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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)http://iontrap.physics.lsa.umich.edu/US 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

    SN

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

    NN

    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)0.00.20.40.60.81.00.00.20.40.60.81.0Time (ms)0.00.20.40.60.81.00.00.20.40.60.81.01,11,01,-10,0Microwave Rabi FloppingProb(10|00)Prob(11|00)prepare00tmwavesmeasurefluorescence(bright or dark)sweep tgm 10-100kHz

  • t (ms)00.20.40.60.81050100150200250300350400prepare00tmwavesmeasurefluorescence(bright or dark)incrementtSingle shot Rabi FloppingProb(10|00)

  • Time (ms)0.00.20.40.60.81.00.00.20.40.60.81.0Time (ms)0.00.20.40.60.81.00.00.20.40.60.81.01,11,01,-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 |)0.00.51.0PRedSideband|,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 < 0.050.00.51.0PRedSideband|,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]0.040.10.20.30.610-310-210-1100101102137Ba+heating 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]0.040.10.20.30.610-210-1100101102SE(w) 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