Fernando LUIS

Instituto de Ciencia de Materiales de Aragón

Martes cuántico Zaragoza, 8th October 2013

Atomic and molecular spin qubits

Outline

Quantum information with spins

Molecular quantum bits & gates

0

1

Atomic defects in semiconductors

Outline

Quantum information with spins

Molecular quantum bits & gates

0

1

Atomic defects in semiconductors

R. P. Feynman, Int. J. Theoret. Phys. 21,

467 (1982)

1

0

• Process information using quantum laws • Bit Qubit

Quantum computers

Single qubits

0

1

Qubits

100

10 1HR

Qubits

Single qubits

100

0

1

10 1HR

DE /h 1-40 GHz

2006 2008 2010 20120.1

1

10

100

T2(

s)

year

M. H. Devoret and R. J. Schoelkopf, Science 339, 1169 (2013)

Spin qubits

Bdc

S = ½ g = 2

Electron spin in a magnetic field

1

0

DE = gBBdc

26 GHz/T

1.3 K/T

Spin qubits

B1eiwt Bdc

S = ½ g = 2

Electron spin in a magnetic field

1Dt

0

I. I. Rabi, Phys. Rev. B 51, 652 (1937)

Spin qubits

B1eiwt Bdc

S = ½ g = 2

Electron spin in a magnetic field

1

131 Bh

BR

MHz/mT

Dt

0

En resonancia: w = DE/h

12

)(sin0

2

)(cos0 )(

te

t ti

I. I. Rabi, Phys. Rev. B 51, 652 (1937)

Decoherence

12

)(sin0

2

)(cos0 )(

te

t ti R T1

Decoherence

12

)(sin0

2

)(cos0 )(

te

t ti R

T2

Decoherence

12

)(sin0

2

)(cos0 )(

te

t ti R

T2

• Two well defined states • High quantum coherence: • Integration into a scalable architecture:

• Read-out • Control • Communicate

6

2 102 TQ RM

Outline

Quantum information with spins

0

1

Atomic defects in semiconductors

Molecular quantum bits & gates

31P donors in silicon

Si

31P+

31P donors in silicon

Si

31P+

e-

B. E. Kane, Nature 393, 133 (1998)

31P donors in silicon

Si

31P+

e-

Very low decoherence because of: • Weak spin-lattice interactions • Low concentration of e- spins (1014-1015 cm-3) • Low concentration of nuclear spins (5% 29Si)

T2 1 s at T = 1.8 K

A. M. Tyrishkin et al., Nature Mater. 11, 143 (2011)

Read-out

Translate spin state into charge current

ISET

SET

A. Morello et al., Nature 467, 687 (2010)

Read-out & coherent control

Translate spin state into charge current

ISET

SET

Dt(s) A. Morello et al., Nature 467, 687 (2010)

J. J. Pla et al., Nature 489, 541 (2012)

NV centers in diamond

NV-

NV centers in diamond

S = 1 g = 2

SHgSSEDS Byxz

)( 222H

DE = 2.9 GHz mS = 0

mS = +1

mS = +1 3A

NV centers in diamond

S = 1 g = 2

SHgSSEDS Byxz

)( 222H

DE = 2.9 GHz mS = 0

mS = -1

mS = +1 3A

3E mS = 0

mS = ±1

LASER FLUORESCENCE

NV centers in diamond

S = 1 g = 2

SHgSSEDS Byxz

)( 222H

DE = 2.9 GHz mS = 0

mS = -1

mS = +1 3A

3E mS = 0

mS = ±1

LASER FLUORESCENCE

51014 cm-2 1014 cm-2 1013 cm-2

A. Gruber et al., Science 276, 2012 (1997)

Single-spin read-out

mS = 0 0

mS = -1 mS = +1 1

3A

3E mS = 0

mS = ±1

LASER

Spin-dependent fluorescence spin read-out and state initialization

3A mS = 0

F. Jelezko et al., Appl. Phys. Lett. 81, 2160 (2002)

Single-spin read-out

mS = 0 0

mS = -1 mS = +1 1

3A

3E mS = 0

mS = ±1

LASER

3A mS = 0

F. Jelezko et al., APL 81, 2160 (2002)

Spin-dependent fluorescence spin read-out and state initialization

Coherent control

mS = 0 0

mS = -1 mS = +1 1

3A

3E mS = 0

mS = ±1

LASER

3A mS = 0

Dt

Microwaves 2.9 GHz

Dt(ns)

