Entanglement and Transfer of of Quantum Information with Trapped Ca + Ions Rainer Blatt Institut für Experimentalphysik, Universität Innsbruck, Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften Ion traps for quantum information processing Spectroscopy, addressing and cooling of trapped ions Cirac-Zoller CNOT gate operation Entanglement and Bell state generation Quantum teleportation Interfacing quantum information using cavities FWF SFB QUEST QGATES Industrie Tirol IQI GmbH $
Quantum gate proposals with trapped ions Controlled NOT : ε ε ε ε ε 1 2 1 1 2 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 control bit bit target bit bit other gate proposals (and more): Cirac & Zoller Mølmer & Sørensen, Milburn Jonathan & Plenio & Knight Geometric phases Leibfried & Wineland
Quantum Quantumcomputer computer with withtrapped trappedions ions J. I. Cirac, P. Zoller; Phys. Rev. Lett. 74, 4091 (1995) L Ions in linear trap z state vector of quantum computer z quantum bits, quantum register - narrow optical transitions - groundstate Zeeman coherences z 2-qubit quantum gate laser pulses entangle pairs of ions z state measurement with 100% efficiency control controlbit bit target targetbit bit z decoherence small z quantum computer as series of gate operations (sequence of laser pulses)
Innsbruck linear ion trap (2000) 1.0 mm 6 mm ω z 0.7 2 MHz ω x, y 1.5 4 MHz
String of 40 40 Ca + ions in in a linear Paul trap row of qubits in a linear Paul trap forms a quantum register 70 µm
Level scheme of of Ca + qubit on narrow S - D quadrupole transition P 3/2 854 nm P 1/2 393 nm 397 nm 866 nm D 5/2 D 3/2 729 nm S 1/2
Spectroscopy with withquantized fluorescence (quantum jumps) P monitor Fluorescence intensity S time (s) D spectroscopy S D Anzahl # of measurements der Messungen absorption and emission cause fluorescence steps (digital quantum jump signal) 8 7 6 5 4 3 2 1 detection efficiency: 99.85% D-Zustand D state occupied besetzt S S-Zustand state occupied besetzt 0 0 20 40 60 80 100 120 counts Zählrate per pro 9 ms
Quantized Ion Motion 2-level-atom e Ω Γ g harmonic trap ν {... coupled system... n 1,e n 1, g n,e n,g n +1,e n +1, g... excitation: various resonances spectroscopy: carrier and sidebands n = 0 D 5/2 n = -1 n = 1 S 1/2 ω n = 0 1 2
Spectroscopy of of the S 1/2 1/2 D 5/2 5/2 transition Zeeman structure in non-zero magnetic field: D 5/2-5/2-3/2-1/2 1/2 3/2 5/2 2-level-system: 12 52 ( 12) S 1/2-1/2 1/2 + vibrational degrees of freedom sideband cooling quantum state processing
Excitation spectrum of of single ion in in linear trap ω ax = 1.0 MHz ω rad = 5.0 MHz
Addressing of of individual ions in in a linear Paul trap Experimental setup: CCD images: laser beam steering with an electrooptic deflector Fiber output 729nm viewport Paul trap lens 20µm P 3/2 P 1/2 40Ca + 854nm 866nm telescope 397nm 729nm D 5/2 D 3/2 dichroic beamsplitter S 1/2 detection at 397nm CCD H.C. Nägerl et al., Phys. Rev. A 60, 145 (1999)
Coherent state manipulation D,0 D,1 carrier S,0 S,1 carrier and sideband Rabi oscillations with Rabi frequencies sideband time (µs) Lamb-Dicke parameter time (µs)
The Cirac-Zoller CNOT gate operation with 2 ions allows the realization of a universal quantum computer! 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 control bit bit target bit bit F. Schmidt-Kaler et al., Nature 422, 408 (2003)
Cirac --Zoller two-ion controlled-not operation ion 1 motion ion 2 S S, D SWAP SWAP -1 0 0, D control qubit target qubit pulse sequence: Ion 1 laser frequency pulse length optical phase Ion 2
Experimental fidelity of of Cirac-Zoller CNOT operation F. Schmidt-Kaler et al., Nature 422, 408 (2003) input output
measure the parity Π: Entanglement C. A. Sackett et al., Nature 404, 256 (2000) Ion 1 Ion 2 π/2 0 CNOT π/2 ϕ π/2 ϕ Π oscillates with 2ϕ! 54% visibility Fidelity = 0.5(P SS SS +P +P DD DD +visibility) = 71(3) % F. Schmidt-Kaler et al., Nature 422, 408 (2003)
Gate tomography characterizes gate operation completely
ideal CNOT gate operation Gate tomography, theory
real CNOT gate operation Gate tomography, experiment
