Real and futuristicspin qubits –from GaAs to graphene

Yukawa International SeminarKyoto, November 2007

Lieven Vandersypen

Spin qubits in quantum dots – key elements

Initialization 1 electron, low T, high B0

Read-out spin-to-charge conversion

ESR pulsed microwave magnetic field

SWAP exchange interaction

Coherence T1, T2

↑

↓EZ = gµµµµBB

↑

↓EZ = gµµµµBB

↑ ↓J(t)↑ ↓J(t)

SL SR

↑ ↓

Loss & DiVincenzo, PRA 1998LMKV et al., Proc. MQC02 (quant-ph/0207059)

Delft Nature 2004

Harvard Science 2005

Single-electron spin resonanceF. Koppens et al., Nature 2006

↑

↓EZ = gµµµµBB

↑

↓EZ = gµµµµBB

VAC

ICPS

1 mmBext

BAC

0 50 100 150-50-100-150

100

200

300

400

500

600

700

0Magnetic field (mT)

200

300

400

I dot(fA

0

100R

F fr

eque

ncy

(MH

z)

|g|-factor ~ 0.35

S(0,2)

T(0,2)

0

0.5

RF offDot

cur

rent

(pA

)

Magnetic field (mT)-150 150

RF at 460 MHz

Driven rotations of a single electron spin

Dot current (fA)

Koppens, Buizert, Tielrooij, Vink, Nowack, Meunier, Kouwenhoven, LMKV, Nature 2006

1000

110

0

12

70 3.5

fRabi

(MHz)

Stripline current (mA)

π/2 pulse in 25ns

max B1 ~ 1.9 mT, compare BN,z ~ 1.3 mT

BN,z

B1

Beff

Electrical single-spin control

Vac (a.u.)0 5 10 150

1

2

3

4

Rab

i fre

q (M

Hz) 14 GHz

Nowack, Koppens, Nazarov, LMKV, Science Express 2007

DC

AC

0 0.5 1 1.5 2 2.5 30

5

10

15

RF

freq

uenc

y (G

Hz)

external magnetic field (T)0 1 2 3Bext (T)

RF

freq

. (G

Hz)

0

5

10

15 g ~ 0.39

0 200 400 600 80020

40

60

80

100

120

140

160

180

200

Burst time (ns)

Dot

cur

rent

(fA

)

15.2 GHz

0 400 800

RF burst length (ns)

0.2

0.1

0

dot c

urre

nt (

pA)

Easier local addressingAll-electrical control possible

Mechanism: spin-orbit interaction

Theory: Golovach, Borhani, Loss, PRB 2006

Efl

fB acSO

Rabi

r1~,1

)()( yyxxxyyxR ppppH σσβσσα −+−=Rashba Dresselhaus

)( αβ ±=

mlSO

h

fac (GHz)

lSO ~ 30 µµµµm

Bext // E(t) // [110] or [110]

Ramsey fringes and dephasing

Free evolution

xy

z

xy

z

xy

z3π/2

xy

zπ/2

Free evolution time (ns)

T2*~35ns

average over nuclear fields

T2* ~ 35 ns

60

80

100

120

140

160

Relative phase 2nd pulse0 π 2π−2π −π

curr

ent (

pA)

Spin echo – unwind dephasingnuclear spins evolve only slowly Koppens, Nowack, LMKV,

arXiv:0711.0479

π/2 π/2τ τ

π

2τ (ns)

Bext = 48 mT

T2,echo~ 0.26 µsBext = 70 mT

T2,echo~ 0.47 µs

2τ (ns)

Y

X

Nuclear spin dynamics

Theory:de Sousa, das Sarma, PRB 2003Coish, Loss PRB 2004Witzel, de Sousa, das Sarma, PRB 2005

• nuclear-nuclear flip-flops through direct dipole-dipole coupling (> 100 µs)

• electron-nuclear flip-flops (strongly suppressed for B ≠≠≠≠ 0)

• nuclear-nuclear flip-flops through two virtual electron-nuclear flip-flops

T2,echo depends on timescale (tnuc) and magnitude (1/T2*)of nuclear field fluctuations

Klauder & Anderson, PR 1962

E.g. can have tnuc = 10 sec, T2* = 10 ns, giving T2,echo = 10 µs

Yao, Liu, Sham, PRB 2006Deng & Hu, PRB 2006…

C = 1.5µF

Faster charge detection (cryogenic amplifier)

1K

4K

RT

40mK

0 200

I QP

C[a

.u.]

