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Mark Acton (grad) Kathy-Anne Brickman (grad) Louis Deslauriers (grad) Patricia Lee (grad) Martin Madsen (grad) David Moehring (grad) Steve Olmschenk (grad)

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Text of Mark Acton (grad) Kathy-Anne Brickman (grad) Louis Deslauriers (grad) Patricia Lee (grad) Martin...

  • Mark Acton (grad)Kathy-Anne Brickman (grad)Louis Deslauriers (grad)Patricia Lee (grad)Martin Madsen (grad)David Moehring (grad)Steve Olmschenk (grad)Daniel Stick (grad) Advanced Researchand Development ActivityUS Army Research OfficeUS National Security AgencyNational ScienceFoundationFOCUSFOCUS CenterBoris Blinov (postdoc)Paul Haljan (postdoc)Winfried Hensinger (postdoc)Chitra Rangan (postdoc/theory to U. Windsor)

    Luming Duan (Prof., UM)Jim Rabchuk (Visiting Prof., West. Illinois Univ.)David Hucul (undergrad)Rudy Kohn (undergrad)Mark Yeo (undergrad)NSF

  • Trapped Atomic Ions IQuantum computing and motional quantum gatesChristopher MonroeFOCUS Center & Department of PhysicsUniversity of Michigan

  • When we get to the very, very small world say circuits of seven atoms - we have a lot of new things that would happen that represent completely new opportunities for design. Atoms on a small scale behave like nothing on a large scale, for they satisfy the laws of quantum mechanicsThere's Plenty of Room at the Bottom(1959 APS annual meeting)Richard Feynman

  • A quantum computer hosts quantum bits that can store superpositions of 0 and 1

    classical bit: 0 or 1 quantum bit: |0 + |1

  • GOOD NEWSquantum parallel processing on 2N inputs

  • depends on all inputsquantumlogic gatesGOOD NEWS!quantum interference

  • Key resource: Quantum Entanglement not just a choice of basis e.g. - vs. |0,0 must be able to access subsystems individually (see Bell )

  • 1 = | + |2 = | + | + | + | + | + | very hard to quantify (esp. mixed states)

  • Quantum computer hardware requirementsMust make states like

    |0000 + |1111

  • N qubitscontrolledcoupling to >99% accuracy** provided things have been done rightQuantum Information and Atomic Physics

  • 0.3 mm199Hg+J. Bergquist, NISTAarhusBoulder (NIST)Munich (MPQ)HamburgInnsbruckLos AlamosMcMasterMichiganOxfordTeddington (NPL)Ion Trap QC Groups:Trapped Atomic IonsJ. Bergquist (NIST)

  • 2 Cd+ ions

  • SPD||Ca+, Sr+, Ba+, Yb+ optical(1015 Hz)t 1 secEnergyAtomic Ion Internal Energy Levels (think: HYDROGEN)

  • State |N


    SHyperfine Structure: States of relative electron/nuclear spinState |S



  • 111Cd+ atomic structure1,11,01,-10,0l=215nm2S1/22P3/22,22,114.53 GHz||

  • 1,11,01,-10,0l=215nm2S1/22P3/22,22,114.53 GHz||g/2p = 50 MHzbright111Cd+ qubit measurement

  • 1,11,01,-10,0l=215nm2S1/22P3/22,22,114.53 GHz||g/2p = 50 MHz 99.7% detectionefficiencydark111Cd+ qubit measurement

  • 1,11,01,-10,0l=215nm2S1/22P3/22,22,114.53 GHz||111Cd+ qubit manipulation: microwavesmicrowavescoupling rate: gm

  • Time t (ms) (ms),11,01,-10,0Microwave Rabi FloppingProb(10|00)Prob(11|00)prepare00tmwavesmeasurefluorescence(bright or dark)sweep tgm 10-100kHz

  • t (ms) or dark)incrementtSingle shot Rabi FloppingProb(10|00)

  • Time (ms) (ms),11,01,-10,0Microwave Ramsey InteferometryProb(|)Prob(|)prepare00tmwavesmeasurefluorescencesweep tp/2p/2

  • 1,11,01,-10,0l=215nm2S1/22P3/22,22,114.53 GHz||g/2p = 50 MHz111Cd+ qubit manipulation: optical Raman transitions/2p 0.1-1 THzcoherent coupling rate (good):gR = g1g2/D

    direct coupling to P (bad): Rdec = g g1g2/D2

    want small g/D (but D

  • 0.3 mmJ. Bergquist, NIST

  • Thanks: R. Blatt, Univ. Innsbruck40Ca+

  • logical |0mlogical |1mAnother Qubit: The quantized motion of a single mode of oscillation harmonic motion of a collective single mode described byquantum states |nm = |0m, |1m, |2m,..., where E = w(n+)PHONONS: FORMALLY EQUIVALENT TO PHOTONS

    motional data-bus quantum bit spans|nm = |0m and |1m 012

  • Coupling (internal) qubits to (external) bus qubitradiation tuned to w0-w|||||

  • excitation on 1st lower (red) motional sideband (n=0)w ~ few MHz

  • 012012S1/2P3/2||excitation on 1st lower (red) motional sideband (n=0)

  • Mapping: (| + |) |0m | (|0m + |1m)012012S1/2P3/2||012012S1/2P3/2||

  • Mapping: (| + |) |0m | (|0m + |1m)012012S1/2P3/2||012012S1/2P3/2||

  • Spin-motion coupling: some math

  • stationary terms arise in H at particular values of d :

  • DopplerCoolingRaman spectrum of single 111Cd+ ion (start in |)|,n |,n+1Bluesideband|,n |,n-1-3.6 +3.6d/2p (MHz)

