Trapped ion quantum control. Jonathan Home IDEAS league school,

Transcription

1 Trapped ion quantum control Jonathan Home IDEAS league school,

2 Lectures Ken Brown, IDEAS League school, Sweden 1) Basics (review). Measurement, Preparation, Coherent control fields 2) Quantum state engineering and control of oscillators 3) Quantum computing and control of qubits (+ scaling considerations)

3 What s to like (and dislike) about ions? High gate rate (us) vs coherence time (10 s) High fidelity, single shot readout High fidelity laser and microwave gates Identical systems (Decoherence-Free-Subspace encoding) Why not? Slow (compared to solid state systems). Microseconds vs nanoseconds Cannot pick our frequency wavelengths etc. set by nature Identical systems need to work to achieve individual addressing Challenges: Long-distance links (coupling to single-mode photons) Immature integration with scalable electronics/optics eg. CMOS, waveguides etc. Ions don t like surfaces charging, noise

4 Two state systems in an atomic ion Calcium ion 7 ns lifetime Group 2, with one electron removed (Alkali-like) 1 s lifetime Electron/nuclear spin Orbital angular momentum Principal quantum number year lifetime We are looking for two long-lived states

5 Storing qubits in an atom - phase coherence Problem: noise! mainly from classical fields

6 Storing qubits in an atom Field-independent transitions F = Gauss 1 GHz 1207 MHz F = 2 Langer et al. PRL 95, (2005) Time (seconds!)

7 Entanglement for protection Rejection of common-mode noise DFS states for identical qubits Now consider entangled state If noise is common mode, entangled states can have very long coherence times Haffner et al., Appl. Phys. B 81, (2005)

8 Preparing the states of ions Optical pumping state initialisation Use a dipole transition for speed Example: calcium Calcium: scatter around 3 photons to prepare

9 Reading out the quantum state Collect 0.6 % of emitted photons eg. 300 us detection time, events Detection fidelity > in 150 us (Myerson et al. PRL 100, 20, (2008), Oxford)

10 Manipulating single qubits Resonant microwaves/laser Raman transition, hyperfine Microwaves F > Harty et al. PRL 113, (2014) Lasers F > (Masters thesis Oxford)

11 Isolating single charged atoms Laplace s equation no chance to trap with static fields Paul trap: Use a ponderomotive potential change potential fast compared to speed of ion Time average - Effective potential energy which is minimal at minimum E Penning trap: Add a homogeneous magnetic field overides the electric repulsion

12 Traps traditional style RF electrode DC RF Trap Frequencies Axial : < 3 MHz Radial: < 20 MHz Radial Freq 1/Mass Potentials gives almost ideal harmonic behavior in 3D Single ion n = 2 n = 1 n = 0

13 Motional state control Rich history of experiments Nobel prize 2012: Haroche and Wineland "for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems" Key to understanding all multi-ion work

14 Physics of a trapped ion + laser Internal states Ion motion 3 oscillators per ion Laser-induced coupling

15 Light-atom Hamiltonian Interaction with a classical laser field Electric dipole approximation + Rotating wave approximation Atomic centre of mass position Displacement of atomic centre of mass

16 Lamb-Dicke approximation Interaction picture: motion Interaction picture: internal Calcium optical Microwaves (not usually far field) If LD parameter is small and we are cold enough, can neglect higher orders

17 Lamb-Dicke parameter Tells us the influence of the light on the motion Atomic recoil energy from photon emitted along laser beam Ratio of atomic wavefunction r.m.s size to wavelength

18 Optical pumping + LD parameter In LD regime, spin decays most strongly on the carrier, ie. No motional change In fact, on average each decay picks up 1 recoil In LD regime we can neglect this

19 Ground state laser cooling Spin dissipation can be used as a zero-temperature reservoir Monroe et al. PRL 75, 4011 (1995), Meekhof et al. PRL 76, 1796 (1996) Red sideband + dissipation P X

20 Reservoir engineering Proposals: Cirac et al. PRL 70, 556 (1993), Poyatos et al, PRL 77, 4728 (1996), Carvalho et al PRL 86,22 (2000) Red sideband Carrier Blue sideband D. Kienzler et al. Science 347, 6217 (2015) Squeezed state Displacement P Squeezing P X X

