Coherent manipulation of qubits for quantum hardware : the example of spins in diamond

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1 GDR CNRS <IQ FA> - Nice, 25 mars 2011 Coherent manipulation of qubits for quantum hardware : the example of spins in diamond Jean-François ROCH Lab. de Photonique Quantique et Moléculaire Ecole Normale Supérieure Cachan, France jean-francois.roch@ens-cachan.fr

2 Quantum information: qubits If the state of a quantum system is a kind of information, then its dynamics is a kind of information processing Idealized quantum circuit : set of n-qubit system for which the dynamical evolution is completely under control Evolution is a sequence of unitary operations done on the n-qubit ensemble, built with step-by-step operations on the qubits called quantum gates by analogy with classical digital information processing

3 Qubits : Di Vincenzo s criteria Scalable physical system with n well-characterized qubits! well defined extensible qubit array Ability to initialize the state of the n-qubit system! preparable in the quantum state for the beginning of the computation Long relevant decoherence time, much longer than the gate operation time! control of qubit isolation from its environment Universal set of quantum gates Qubit-specific measurement capability! perform single quantum measurement Fortsch. Phys. 48, 771 (2000) Finding such system is not an easy task!

4 Physical system suitable as a qubit Anything that can be quantized and follows Schrödinger s equation! Electron : number, spin, energy level Nucleus : spin Atom and ion : energy level Photon : number, polarization, time angular momentum, momentum (energy) Flux (current)...

Some quantum enabling technologies Photons: ideal candidates for

interact directly, hard to store Spins, especially nuclear spins: good

interact strongly, hard to isolate and measure at individual level

quantum state But difficult to interact, hard to integrate Charged

5 Some quantum enabling technologies Photons: ideal candidates for long-distance communication, nearunity detection efficiency But: do not interact directly, hard to store Spins, especially nuclear spins: good isolation from environment, control with NMR techniques But do not interact strongly, hard to isolate and measure at individual level Isolated ions and atoms: excellent isolation, optical control of quantum state But difficult to interact, hard to integrate Charged solid-state systems: integration, design, very strong interaction But complex solid-state environment

bound Control of qubits by different frequencies of magnetic

6 Liquid solution NMR "(+&,-.& Billions of molecules are used, each one acting as an individual quantum computer Qubits are associated to nuclear spins of fluorine atoms shielded by electrons in the molecular bound Control of qubits by different frequencies of magnetic pulses Indirect coupling mediated through bounding electrons Very narrow RF transitions: T2 is a few seconds J coupling

7 NMR-based quantum computing Many successes from first experiments in 1997: - NMR scheme (Cory et al, Gershenfeld et al., 1997) - Grover s algorithm (Jones et al., 1998) - Deutsch-Jozsa algorithm (Chuang et al., 1998) - Decoherence (Knill et al., 1998) - Shor s algorithm (Vandersiepen et al., 2001) - Quantum processing with up to 12 qubits (Negrevergne et al., 2006) Poor scalability as molecule design gets difficult to synthetize and SNR falls Mixed-state questions real entanglement

8 State initialization in NMR up E = µb down For 1 H nuclei in 20-T B-field, need temperature T~ 40 mk At room temperature, need magnetic field of 1.5 x 10 5 T Solution for such noisy systems: pseudo-pure state Pseudo-pure state of the n-qubit system : a mixture between a uniform density operator in Hilbert space (dimension d=2 n ) and a particular pure state density operator ρ PPS = 1 η 2 n I + η ψψ Under unitary operation U, this pseudo-pure state for psi> evolves into the pseudo-pure state associated to U psi> with same purity, allowing to perform the computation

9 Pseudo-pure state initialization in NMR Pseudo-pure states are either naturally available or can be constructed experimentally from thermal states. For e.g. temporal labeling for two coupled spins dŝ(1) z Ŝ z (2) then equalize populations of three levels - e.g. by cyclical permutation and adding the results. Time-averaged populations are then: 1 4 : 1 4 ε : ε, : ε 1/3 1 1/3 = 4 ε ε /3 1 0 Unfortunately for n>>1 coupled spins, the signal becomes highly obscured by the fully mixed state 1 4,,

10 Solid-state spin qubits Dynamic nuclear polarization techniques for solid-state systems, with dipole-dipole coupling B.E. KANE proposal - Nature 393, 133 (1998) -Qubit is the nuclear spin of 31 P nucleus embedded in 28 Si crystal (isotopically purified) -Evolution and measurement of qubit are performed using nearby individual electron -Coupling between two 31 P impurities by weakly localized electron spins 56(,7( 2-3&.%) 4-3&.%) Recently, good progress on fabrication (Sydney, Melbourne) Challenge : spin readout

11 Defects in diamond conduction band valence band Bandgap ~ 5.5 ev, so that a perfect diamond crystal would not absorb visible light e.g. Boron (B) impurities but many defects in the crystal matrix, associated to vacancies or substitutional impurities are optically active. Color centers conduction band acceptor Red absorption valence band Blue color The Hope diamond

Nitrogen-Vacancy (NV) center in diamond Substitutional nitrogen atom (N) associated to a vacancy (V) in the adjacent lattice site of the diamond matrix.

