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Hartmut Häffner Institut für Experimentalphysik, Universität Innsbruck and

Quantum information processing with trapped ions. FWF SFB. QUEST QGATES. Industrie Tirol. IQI GmbH. €. $. Hartmut Häffner Institut für Experimentalphysik, Universität Innsbruck and Institut für Quantenoptik und Quanteninformation Innsbruck. Basic experimental techniques

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Hartmut Häffner Institut für Experimentalphysik, Universität Innsbruck and

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  1. Quantum information processingwith trapped ions FWF SFB QUEST QGATES Industrie Tirol IQI GmbH € $ Hartmut Häffner Institut für Experimentalphysik, Universität Innsbruck and Institut für Quantenoptik und Quanteninformation Innsbruck • Basic experimental techniques • Robust two-particle entanglement • Process tomography of a CNOT gate • Teleportation • Multi-particle entanglement • Outlook Quantum optics VI, 17.5. 2005

  2. Why quantum information? Quantum information offers a completely new view on quantum mechanics: we might “understand” what quantum mechanics is about. • In quantum information you can see natures strange rules at work: do “real“ bizarre Gedanken experiments! • A most fascinating topic is to look at non-local superpositions.

  3. Progress in technology … How many atoms per bit? ENIAC (1947) ~ 2017 number of atoms per bit Pentium 4 (2002) 1 atom per bit 1960 1970 1980 2020 2010 1990 2000 year faster = smaller 1 atom

  4. P1/2 D5/2 qubit S1/2 Experimental Setup

  5. The fate of visionaries 20th century about the ENIAC: „Where a calculator on the ENIAC is equipped with 18000 vacuum tubes and weighs 30 tons, computers in the future may have only 1000 tubes and weigh only 1 ½ tons.“ Popular Mechanics, March 1949

  6. Qubits with trapped ions Encoding of quantum information requires long-lived atomicstates: • optical transitions Ca+, Sr+, Ba+, Ra+, Yb+, Hg+ etc. • microwave transitions 9Be+, 25Mg+, 43Ca+, 87Sr+, 137Ba+, 111Cd+, 171Yb+ P3/2 P1/2 qubit (quoctet) D5/2 S1/2 qubit S1/2

  7. Initialization in a pure quantum state: • laser cooling,optical pumping P1/2 P1/2 D5/2 D5/2 t=1s 2. Quantum state manipulation on S1/2 – D5/2 qubit transition Fluorescence detection 40Ca+ S1/2 3. Quantum state measurement by fluorescence detection S1/2 8 One ion : Fluorescence histogram 7 P1/2 P1/2 D5/2 D5/2 6 D5/2 state S1/2 state 5 Quantum state manipulation 50 experiments / s Repeat experiments 100-200 times Doppler cooling 4 Sideband cooling 3 2 S1/2 S1/2 1 0 0 20 40 60 80 100 120 counts per 2 ms Experimental procedure

  8. Initialization in a pure quantum state: • Laser sideband cooling P1/2 P1/2 D5/2 D5/2 t =1s 2. Quantum state manipulation on S1/2 – D5/2 transition Fluorescence detection 40Ca+ S1/2 3. Quantum state measurement by fluorescence detection S1/2 P1/2 P1/2 D5/2 D5/2 Quantum state manipulation 50 experiments / s Repeat experiments 100-200 times Doppler cooling Sideband cooling S1/2 S1/2 Experimental procedure Multiple ions: Spatially resolved detection with CCD camera:

  9. coherent manipulation of qubits 0.8 0.7 electrooptic deflector 0.6 0.5 Excitation 0.4 0.3 • inter ion distance: ~ 4 µm • addressing waist: ~ 2 µm • < 0.1% intensity on neighbouring ions 0.2 0.1 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 dichroic Deflector Voltage (V) beamsplitter Addressing of individual ions Paul trap Fluorescence detection CCD

  10. Addressing of individual ions Rabi oscillations D-state population

  11. Rabi oscillations D-state population Picture atomic polarization laser phase

  12. Rabi oscillations D-state population

  13. Rabi oscillations D-state population To prepare the state shift the phase of the preparation -pulse with respect to all other pulses by .

  14. Phase switched byp/2 1 0.9 0.8 0.7 0.6 0.5 D-state population 0.4 0.3 0.2 0.1 0 0 10 20 30 40 50 60 70 Time (ms) Coherent manipulation Coherent manipulation

  15. External degree of freedom: ion motion row of qubits in a linear Paul trap forms a quantum register

  16. External degree of freedom: ion motion The common motion acts as the quantum bus. 50 µm

  17. External degree of freedom: ion motion The common motion acts as the quantum bus. 50 µm

  18. … External degree of freedom: ion motion harmonic trap . . .