Time [ µµµµs]

Signal bandwidth: ~1 kHz – 1 MHz

Single-charge detection in smaller bandwidth

Vink, Nooitgedagt, Schouten, LMKV, APL 2007

Other decoherence mechanismsvirtual tunneling processes to the reservoirs

• was limitation for max. power in ESR • can be suppressed by raising tunnel barriers

B = 0.02T

0 4 8 20

//1

0.5

0

waiting time (ms)

frac

tion

of ‘T

’

1/T1

T

S

//

Hanson et al., PRL 2005 Elzerman et al.,Nature 2004Amasha et al., cond-mat/0607110

T1 up to 1 sec !

spin-orbit interactionT2 = 2 T1 Golovach, Khaetskii, Loss, PRL 04

Spin-orbit with phonons dominates T1

Meunier, Vink, Willems v Beveren, Tielrooij, Hanson,Koppens, Tranitz, Wegscheider, Kouwenhoven, LMKV, PRL 2007

Theory: Golovach, Khaetskii, Loss, PRL 2004

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40

1

2

3

T1

[ms]

S-T splitting [meV]

|`↑↑↑↑´⟩⟩⟩⟩ = |↑↑↑↑g⟩⟩⟩⟩ + α|↓↓↓↓e⟩⟩⟩⟩

|`↓↓↓↓´⟩ = |↓g⟩⟩⟩⟩ - α|↑↑↑↑e⟩⟩⟩⟩

phonon wavelengthmatches dot size

|g⟩⟩⟩⟩

|e⟩⟩⟩⟩

Spin qubits in quantum dots – status

Initialization 1-electron, low T, high B0

1-qubit gate electron spin resonancegate duration ~ 25 ns; observed 8 periods

2-qubit gate exchange interactiongate duration ~ 0.2 ns; observed 3 periods

SL SR

Read-out via spin-charge conversion

See also Hanson et al, Rev. Mod. Phys. 2007

duration ~ 100 µs; 82-97% fidelity

duration ~ 5 T1; 99% fidelity ?

Decoherence T1 ~ 1 ms – 1 secT2* ~ 20 ns; T2 > 1 µs

spin-orbit + phononsnuclear spins

Main themes in the coming years

Controlling thenuclear spin bath

Bell’s inequalities

Novel materialssystems

Quantum control and entanglement

RF1

RF2

J

Hyperfine in graphene is tiny

1) Only 1% of carbon atoms have a nuclear spin (13C)Furthermore, 99.9% pure 12C is easily available,and synthetic graphene exists

| ( ) |H E kψ ψ>= >r

2pz2s

2) The conduction and valence band are made from p-orbitals,which don’t overlap with the nuclei (no contact hyperfine)

Spin coherence time ?dipole dipole coupling?anisotropic hyperfine?

Spin-orbit in graphene is weak as well

Carbon is a light element

HSO = λSO σz sz τz

HR = λR (σx sy τz - σy sx)

λSO ~ 0.5 µeV

λR ~ 0.1 µeV / VG

Min et al, cond-mat/0606504Yao et al, cond-mat/0606350Huertas-Hernando et al, cond-mat/0606580

sublatticespin

valley

HD = β ( -σx px + σypy)

HR = α ( σx py - σypx)

β pF ~ 150 µeV (n=1011cm-2)

comparable

Compare GaAs:

Spin relaxation time ?electron phonon coupling?

other heat baths?