12 Nitrogen-Vacancy (NV) center in diamond Substitutional nitrogen atom (N) associated to a vacancy (V) in the adjacent lattice site of the diamond matrix. Detection as single emitter using confocal microscopy. energy v absorption ZPL emission λ 637 nm 750 nm 1 µm Single NV Gruber et al., Science 276, 2012 (1997)

800 C to stabilize NV defects Also works

Chang (IAMS, Taiwan) In our group at ENS

13 Creation of NV defects in diamond Diamond with a high N content (>100 ppm) Irradiation (e -,H +,!...) to create of vacancies 800 C to stabilize NV defects Also works for diamond nanocrystals nm diamond nanocrystals hosting single NV defects H.-C. Chang (IAMS, Taiwan) In our group at ENS Cachan in collaboration with G. Dantelle, T. Gacoin (PMC, France) AFM image 1 µm Confocal image

, APL 87, 261909 (2005) PLASMA hydrogen + methane layer of CVD diamond substrate diamond N +

14 Engineering defects in high-purity CVD diamond microwaves CVD diamond Nitrogen implantation 2-MeV ions with beam ø ~ 0.5 µm J. Meijer et al., APL 87, (2005) PLASMA hydrogen + methane layer of CVD diamond substrate diamond N + ions [N] < 1 ppb Confocal map g (2) measurement CEA Saclay P. Bergonzo LIHMP Villetaneuse J. Achard, F. Silva, A. Gicquel Element 6, UK D. Twitchen 10 µm

Luminescence properties NV defects are perfectly photostable at room T Efficient solid-state single-photon source 3E delay " Antibunching! QKD experiments Beveratos et al.

15 Luminescence properties NV defects are perfectly photostable at room T Efficient solid-state single-photon source 3E delay " Antibunching! QKD experiments Beveratos et al., PRL 89, (2002) Alléaume et al., NJP 6, 92 (2004) 532 nm! Delayed-choice interference 3A HBT Jacques et al., Science 315, 966 (2007) which is even commercially available!!! Quantum Communication Victoria

Application of NV centers in biology! NV defects are perfectly photostable at room T Used as fluorescent label in biology NV defect in nanodiamonds (10nm) No toxicity a priori F.

16 Application of NV centers in biology! NV defects are perfectly photostable at room T Used as fluorescent label in biology NV defect in nanodiamonds (10nm) No toxicity a priori F. Treussart (LPQM, ENS Cachan) Falkaris et al. Small 4, 2236 (2008) H.-C. Chang (IAMS, Taiwan) Nature Nanotechnology 3, 284 (2008) - 3D tracking of a nanodiamond hosting NV defects in a live HeLa cell

17 Spectroscopy of NV - color centers : Beyond Perrin-Jablonski s diagram energy + electron spin absorption ZPL emission λ 637 nm 750 nm 6 electrons { 3 from C 2 from N 1 from other N (or donor)

C N V NV electron spin structure Optical transitions between triplet levels 3 A et 3 E preserve electron spin stage Leak of 3 E to metastable 1 A singlet state induces spin-flop Egap = 5.

18 C N V NV electron spin structure Optical transitions between triplet levels 3 A et 3 E preserve electron spin stage Leak of 3 E to metastable 1 A singlet state induces spin-flop Egap = 5.5 ev 3 E (S = 1) ev m { S m S ±1 3 A (S = 1){ 0 1 A (S = 0) 2.88 GHz m S ±1 { 0 Dark Bright optical pumping into S z state S z bright and S x,s y dark luminescent levels N. B. Manson et al., Phys. Rev. B 74, (2006) 18

Single-electron spin resonance 1.00 luminescence 0.

90 fréquence micro-onde (GHz) Single-spin readout

19 Single-electron spin resonance 1.00 luminescence fréquence micro-onde (GHz) Single-spin readout at room temperature The NV center is a spin-based qubit at room T 19

Lett. 92, 076401 (2004) Excited-state MW!

