current fabrication method: Liftoff with substrate etch photoresist • Coat substrate and define wire pattern in resist • Deposit metal • Remove resist • Etch trenches in substrate (RIE or HF) and remove resist substrate metal 2 mm Microfabricated filter resistor RF lead Filter capacitor Control electrodes RF electrode 200 um Ground

38. R z Turchette et al., PRA 61, 063418 (2000) z-axis heating quanta/ms    R = 270 m (Mary Rowe et al. ‘02) z/2 (MHz)  Heating in linear traps (greater than Johnson noise heating !)

39. Sympathetic Cooling Approaches: Cooling Light Cooling with same species Innsbruck group: Rhode, et al., J. Opt. B 3, S34 (2001) 40Ca+ 40Ca+ Cooling with different isotopes Michigan group: Blinov, et al., PRA 65, 040304 (2002) 114Cd+ 112Cd+ Cooling with different ion species NIST (Barrett et al., PRA68, 042302 (2003) 24Mg+ 9Be+

40. Next … • Quantum-information processing: put together all elements of • multiplexed trap, improve fidelity, increase N more complicated algorithms, quantum error correction, … II. build larger (and more reliable) trap arrays lithography, chemical machining, MEMS, ? III. “scale” electronics and optics integrated electronics and optics (multiplexers, DACs, MEMS mirrors, …) V. Future? •  crack secret codes and make Schrödinger’s cat? • or: discover fundamental source of decoherence! • better clocks • ???

41. NIST ions, March, ‘04 From left to right:Joe Britton, Jim Bergquist, John Chiaverini, Windell Oskay, Marie Jensen, John Bollinger, Vladislav Gerginov, Taro Hasegawa, Carol Tanner, Wayne Itano, Jim Beall, David Wineland, Dietrich Leibfried, Chris Langer, Tobias Schaetz, John Jost, Roee Ozeri, Till Rosenband, Piet Schmidt, Brad Blakestad