Preparation of of Bell states and measurement Ion 1 Ion 2 bsb π/2 carrier bsb carrier π π τ carrier π/2 ϕ carrier π π/2 ϕ parity measurement C. Roos et al., Phys. Rev. Lett. 92, 220402 (2004)
Push-button preparation and tomography of of Bell states Ψ + Φ + Fidelity: F = 0.91 SS SDDS SS SDDS DD SS SD DD DS DD SS SD DD DS Entanglement of formation: E(ρ exp ) = 0.79 Ψ Φ SS SDDS SS SDDS Violation of Bell inequality: DD SS SD DD DS DD SS SD DD DS S(ρ exp ) = 2.53 > 2 C. Roos et al., Phys. Rev. Lett. 92, 220402 (2004)
Time evolution of of the Bell state: phase evolution Bell state production analysis Time evolution in the presence of a magnetic field gradient b :
Decoherence-free Bell states C. Roos et al., Phys. Rev. Lett. 92, 220402 (2004) decoherence-time: 0.5 x 1.05(15) s
Decoherence-free Bell states prepare qubits in S states D 1/2 3/2-1/2-5/2-3/2 5/2 Hiding states in S, S states avoids decoherence from spontaneous emission D 5/2 1.0 0.8 Lifetime: 11.6 ± 1.3 s S 1/2 S -1/2 1/2 S Contrast 0.6 0.4 0.2 0.0 0 2 4 6 8 10 Time (s)
Entangled states with three ions GHZ states: W states: C. Roos et al., Science 304, 1478 (2004)
3 Ions: Preparation of of W states Ion 1 Ion 2 Ion 3
W states: populations Fidelity: 85 % DDD DDS DSD DSS SDD SDS SSD SSS experimental result DDD DDS DSD DSS SDD SDS SSD SSS theoretical expectation C. Roos et al., Science 304, 1478 (2004)
Preparation Preparationof ofaaghz GHZstate state Ion 1 Ion 2 Ion 3
GHZ states: populations Fidelity: 72 % DDD DDS DSD DSS SDD SDS SSD SSS DDD experimental result DDS DSD DSS SDD SDS SSD SSS theoretical expectation C. Roos et al., Science 304, 1478 (2004)
Measuring GHZ and W states coherence destroyed projection of the center ion Bell state survives!
Selective readout of of the 2nd qubit C. Roos et al., Science 304, 1478 (2004) ion #2 in D> ion #2 in S> Read out of ion #2 of a W state does not destroy the coherence between ion #1 and #3. The information on the state of ion #2 is available before the tomography of the remaining quantum register is carried out.
ALICE Teleportation measurement in Bell basis recover input state unknown input state class. communication rotation Bell state BOB M. Riebe et al., Nature 429, 734 (2004)
Quantum teleportation protocol Ion 1 classical communication Ion 2 Ion 3 Bell state C initialize #1, #2, #3 #2 and #3 entangled CNOT operation, Bell basis state prepared on #1 Bell measurement conditional rotations on #3 recovered on #3 check #3
Hiding qubits detect quantum state of ion #1 only D 5/2 D 5/2 π D 5/2 π S 1/2 S 1/2 S 1/2 ion #1 ion #2 ion #3
Hiding qubits detect quantum state of ion #1 only superpositions of ions #2, #3 protected D D D D D 5/2 D 5/2 D 5/2 S 1/2 S 1/2 S 1/2 ion #1 ion #2 ion #3
Quantum teleportation protocol, hiding states Ion 1 Z C H Ion 2 Ion 3 Bell state H C H state protected U H U C Z X Hiding state in D Unhiding state to S
Quantum teleportation protocol, details Ion 1 Ψ B B B B C C H conditional rotations using electronic logic, triggered by PM signal Ion 2 C B B B C H U H Ion 3 C H U C H U C C C C 1 Ψ B C blue sideband pulses carrier pulses spin echo sequence full fullsequence: 26 26 pulses + 2 measurements
Teleportation procedure, analysis Initial Input state Output state Final U TP U -1 Fidelities
Quantum teleportation with atoms: result 75 % 67 % 50 % M. Riebe et al., Nature 429, 734 (2004) similar results by NIST Boulder, ibid., 737 (2004)
Quantum teleportation with atoms: result 83 % class.: 67 % no cond. op. 50 % latest results!
Scaling the ion trap quantum computer. more ions, larger traps, phonons carry quantum information Cirac-Zoller, slow for many ions (few 10 ions maybe possible) move ions, carry quantum information around Kielpinski et al., Nature 417, 709 (2002) requires small, integrated trap structures, miniaturized optics and electronics
Scaling the ion trap quantum computer. cavity QED: atom photon interface, use photons for networking J. I. Cirac et al., PRL 78, 3221 (1997) C. Becher et al., Univ. Innsbruck trap arrays, using single ion as moving head motion I. Cirac und P. Zoller, Nature 404, 579 (2000) head ion solid state qubits (e.g. charge qubit) L. Tian et al., PRL 92, 247902 (2004) target pushing laser more ideas?