20 Coherent spin manipulation coherently driven electron spin Rabi oscillations Laser 532 nm initialize m s =0 3 µs MW pulse read-out Jelezko et al., Phys.Rev. Lett. 92, (2004) Excited-state MW!! effective 2-level system by Zeeman splitting Faster Rabi oscillation achieved #~1GHz Fuchs et al. Science 326, 1520 (2009)

magnetic fields Type-IIa diamond is an almost spin-free lattice (99 % of 12 C) But Dephasing due to

21 Phase memory time of the electron spin Laser 532 nm initialize m s =0 " $/2 $/2 read-out Ramsey fringes Spin-orbit interaction is weak so decoherence due to phonons is negligeable Spin bath produces random magnetic fields Type-IIa diamond is an almost spin-free lattice (99 % of 12 C) But Dephasing due to uncontrolled 13 C (1%) nuclear spins I=1/2 T 2 a few µs Childress et al. Science (2006) Hanson et al. Science (2008)

22 Engineering the nuclear spin bath Isotopically modified CVD-diamond Daniel Twitchen - Element 6 99,97 % 12 C diamond Spin free matrix T 2 * ~ 50 µs G. Balasubramanian et al., Nature Materials 8, 383 (2009) N. Mizuochi et al., Phys. Rev. B 80, (2009)

23 Record coherence time for electron spin initialize m s =0 Read-out Laser 532 nm Echo amplitude T 2 ~ 2 ms Free precession interval 2" (s) Ultra-pure CVD-grown diamond (99,97 % 12 C diamond, spin free matrix) D. Twitchen Element 6 G. Balasubramanian et al., Nature Materials 8, 383 (2009)

24 Coupling to other spins: 13 C in the 1 st shell Electron spin resonance of NV center m S =0 m S = 1 12 C 13 C NV

25 Three coupled spin qubits Two nearest-neighbor 13 C nuclear spins coupled to a single NV center m S = 1 " # $ RF NV 13 C 12 C 13 C! " # $ MW! m S =0 Ground state spin sublevels 100 MHz

26 Nuclear spin Rabi oscillations! " # $ RF $ " RF ms = 1 Initial. m s =0 Read MW! # Ground level spin states ms =0 0,0 0,5 1,0 1,5 2,0 RF pulse duration (µs) CNOT gate Jelezko et al., Phys. Rev. Lett. 92, (2004) Quantum register Gurudev Dutt et al., Science 316, 1312 (2007)

27 Ramsey fringes on single 13 C nuclear spin Echo measurement: T 2 > 40 ms Gurudev Dutt et al., Science 316, 1312 (2007)

28 Two nuclear spins: entangled Bell-states NV 13 C 12 C 13 C m s = 1 $ Tomography Re(% - ) Coherence time T 1 e-spin RF $/2 & % m s = 0 $ Neumann et al., Science 320, 1326 (2008)

Scaling up: spin lattice of NV centers NV!

NV defects can be used to increase the number

coupling between two electron spins of NV

29 Scaling up: spin lattice of NV centers NV!!"#$Å Magnetic dipole interaction of separated NV defects can be used to increase the number of coupled qubits Demonstration of coherent coupling between two electron spins of NV defects with ~10 nm distance Neumann et al., Nature Phys. 6, 249 (2010) %& %& spin resonance of NVA depending of magnetic state of NVB ms = +1, 0, -1

30 Back to diamond material coupling if Ω dip > 1/T 2 T 2 1 ms r<40 nm Implantation and detection with nm-spatial resolution is required! Implantation of NV defect with a focused ion beam Using high-energy ions and 15-T superconducting solenoid lens Best focus achieved ~500nm 10 µm J. Meijer - RUBION, Bochum

Improving the spatial resolution (1) Implantation through nano-apertures ENS Cachan, Bochum, Thales TRT 14 N PMMA (~200nm) e-beam lithography diamond MEB

31 Improving the spatial resolution (1) Implantation through nano-apertures ENS Cachan, Bochum, Thales TRT 14 N PMMA (~200nm) e-beam lithography diamond MEB image of implantation mask 2 µm 80 nm N content [a.u.] PMMA (e) Depth (nm) 250 Diamond N content [a.u.] Depth (nm) 60 70