Trombos et al., Nature 2007But: spin flip time in 2D graphene ~ few 100 ps

Graphene quantum dots ?Etching

Top gating

“Bad” contacts

by far preferred(control and tunability)

© Geim© McEuen

© Dekker © Eriksson

Electrostatic barriers and Klein tunneling

No electrostatic confinement!Need to create a semiconducting gap

Katsnelson, Novoselov, Geim, Nature Phys. 2006

Bandgap from confinement (ribbons)

Armchair edges: insulating, except for N=3n-1

Zigzag edges: always metallic (edge states at zero energy)

Tight binding Nakada et al., PRB 54, 17954, 1996

Gap from spin-ordering at edges ? Son, Cohen, Louie PRL 2006

Always gap from lattice deformation at edges ? Son et al., PRL 2006

Bandgap in ribbons (1)

-40 0 40-3

-2

-1

0

1

2

3

10V 20V 0V

I sd(n

A)

VSD

(mV)

r60_iv5,6,8

Wehenkel, Heersche et al, See also Han et al, PRL 2007

0 5 10 15 20 25 30 35 40 45 50

5

10

15

20

25

30 C

G (

µS)

Vg (V)

r70_li1

VG (V)

G (

µS)

70 nm

60 nm

Bandgap in ribbons (2)

Delft (Wehenkel, Heersche et al) Columbia , PRL 2007

Always gapped even though edges were not controlled

In addition: charging contributionVG (V)

10 200

0

100

-100

VS

D(m

V)

60 nm

0 20 40 60 80 100 1200.0

0.2

0.4

0.6

0.8

1.0

gap-1

(m

eV-1)

width (nm)

Extracted gap size versus ribbon width

0 20 40 60 80 100 1201

10

100

gap

(meV

)

width (nm)

Kim Delft

Bandgap in asymmetrically doped bilayers

Expt.: Ohta et al, Science 2006Also: Castro et al, cond-mat/0611342

Chemical doping of top layer (SiC substrate)

Theory: McCann & Falko, PRL 2006McCann, PRB 2006Min et al, PRB 2006

Vbg > 0 > Vtg

McCann, PRB 2006Min et al, PRB 2006

SiO2

backgate

Bare gap (meV)

Sel

fcon

sist

ent g

ap (

meV

)

1000 50

40

20

0

EF

Vbg > 0

Electric control of bandgap and Fermi level

bilayer

topgate

300 nm

15 nm

-50 V

2.5 V

50 mV bare gap

< 10 meV actual gap0.3 nm

Single layer

Bilayer

Low temperature measurements of bilayer graphene

Oostinga, Heersche, Liu, Morpurgo, LMKV, arXiv:0707.2487

T = 55, 270, 600, 1200 mK

Electrically induced insulating state

Temperature dependence peak resistance

55 mK – 5 K range: variable-range hopping (for highest fields)

Points at gap with localized states inside the gap (disorder)

Oostinga, Heersche, Liu, Morpurgo, LMKV, arXiv:0707.2487

Magnetoresistance in graphene rings

Russo, Oostinga, Wehenkel, Heersche, Sobhani, LMKV, Morpurgo, arXiv:0711.0479

150 mK

Observations:• Weak localization (probably)• Aperiodic conductance fluctuations• Aharonov-Bohm conductance oscillations

Procedure:lock-intwo-terminalcurrent-biased

Temperature dependence AB amplitude

Expect ∆Grms ~ exp[-πR/Lφ(T)] (ETh / kT)-1/2

Observe thermal averaging (note Eth ~ 10 µeV < 150mK ~ kB T)

Indicates Lφ > few µm

See also WL data of Tikhonenko et al, arXiv:0707.0140

Gate voltage dependence AB amplitude

AB amplitude linear in conductance

Russo, et al, arXiv:0711.0479

Magnetic field dependence AB amplitude

Not due to magnetic impuritiesPossibly orbital origin

800 mK

150 mK

Message for graphene spin qubits

It may be possible to define dots using electrostatic gates

Role of disorder to be explored further

Spin coherence time could be very long

Jeroen Elzerman (ETH)Ronald Hanson (UCSB)

Laurens Willems v Beveren (UNSW)Josh Folk (UBC)Frank Koppens

Ivo VinkChristo Buizert (U Tokyo)

Klaas-Jan Tielrooij (AMOLF)Tristan MeunierKatja Nowack

Tjitte NooitgedachtHan Keijzers

Leo KouwenhovenLieven Vandersypen

External collaborationsLoss group (Basel)Nazarov (Delft)Rudner & Levitov (MIT)Wegscheider (Regensburg)Tarucha group (Tokyo)

GaAs spin qubits

People and collaborations

GrapheneHubert Heersche

Pablo Jarillo-Herrero (Columbia) Jeroen Oostinga

Xinglan LiuAlberto Morpurgo

Lieven Vandersypen