Martes cuántico Zaragoza, 8 th October Atomic and molecular spin qubits. Fernando LUIS Instituto de Ciencia de Materiales de Aragón

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1 Martes cuántico Zaragoza, 8 th October 2013 Atomic and molecular spin qubits Fernando LUIS Instituto de Ciencia de Materiales de Aragón

2 Outline Quantum information with spins 1 0 Atomic defects in semiconductors Molecular quantum bits & gates

3 Outline Quantum information with spins 1 0 Atomic defects in semiconductors Molecular quantum bits & gates

4 Quantum computers Process information using quantum laws Bit Qubit 1 R. P. Feynman, Int. J. Theoret. Phys. 21, 467 (1982) 0

5 Qubits Single qubits 1 0 R 0 H

6 T 2 (s) Qubits Single qubits DE /h 1-40 GHz R 0 H year M. H. Devoret and R. J. Schoelkopf, Science 339, 1169 (2013)

7 Spin qubits Electron spin in a magnetic field B dc S = ½ g = GHz/T DE = g B B dc K/T

8 Spin qubits Electron spin in a magnetic field B dc B 1 e iwt S = ½ g = 2 1 Dt 0 I. I. Rabi, Phys. Rev. B 51, 652 (1937)

9 Spin qubits Electron spin in a magnetic field B dc B 1 e iwt En resonancia: w = DE/h S = ½ g = 2 1 Dt 0 I. I. Rabi, Phys. Rev. B 51, 652 (1937) 0 ( t) cos 2 R B h 0 e i ( t) ( t) sin 2 B1 13 MHz/mT 1

10 Decoherence T1 R 0 ( t) cos 2 0 e i ( t) ( t) sin 2 1

11 Decoherence T 2 R 0 ( t) cos 2 0 e i ( t) ( t) sin 2 1

12 Decoherence Two well defined states High quantum coherence: Q M 2RT Integration into a scalable architecture: Read-out Control Communicate T 2 R 0 ( t) cos 2 0 e i ( t) ( t) sin 2 1

13 Outline Quantum information with spins 1 0 Atomic defects in semiconductors Molecular quantum bits & gates

14 31 P donors in silicon Si 31 P +

15 31 P donors in silicon Si e - 31 P + B. E. Kane, Nature 393, 133 (1998)

16 31 P donors in silicon Si e - 31 P + Very low decoherence because of: T 2 1 s at T = 1.8 K Weak spin-lattice interactions Low concentration of e - spins ( cm -3 ) Low concentration of nuclear spins (5% 29 Si) A. M. Tyrishkin et al., Nature Mater. 11, 143 (2011)

17 Read-out Translate spin state into charge current SET I SET A. Morello et al., Nature 467, 687 (2010)

18 Read-out & coherent control Translate spin state into charge current J. J. Pla et al., Nature 489, 541 (2012) SET I SET A. Morello et al., Nature 467, 687 (2010) Dt(s)

19 NV centers in diamond NV -

20 NV centers in diamond DE = 2.9 GHz H S = 1 g = DS E( S S ) g HS z 3 A x y m S = 0 B m S = +1 m S = +1

21 NV centers in diamond 3 E m S = ±1 m S = 0 H S = 1 g = 2 LASER DE = 2.9 GHz DS E( S S ) g HS z 3 A FLUORESCENCE x y m S = 0 B m S = -1 m S = +1

NV centers in diamond 3 E m S = ±1 m S = 0 510 14 cm -2

9 GHz 2 2 2 DS E( S S ) g HS z 3 A FLUORESCENCE x y m S =

22 NV centers in diamond 3 E m S = ±1 m S = cm cm cm -2 H S = 1 g = 2 LASER DE = 2.9 GHz DS E( S S ) g HS z 3 A FLUORESCENCE x y m S = 0 B m S = -1 m S = +1 A. Gruber et al., Science 276, 2012 (1997)

Single-spin read-out m S = ±1 m S = 0 3 E 3 A m S = 0 LASER m S = -1 m S = +1 1 m S = 0 0 3 A

23 Single-spin read-out m S = ±1 m S = 0 3 E 3 A m S = 0 LASER m S = -1 m S = +1 1 m S = A Spin-dependent fluorescence spin read-out and state initialization F. Jelezko et al., Appl. Phys. Lett. 81, 2160 (2002)

24 Single-spin read-out m S = ±1 m S = 0 3 E 3 A m S = 0 LASER m S = -1 m S = +1 1 m S = A Spin-dependent fluorescence spin read-out and state initialization F. Jelezko et al., APL 81, 2160 (2002)

Coherent control m S = ±1 m S = 0 3 E 3 A m S = 0 LASER m S = -1 m S = +1 1 Dt m S = 0 0 3 A Microwaves 2.

25 Coherent control m S = ±1 m S = 0 3 E 3 A m S = 0 LASER m S = -1 m S = +1 1 Dt m S = A Microwaves 2.9 GHz Dt(ns) F. Jelezko et al., Phys. Rev. Lett 92, (2004) L. Childress et al., Science 314, 281 (2006)

26 Decoherence Substitutional N atoms (s = ½): spin bath Polarization (high B dc, low T) R. Hanson et al., Science 320, 352 (2008)

27 Decoherence Substitutional N atoms (s = ½): spin bath Dynamical decoupling Polarization (high B dc, low T) R. Hanson et al., Science 320, 352 (2008) G. De Lange et al., Science 330, 60 (2010)

Spin qubits in semiconductors Two well defined states High quantum coherence: Integration into a scalable architecture: Read-out Control Communicate Further reading (reviews) R. Hanson & D.