21 Steady-states: Fock state analysis Wineland group: Meekhof et al. PRL 76, 1796 (1996) Anti-Jaynes-Cummings Hamiltonian Use Rabi frequency decomposition to obtain Fock state pop. distribution. Fit to data allows to be extracted

22 Fock state decompositions D. Kienzler et al. Science 347, 6217 (2015) Coherent state Squeezed state Displaced + squeezed

23 Measurement in an engineered basis Problem for large Fock state variance: bad signal/noise for higher Fourier components - no information about the coherences >20 % of population New method: Choose the correct basis for analysis Pumping Probe

24 Measurements in an engineered basis (D. Kienzler, H-Y. Lo et al. Science 347, 6412 (2015))

25 Squeezed-Fock state basis Quantum state engineering in the squeezed-fock state basis

26 The forced quantum harmonic oscillator Resonant Detuned returns after Excitation amount Evolution Transient excitation, phase acquired

27 Driving both sidebands Measure spin in z basis (trace out motion) Schrodinger s cat state P P X Long axis Ground state X Short axis P X

28 Even and odd cats Daniel Kienzler, C. Flühmann, V. Negnevitsky, P 1/2 D 5/2 λ = 397 nm D 3/2 λ = 729nm S 1/2 If ion dark, analyse state

29 Detuning the force Start in Data from: Haljan et al. Phys. Rev. Lett. 94, (2005).

30 Connecting interactions to internal states Independent normal mode oscillations - shared motion Stretch mode Oscillating force close to resonance with Stretch mode of motion F F F F No Motion Motion Motion No Motion

31 Realisations basis, polarisation standing wave F F F F (Leibfried et al. Nature 422 (2003)) basis, interference effect

32 Two-qubit gate, state-dependent excitation Force is out of phase; excite Stretch mode Force is in-phase; excite COM mode

33 One vs two qubits detuned SD force Single ion (periodic loss of overlap) Benhelm et al. Nat. Phys 4, 463(2008)

34 Examples: trapped-ion quantum computing Choose the duration and power: G + single qubit gates is universal can create any unitary operation. Universal two-qubit ion trap quantum processor: Hanneke et al. Nature Physics 6, (2010)

35 Two qubit gate performance analysis Different measurements of performance Detect 8, 6, 7, 4, 9, 0, 0, 1, 1, 6, 1, 9, 0, 0 5, 4, 3,11, 4, 1, 0, 0, 1, 8, 0, 8, 1, 0 Entanglement correlations For a Bell state: apply same rotation to each ion + scan phase Amplitude of fringe 98.3(3)% < Fidelity Best results worldwide: Gate deduced F = 99.9% (Oxford, hyperfine) Bell state F = 99.3% (Innsbruck, optical) Also: randomized benchmarking (Gaebler et al. PRL PRL 108, (2012))

36 GHZ Entanglement of up to 14 ions Monz et al., PRL 106, (2011) High contrast 3 ions Reduced contrast 14 ions

37 Approaches to algorithms/scaling Best system thus far for algorithms single ion string (Blatt, Roos, Innsbruck) Universal operations: - Multi-qubit gate (all ions) - Spin rotation (all ions) - Phase rotation (individual addressing) Example: Quantum error correction Pictures: T. Monz, R. Blatt State of the art: Transversal operations on a Topological 7-qubit Steane code Science 345, 6194 (2014)

38 Collective rotations - challenges Data: C. Hempel, C. Roos, R. Blatt (Innsbruck) 51 ion chain Rabi oscillations (size of ion chain becomes big compared to laser beam)

39 20 ion individual addressing (AC Stark) Data: C. Hempel, C. Roos, R. Blatt (Innsbruck) Global Ramsey, Individually addressed Stark

40 Quantum simulation Go to limit of large motional detuning (very little entanglement between spin and motion) Allows creation of many-body Hamiltonians (Friedenauer et al. Nat. Phys 4, (2008) Kim et al. Nature 465, 7298 (2010))