High finesse cavity: Cavity QED with single trapped ions Paul trap qubit photons Experimental sequence: i) Ion in superposition state ii) iii) Cavity tuned to qubit transition, vacuum cavity field induces spontaneous decay Photonic qubit leaves cavity P 1/2 D 5/2 S 1/2 729 nm cavity Applications: single photon source Interface: static qubits flying qubits Cavity QED with continuously trapped atoms Quantum feedback
Nanoscopic mapping of of a standing wave A. Mundt et al., Phys. Rev. Lett. 89, 103001 (2002) Excitation probability 0.30 0.25 0.20 0.15 0.10 0.05 Visibility 96% wavepacket 16 nm Spatial Spatial precision of of positioning the the ion ion is is given given by by uncertainty in in the the excitation probability 0.00 120 140 160 180 200 220 240 Piezo offset voltage (V) (7, (7, 12, 12, 36) 36) nm nm @ (slope,min,max) See also MPQ group, Nature 414, 49 (2001)
Coherent ion --field coupling n Cavity stabilized to laser frequency n Few µs laser pulse coupled into cavity n Rabi oscillations on carrier excited by cavity field n State detection after ~ 1ms n Ion Doppler-cooled to <n> 15 A.B. Mundt et al., Appl. Phys. B 76, 117 (2003).
Cavity parameters Ion - cavity field coupling: Cavity decay rate: Spontaneous emission rate: g / 2π = 134 Hz κ / 2π = 102 khz γ / 2π = 0.17 Hz Cooperativity parameter: C = g 2 / (2κγ) = 0.52 Purcell factor: F = 2C+1 = 2 Spontaneous emission factor: β = 2C / (2C+1) = 51% Demonstration of cavity-modified spontaneous emission Potential for deterministic single photon source Atom-photon interface
Lifetime in in the cavity vacuum field standing wave n Place ion at specific point in standing wave n Measure lifetime: excite to m j =-5/2 state, 20.000 experiments with 50 ms waiting time for each data point (19 min) n Drift: ~linear ~λ/50 (15 nm) for each data point n Purcell-effect: 15(5)% A. Kreuter et al., PRL 92, 203002 (2004) n Map of cavity standingwave vacuum field!
Qubit interfacing: Transferring quantum information S 1/2 P 3/2 D 5/2 π/2 Cavity Transfer quantum state state of of the the ion ion to to cavity cavity photon: qubit qubitinterface Create Create superposition photon photon state state (STIRAP) Detect Detect cavity cavity output output and and ion ion state state qubit 1 Choose coupling g by by STIRAP detuning Controlled ion-cavity interaction photonic channel J. I. Cirac et al., PRL 78, 3221 (1997) qubit 2
Outlook: Deterministic single photon source P 3/2 P 1/2 393 nm 1 GHz 854 nm cavity D 5/2 D 3/2 Couple P 3/2 -D 5/2 : high-finesse cavity @ 854 nm Emission of a single photon into cavity: adiabatic Raman passage (STIRAP) Photon leaves cavity within decay time of ~8.5µs S 1/2 Proposals: A.S. Parkins et al., PRL 71, 3095 (1993); C.K. Law and H.J. Kimble, J. Mod. Opt. 44, 2067 (1997); A. Kuhn et al. Appl. Phys. B 69, 373 (1999) Experiment: A. Kuhn et al. PRL 89, 067901 (2002)
Cavity and ion trap (2004) 2 cm C. Becher, C. Russo
Ion trap and cavity (2004) 2 cm
Cavity and ion trap as single photon source Finesse ~ 80000 waist ~ 13 µm (nearly concentric cavity) expect ~ 20 khz single photons with ~ 90% emission into cavity details: 2 cm C. Maurer, C. Becher et al. New Journ. Physics 6, 94 (2004)
Quantum information processing with trapped Ca + ions Innsbruck: Ca + experiments - linear trap (ν z = 1.2 2 MHz, ν x,y = 4 MHz) composite phase gate and CNOT operations realization of two-ion Cirac-Zoller CNOT operation Bell and GHZ measurements, tomography entanglement measurements, teleportation interfacing quantum information with cavities Future: optimization of Cirac-Zoller gate achieve 3-5 CNOT gate operations error correction protocols with three and five qubits implementation with 43 Ca +, logical qubits + scalability
The international team R. Bhat D. Rotter J. Benhelm T. Körber F. Splatt G. Lancaster M. Riebe A. Kreuter V. Steixner RB C. Becher H. Häffner W. Hänsel T. Deuschle C. Russo C. Roos M. Bacher A. Wilson P. Bushev M. Chwalla F. Schmidt-Kaler FWF SFB QUEST QGATES Industrie Tirol IQI GmbH $