28 Spin qubits in semiconductors Two well defined states High quantum coherence: Integration into a scalable architecture: Read-out Control Communicate Further reading (reviews) R. Hanson & D. Awschalom, Coherent manipulation of single spins in semiconductors, Nature 453, 1043 (2008) J. J. L. Morton, D. R. McCaney, M. A. Eriksson & S. A. Lyon, Embracing the quantum limit in silicon computing, Nature 479, 345 (2011) D. D. Awschalom, L. C. Bassett, A. S. Dzurak, E. L. Hu, J. R. Petta, Quantum Spintronics: Engineering and Manipulating Quantum Spins in Semiconductors, Science 339, 1174 (2013)

29 Outline Quantum information with spins 1 0 Atomic defects in semiconductors Molecular quantum bits & gates

30 Molecular spin qubits Leuenberger and Loss, Nature 410, 789 (2001) Mn 12 S = 10 g = 2 m= m=+10

31 Molecular spin qubits Leuenberger and Loss, Nature 410, 789 (2001) Cr 7 Ni, S = 1/2 A. Ardavan et al. Phys. Rev. Lett. 98, (2007); ibid (2012). Mn 12 S = 10 g = 2 V 15, S = 1/2 m= m=+10 S. Bertaina et al. Nature 453 (2008)

32 Single-ion magnets Ligand shell (non magnetic) Lanthanide (Er, Ho, Gd, Tm ) = g J J LnW 10 LnW Å Some outstanding characteristics Simple (just 1 magnetic atom) Weak interactions Magnetic solubility Nuclear-spin free systems Control over parameters M. A. AlDamen et al, J. Am. Chem. Soc. 130, 8874 (2008); M. A. Aldamen et al, Inorg. Chem. 48, 3467 (2009)

9 Å Some outstanding characteristics Simple (just 1 magnetic atom) Weak interactions

33 Single-ion magnets Ligand shell (non magnetic) Lanthanide (Er, Ho, Gd, Tm ) = g J J LnW 10 LnW Å Some outstanding characteristics Simple (just 1 magnetic atom) Weak interactions Magnetic solubility Nuclear-spin free systems Control over parameters M. A. AlDamen et al, J. Am. Chem. Soc. 130, 8874 (2008); M. A. Aldamen et al, Inorg. Chem. 48, 3467 (2009)

34 Molecular design of spin qubits GdW 10 GdW 30 J z J y 4 K 0.5 K Easy axis Easy plane

S z (a.u.) Coherent control: pulsed EPR 1.5 1.0 0.5 0.0-0.

5 Rabi Oscillations H=1000 G (16_32) ns pulse length T 2 0.

35 S z (a.u.) Coherent control: pulsed EPR Rabi Oscillations H=1000 G (16_32) ns pulse length T s Time(ns) J y 6.5 GHz M. J. Martínez-Pérez, et al. Phys. Rev. Lett. 108, (2012).

36 Coupling to Q dots or C nanotubes Read-out and coherent manipulation I M. Urdampilleta et al., Nature Mater. 10, 502 (2011); R. Vincent et al., Nature 488, 357 (2012)

37 Universal CNOT quantum gate control target A. Barenco et al., Phys. Rev. A 52, 3457 (1995)

38 Universal CNOT quantum gate control target 1. Two qubits 2. Coupling 3. Asymmetry A. Barenco et al., Phys. Rev. A 52, 3457 (1995)

39 Molecular design of two-qubit gates Dinuclear [Tb] 2 complex Linked to three asymmetric H 3 L ligands Two anisotropic spins in different coordinations D. Aguilà et al, Inorg. Chem. 49 (2010) 6784 G. Aromí, D. Aguilà, P. Gámez, F. Luis, and O. Roubeau, Chem. Soc. Rev. 41, (2012).

Energy(K) CNOT gate H ( H J H J ) A ( J I J I ) m6 2J exjz1j z2 gjb z1 z1 z2 z2 hf z1 z1 z2 z2

40 Energy(K) CNOT gate H ( H J H J ) A ( J I J I ) m6 2J exjz1j z2 gjb z1 z1 z2 z2 hf z1 z1 z2 z CNOT F. Luis et al, Phys. Rev. Lett. 107, (2011). 0 H (T)

41 Molecular spin qubits Two well defined states High quantum coherence Integration into a scalable architecture: Read-out Control Communicate Further reading (reviews) F. Troiani & M. Affronte, Molecular spins for quantum information technologies, Chemical Society Reviews 40, 3119 (2011) G. Aromí, D. Aguilà, P. Gámez, F. Luis & O. Roubeau, Design of magnetic coordination complexes for quantum computing, Chem. Soc. Rev. 41, 537 (2012). Molecular Magnets: Physics and Applications, edited by J. Bartolomé, F. Luis & J. F. Fernández, Springer (January 2014). ISBN

Molecular prototypes for spin-based CNOT and SWAP quantum logic gates

Bellaterra: anuary 2011 Architecture & Design of Molecule Logic Gates and Atom Circuits Molecular prototypes for spin-based CNOT and SWAP quantum logic gates Fernando LUIS Instituto de Ciencia de Materiales