41 Quantum simulations in ion strings (up to 18 ions Islam et al. Nature )

42 X-Y Hamiltonian / hard-core bosons What if we add a Stark shift to the spin levels? Off-resonant terms These can be written as, hence X-Y Initial excitation (not the gs, or any eigenstate) Colour denotes spin up probability Jurevic et al. Nature 511, 202 (2014)

43 Beyond nearest neighbour long range interactions Entanglement spreads fast Denotes range Jurevic et al. Nature 511, 202 (2014) Nearest neighbour prediction Observed propagation

44 Scalable ion-trap QIP architecture Wineland et al., J. Res. N.I.S.T. (1998), Kielpinski et al. Nature 417, 709 (2002) "Gate" "Move, separate" "Gate" Cooling Logic Transport of ions is a critical ingredient How do we scale up the optical delivery?

45 Integrated components eg. Quantum control using microwaves removes the need for high-power lasers Gradients produce state-dependent potentials through Zeeman shifts Single-qubit gate 2-qubit gate C. Ospelkaus et al. Nature 182, 476 (2011)

46 Integrated components 1 Vandevender et al. PRL 105, (2010)

47 Possible architecture Multiple small processors linked by probabilistic entanglement generation and teleportation Monroe et al. Phys. Rev. A (2014)

48 CMOS ion traps Gate electrodes CMOS electronics doping in substrate First demonstration: Chiaverini et al. Lincoln Labs (also now with integrated waveguides) K. K. Mehta et al. Appl. Phys. Lett 105, (2014)

49 Scaling - electronics In-sequence update time (16 RF outputs) now at 20 us (faster than detection etc.) (critical parameter for error-correction)

50 Bang-bang control of trapped ions (Proposal: J. Alonso et al. New J. Phys. 15, (2013)) DC electrode RF (100 MHz) electrode DC electrode DC electrode DAC 2 DAC 1 Filter distorts time-dependent controls CMOS Switches at 4 Kelvin Access to sudden bang-bang control

51 Transport quantum logic gates Proposal: D. Leibfried et al. PRA 76, (2007) Advantages: reduces switching optics waveforms required anyway parallel use of laser beams in different zones simultaneously

52 Rabi oscillations and qubit rotations L. de Clercq, H-Y. Lo, M. Marinelli Laser Sequence Qubit rotation Readout t Transport t Be+ Raman transition hyperfine qubit, ~1s coherence time t off Pulse sequences (multiple transports) Ramsey separated pulse experiment

53 Parallel transport quantum logic gates L. de Clercq, H-Y. Lo, M. Marinelli Retro-reflect laser beams to different zones A B C z Operation chosen using the transport speed of each ion Ion in zone A Ion in zone A Ion in zone C Ion in zone C

54 Mixed-species ion cahins Be + "logic" Mg + "coolant" Be + "logic" Mg + "coolant" 280 nm 313 nm Be + internal state unaffected by Mg + light Be + external state controlled by Mg + light e.g. Quantum information experiments as ancilla readout + cooling Clock experiments (Aluminium) + Molecular spectroscopy Dissipation in quantum simulation

55 Trapped-ions and optical clocks e.g. Rosenband et al., Science 319, 1808 (2008) Frequency standards Aluminium ion Laser 167 nm 267 nm Require very stable ion transition Has a very stable transition BUT 167 nm is vacuum UV

56 Atomic clocks quantum logic readout Aluminium Clock ion: Shared motion Beryllium Cooling and readout ion Allowed (scatter lots of photons) Among the most accurate and precise frequency standards 8e-18 fractional uncertainty (Chou et al. PRL 104, (2010))

57 Trapped Ion Quantum Information Group ETH Zürich Reservoir engineering + transport gates: Dr. Daniel Kienzler Hsiang-Yu Lo Ludwig de Clercq Vlad Negnevitsky Christa Flühmann Matteo Marinelli Dr. Ben Keitch (Oxford) Bang bang control: Florian Leupold Dr. Joseba Alonso Ursin Soler Zhang Chi Optical traps: Christoph Fischer SNSF Consolidator grant PCF trap: Frieder Lindenfelser Simon Ragg Erlangen: Philip Russell Patrick Uebl, Dmitry Bykov Markus Schmidt