F. Jelezko et al., Phys. Rev. Lett 92, 076401 (2004)

L. Childress et al., Science 314, 281 (2006)

Decoherence

Substitutional N atoms (s = ½): spin bath

Polarization (high Bdc, low T)

R. Hanson et al., Science 320, 352 (2008)

Decoherence

Substitutional N atoms (s = ½): spin bath

Polarization (high Bdc, low T)

Dynamical decoupling

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. 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)

Outline

Quantum information with spins

Molecular quantum bits & gates

0

1

Atomic defects in semiconductors

Molecular spin qubits

+

- m=-10 m=+10

Leuenberger and Loss, Nature 410, 789 (2001)

Mn12

S = 10 g = 2

Cr7Ni, S = 1/2

Molecular spin qubits

+

- m=-10 m=+10

Leuenberger and Loss, Nature 410, 789 (2001)

A. Ardavan et al. Phys. Rev. Lett.

98, 057201 (2007); ibid (2012).

V15, S = 1/2

S. Bertaina et al. Nature 453 (2008)

Mn12

S = 10 g = 2

Single-ion magnets

LnW10 LnW30

Ligand shell (non magnetic)

Some outstanding characteristics…

• Simple (just 1 magnetic atom)

• Weak interactions

• Magnetic solubility

• Nuclear-spin free systems

• Control over parameters

17.9 Å

Lanthanide (Er, Ho, Gd, Tm…)

= gJ J

M. A. AlDamen et al, J. Am. Chem. Soc. 130, 8874 (2008); M. A. Aldamen et al, Inorg. Chem. 48, 3467 (2009)

Single-ion magnets

Some outstanding characteristics…

• Simple (just 1 magnetic atom)

• Weak interactions

• Magnetic solubility

• Nuclear-spin free systems

• Control over parameters

LnW10 LnW30

17.9 Å

Ligand shell (non magnetic)

Lanthanide (Er, Ho, Gd, Tm…)

= gJ J

M. A. AlDamen et al, J. Am. Chem. Soc. 130, 8874 (2008); M. A. Aldamen et al, Inorg. Chem. 48, 3467 (2009)

Easy axis

Jz Jy

Easy plane

4 K

0.5 K

Molecular design of spin qubits GdW10

GdW30

Jy

M. J. Martínez-Pérez, et al. Phys. Rev. Lett. 108, 247213 (2012).

Coherent control: pulsed EPR

0 200 400 600 800

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Sz(a

.u.)

Time(ns)

Rabi Oscillations

H=1000 G

(16_32) ns pulse length

6.5 GHz

T2 0.5 s

Read-out and coherent manipulation

Coupling to Q dots or C nanotubes

I

M. Urdampilleta et al., Nature Mater. 10, 502 (2011); R. Vincent et al., Nature 488, 357 (2012)

“control” “target”

Universal CNOT quantum gate

A. Barenco et al., Phys. Rev. A 52, 3457 (1995)

“control” “target”

1. Two qubits

2. Coupling

3. Asymmetry

Universal CNOT quantum gate

A. Barenco et al., Phys. Rev. A 52, 3457 (1995)

D. Aguilà et al, Inorg. Chem. 49 (2010) 6784 G. Aromí, D. Aguilà, P. Gámez, F. Luis, and O. Roubeau, Chem. Soc. Rev. 41, 537-546 (2012).

Dinuclear [Tb]2 complex

Linked to three asymmetric H3L ligands

Two anisotropic spins in different coordinations

Molecular design of two-qubit gates

0.0 0.2 0.4 0.6 0.8

-4

-2

0

2

4

En

erg

y(K

)

0H (T)

( ) )(2 22112211216 zzzzhfzzzzBJzzexm IJIJAJHJHgJJJ H

CNOT

CNOT gate

F. Luis et al, Phys. Rev. Lett. 107, 117203 (2011).

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 978-3-642-40608-9