32 Figure 2. (a) PL raster scan of the sample, displaying an emission patt low-energy nitrogen implantation [16, 28]. In conclusion, we showed that arrays of NV color centers can be reliabl by implanting CN molecules through the 80 nm diameter holes in a PM of 200 nm thickness which was deposited on top of a single-crystal diamo The joint implantation of carbon increased the conversion of the implant Improving the spatial resolution (1) Implantation through nano-apertures (ENS Cachan, Bochum, Thales TRT) 14 N diamond PMMA (~200nm) (a) e-beam lithography 2 µm (b) MEB image of implantation mask Confocal image of implanted sample µm 2 µm (b) 80 nm Delay τ(ns) Delay (ns) Delay τ(ns) Delay (ns) Figure 2. (a) PL raster scan of the sample, dis the array of holes drilled in the PMMA layer. ( spot, corresponding to the determination of the associated to the time delay τ between consecutiv of the luminescence spectrum. The zero-phonon the center 550 as negatively charged NV. The si Wavelength (nm) single emitter, as observed in the circled spot, w PL [a.u.] ( ) (c) Wa

33 Improving the spatial resolution (2) Low energy ion-beam focused through an AFM tip Hole realized with a Focused Ion Beam Ga + 30 kev AFM tip Meijer et al., Appl. Phys. A 91, 567 (2008)

34 Deterministic single-ion implantation Schnitzler et al., Phys. Rev. Lett. 102, (2009)

35 How to check the spatial resolution Ion beam focused into an AFM tip Sub-diffraction optical imaging is required 1!m STED S. Hell and Wichmann, Opt. Lett. 19, (1994)

36 Nanoscale optical addressing with STED Principle of STimulated Emission Depletion imaging NV luminescence spectrum Exc. STED Excitation + PL (a.u.) detection off Wavelength (nm) 800 Nanoscale optical resolution Excitation + doughnut works remarkably well with NV centers due their photostability (no photobleaching)

37 Nanoscale optical addressing with STED Excitation + E. Rittweger et al., Nature Photonics 3, 144 (2009) Back to Nitrogen implantation through the AFM tip Confocal STED 100 nm 1!m S. Pezzagna et al., Small 6, 2117 (2010)

Phase coherence of implanted NV centers Native NV centers i.e. directly created in the sample growth T 2 200 µs Fabricated NV centers i.

Electron spin of implanted nitrogen atoms remaining non converted into NV defects improve conversion yield

38 Phase coherence of implanted NV centers Native NV centers i.e. directly created in the sample growth T µs Fabricated NV centers i.e. from implanted N impurities T 2 few µs Ions N+ Why decreased spin coherence? Electron spin of implanted nitrogen atoms remaining non converted into NV defects improve conversion yield N NV!! Other defects which have parasitic electron spin, e.g. di-vacancies high-t annealing (> 1200 C)

39 Outlook: Hybrid way for Quantum Computing Microscopic systems : atoms, ions, spins Artificial atoms : supraconducting qubits Both do not meet the Di Vincenzo criteria for QC, but for different reasons Atom - ion - spin : microscopic degrees of freedom - Long coherence time - Microwaves to optical frequencies - Nature given, reproducibility - Small coupling : slow - Limited scalability Artificial supraconducting atoms: collective degrees of freedom - Design flexibility - Microwave frequency - Large coupling : speed - Short coherence time (us) - Scalability? Quantum hybrid system: try to combine best (only!) of both worlds

NV centers and microwave photons propagating

w out B NV Expt by Kubo et al. Phys. Rev.

electronic spin qubit and the motion of a

40 Outlook: quantum hybrid systems Strong coupling regime between an ensemble of ~10 12 NV centers and microwave photons propagating in a on-chip superconducting resonator!w in!w out B NV Expt by Kubo et al. Phys. Rev. Lett. 105, (2010) Coupling between an electronic spin qubit and the motion of a mechanical resonator Proposal par Rabl et al., Nat. Phys. (2010)

41 Conclusion Spin-based qubits can be coherently manipulated using magnetic resonance technology The NV- defect in diamond has unique properties Quantum control and computation Decoherence in mesoscopic spin environment Quantum optics % Relying on the engineering of diamond material N ions

42 Piernicola Spinicelli Anaïs Dréau Loïc Rondin Vincent Jacques Collaborations Jocelyn Achard & François Silva (LIMHP) Thierry Debuisschert (Thales TRT) Géraldine Dantelle & Thierry Gacoin (PMC) Philippe Grangier (Institut d Optique) Fedor Jelezko (Universität Ulm) Jörg Wrachtrup (Universität Stuttgart) François Treussart

Magnetic Resonance in Quantum Information

Magnetic Resonance in Quantum Information Christian Degen Spin Physics and Imaging group Laboratory for Solid State Physics www.spin.ethz.ch Content Features of (nuclear) magnetic resonance Brief History