  19. External degree of freedom: ion motion joint energy levels 2-level-atom harmonic trap . . . …

  20. Coherent manipulation Coherent manipulation carrier D-state population sideband

  21. Coherent manipulation carrier sideband carrier and blue sideband Rabi oscillations with Rabi frequencies and is the Lamb-Dicke parameter

  22. Basic experimental techniques • Robust two-particle entanglement • Implementation of a CNOT gate • Teleportation • Multi-particle entanglement • Outlook

  23. … … … … Creation of Bell states

  24. … … … … Creation of Bell states p/2 p/2,BSB

  25. Creation of Bell states … p … … p … p/2,BSB p, carrier

  26. … … … … Creation of Bell states p p p/2,BSB p, carrier p,BSB

  27. SS SD DS SS DD SD Y+ DS DD Measurement of the density matrix: Analysis of Bell states Fluorescence detection with CCD camera: Coherent superposition or incoherent mixture ? What is the relative phase of the superposition ?

  28. Rotation around the x- or the y-axis prior to the measurement yields the phase information of the qubit. => coherences of the density matrix Obtaining a single qubits density matrix (a naïve persons point of view) A measurement yields the z-component of the Bloch vector => Diagonal of the density matrix

  29. Fidelity: F = 0.91 SS SD Entanglement of formation: DS SS DD SD DS DD E(rexp) = 0.79 SS SS SD SD Violation of Bell inequality: DS DS SS SS DD DD SD SD DS DS DD DD SS SD DS SS DD SD S(rexp) = 2.52(6) > 2 DS DD Preparation and tomography of Bell states C. Roos et al., Phys. Rev. Lett. 92, 220402 (2004)

  30. SS SD DS SS DD SD DS DD Lifetime limited by laser frequency stability Lifetime limited only by spontanteous decay of the D level Energy Energy SS SS SD SD DS DS SS SS DD DD SD SD DS DS DD DD SS SD DS SS DD SD DS DD (see e.g. Kielpinski et al.,Science 291, 1013-1015 (2001) Creation of Bell states Decoherence properties of the Bell states long lived (~ 1000 ms) short lived (1 ms)

  31. D5/2 S1/2 Minimum fidelity Ultra-longlived Bell states

  32. Minimum fidelity Ultra-longlived Bell states Lifetime of entanglement > 20 s Line possible death

  33. control target • Basic experimental techniques • Robust two-particle entanglement • Process tomography of a CNOT gate • Teleportation • Multi-particle entanglement • Outlook

  34. control target Cirac-Zoller two-ion controlled-NOT operation ...allows the realization of a universal quantum computer ! control target • other gate proposals include: • Cirac & Zoller • Mølmer & Sørensen, Milburn • Jonathan & Plenio & Knight • Geometric phases • Leibfried & Wineland

  35. Cirac-Zoller two-ion controlled-NOT operation ion 1 SWAP control qubit motion ion 2 target qubit

  36. Cirac-Zoller two-ion controlled-NOT operation ion 1 control qubit motion ion 2 target qubit

  37. Cirac - Zoller two-ion controlled-NOT operation ion 1 control qubit SWAP-1 motion ion 2 target qubit F. Schmidt-Kaler et al., Nature 422, 408 (2003)

  38. laser frequency pulse length optical phase Phase gate Cirac - Zoller two-ion controlled-NOT operation control qubit ion 1 SWAP SWAP-1 motion target qubit ion 2 pulse sequence: Ion 1 Ion 2

  39. Composite 2π-rotation: Phase gate

  40. Mapping between Product and Bell basis Mapping between product and Bell basis Product states Bell states CNOT Ion 1 Ion 2 CNOT Example:

  41. Experimental fidelity of Cirac-Zoller CNOT operation F. Schmidt-Kaler et al., Nature 422, 408 (2003) input output

  42. Gate tomography characterizes gate operation completely

  43. Process tomography, theory ideal CNOT gate operation

  44. Process tomography, experiment real CNOT gate operation

  45. Basic experimental techniques • Robust two-particle entanglement • Process tomography of a CNOT gate • Teleportation • Multi-particle entanglement • Outlook

  46. Alice measurement in Bell basis recover input state classical communication Bob unknown input state rotation Teleportation protocol Phys. Rev. Lett. 70, 1895 (1993) Bell state

  47. classical communication Ion 3 Ion 2 Ion 1 Bell state conditional rotations CNOT -- Bell basis recovered on ion #3 Selective read out Implementation of the teleportation protocol Alice Bob initialize #1, #2, #3

  48. ion #3 ion #2 ion #1 p p Protecting qubits from readout detect quantum state of ion #1 only D5/2 D5/2 D5/2 D5/2 D5/2 D5/2 S1/2 S1/2 S1/2 S1/2 S1/2 S1/2

  49. ion #3 ion #2 ion #1 Protecting qubits from readout detect quantum state of ion #1 only superpositions of ions #2, #3 protected D‘ D D D‘ D5/2 D5/2 D5/2 D5/2 D5/2 D5/2 S1/2 S1/2 S1/2 S1/2 S1/2 S1/2

  50. conditional rotations using electronic logic, triggered by PM signal Y B B B B C C P C B B B C P U P Ion 2 Ion 1 Ion 3 B P U C P U C C C -1 Y spin echo sequence B blue sideband pulses full sequence: 26 pulses + 2 measurements C carrier pulses Teleportation protocol, details

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