real and futuristic spin qubits – from gaas to …ykis07.ws/presen_files/15/v...science express...
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Real and futuristicspin qubits –from GaAs to graphene
Yukawa International SeminarKyoto, November 2007
Lieven Vandersypen
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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
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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
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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
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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
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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]
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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)
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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
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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…
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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
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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
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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⟩⟩⟩⟩
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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
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Main themes in the coming years
Controlling thenuclear spin bath
Bell’s inequalities
Novel materialssystems
Quantum control and entanglement
RF1
RF2
J
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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?
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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
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Graphene quantum dots ?Etching
Top gating
“Bad” contacts
by far preferred(control and tunability)
© Geim© McEuen
© Dekker © Eriksson
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Electrostatic barriers and Klein tunneling
No electrostatic confinement!Need to create a semiconducting gap
Katsnelson, Novoselov, Geim, Nature Phys. 2006
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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
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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
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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
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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
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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
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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
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Single layer
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Bilayer
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Low temperature measurements of bilayer graphene
Oostinga, Heersche, Liu, Morpurgo, LMKV, arXiv:0707.2487
T = 55, 270, 600, 1200 mK
Electrically induced insulating state
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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
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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
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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
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Gate voltage dependence AB amplitude
AB amplitude linear in conductance
Russo, et al, arXiv:0711.0479
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Magnetic field dependence AB amplitude
Not due to magnetic impuritiesPossibly orbital origin
800 mK
150 mK
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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
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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