  • n||Raman Sideband Laser-Cooling.n-1.n-1||n-1stimulated Raman ~p-pulse on blue sidebandspontaneous RamanrecyclingDn=-1Dn wrecoil/wtrap
  • DopplerCoolingRaman spectrum of single 111Cd+ ion (3.6 MHz trap)L. Deslauriers et al., Phys. Rev. A 70, 043408 (2004)Doppler+ Raman CoolingP0.50.01.0n <|,n |,n+1Bluesideband|,n |,n-1n 6-3.6 +3.6-3.6 +3.6d/2p (MHz)d/2p (MHz)x0 ~3 nm

  • Heating of asingle Cd+ ion from n0 Trap Frequency (MHz)Heating rate dn/dt(quanta/msec)

    1234560.010.1110Quadrupole Trap (160 mm to nearest electrode) Linear Trap (100 mm to nearest electrode)Heating Ratedn/dt (quanta/msec)Decoherence of Trapped Ion Motion

  • Heating history in 3-6 MHz traps 40Ca+199Hg+111Cd+9Be+Distance to nearest trap electrode [mm] rate (quanta/msec)137Ba+ IBM-Almaden (2002)40Ca+ Innsbruck (1999)199Hg+ NIST (1989)9Be+ NIST (1995-)111Cd+ Michigan (2003)Q. Turchette, et. al., Phys. Rev. A 61, 063418-8 (2000)L. Deslauriers et al., Phys. Rev. A 70, 043408 (2004)

  • Trap dimension [mm] 10-12 (V/m)2/Hz40Ca+199Hg+111Cd+137Ba+9Be+1/d4 guide-to-eyeElectric Field Noise History in 3-6 MHz traps~ 1/d 4Heating due tofluctuating patch potentials (?)dest. thermal noise

  • Quantum Gate Schemes for Trapped Ions

    Cirac-Zoller Mlmer-Srensen Fast Impulsive Gates

  • Universal Quantum Logic Gateswith Trapped IonsStep 1 Laser cool collective motion to rest Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995)n=0

  • Universal Quantum Logic Gateswith Trapped IonslaserjkStep 2 Map jth qubit to collective motion Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995)

  • Universal Quantum Logic Gateswith Trapped IonslaserjkStep 3 Flip kth qubit depending upon motion Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995)

  • Universal Quantum Logic Gateswith Trapped IonslaserjkStep 4 Remap collective motion to jth qubit (reverse of Step 1) Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995)Net result: [|j + |j] |k |j |k + |j|kn=0

  • CNOT between motion and spin (1 ion): F=85%C.M., et. al., Phys. Rev. Lett. 75, 4714 (1995)

    CNOT between spins of 2 ions: F=71%F. Schmidt-Kaler, et. al., Nature 422, 408-411 (2003). Demonstrations of Cirac-Zoller CNOT Gate

  • = a||0m + b ||1mDuring the gate (at some point), the state of an ion qubit and motional bus state is:Decoherence Kills the Cat

  • Direct coupling between | and | with bichromatic excitation ?uniformillumination| + eif|2||e

  • Bichromatic coupling to sidebandsuniformillumination|, |||n-1nn+1nneMlmer/SrensenMilburn/Schneider/James(1999)

  • Mlmer/Srensen 2-ion entangling quantum gate a super p/2-pulseBig improvement no focussing required no n=0 cooling required less sensitive to heating||||n-1nn+1nnn-1nn+1

  • Can scalable to arbitrary N!e.g., 6 ions Coupling: H = g Jx2 flips all pairs of spins

    Entangling rate N-1/2

  • Four-qubit quantum logic gateSackett, et al., Nature 404, 256 (2000)| | + eif|

  • xpN=1 ion: Force = F0|| (spin-dependent force)Same idea in a different basis

  • Strong Field Impulsive Gates2S1/22P1/2||Ds+0,01,11,01,-10,01,11,01,-1e.g. 111Cd+14.5 GHzstrong coupling: WRabi >> w and WRabit ~ 1off-resonant laser pulse; differential AC Stark shift provides qubit-state-dependent impulse

  • | |= |k = linear shiftf = nonlinear shift = 2Uddt/++dd++dipole engineering: Udd = m1m2/r3 = (ed)2/r3r| e+ik-if/2|= || e-ik-if/2|= || |= eif |quantum phase gated(t)tsub ms Cirac & Zoller (2000)

  • Poyatos, Cirac, Blatt & Zoller, PRA 54, 1532 (1996)Garcia-Ripoll, Zoller, & Cirac, PRL 91, 157901 (2003) |||e|||ep-pulseupp-pulsedowntwo sequential p-pulsesspin-dependent impulse(b) resonant ultrafast kicks

  • The trajectory of a normal motional mode of two ions in phase space under the influence of four photon kicks. Gray curve: free evolution. Black curve: four impulses kick the trajectory in phase space, with an ultimate return to the free trajectory after ~1.08 revolutions.

  • 2S1/22P1/2||s+0,01,11,01,-1l=226.5 nm10 psecnokick2P3/21/(15 fsec) = FS splittingte 3nsec|eFast version of sz phase gate does not require Lamb-Dicke regime!e.g. 111Cd+require tFS
  • Summary

    Trapped Ions satisfy all DiVincenzo requirements for quantum computing:

    1. identifiable qubits2. efficient initialization3. efficient measurement4. universal gates5. small decoherenceSO WHATS THE PROBLEM?!

  • ENIAC(1946)

  • Next: Ion Traps and how to scale them!

    Good-bad-good. Exponential storage. X2 example of parallelism.Shor started it all