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Single-shot read-out of one electron spin
Lieven Vandersypen
Jeroen ElzermanRonald HansonLaurens Willems van BeverenFrank KoppensIvo VinkWouter NaberLeo Kouwenhoven
QIP WorkshopNewton Institute, Cambridge27-30 Sep. 2004
A seven-spin NMR quantum computer
F
F
13C12C
F
12C
F
F
13C
C5H5 CO
Fe
1
3
54
26
7
CO
Vandersypen et al., Nature 414, 883 (2001)
Vandersypen & Chuang, RMP, Oct 2004.
15 = 3 x 5
Quantum computing with electron spins
Initialization 1 electron, low T, high B0
Loss & DiVincenzo, PRA 1998Vandersypen et al., Proc. MQC02 (quant-ph/0207059)
Read-out convert spin to charge
then measure charge
ESR pulsed microwave magnetic field
SWAP exchange interaction
H0 ~ i zi
HJ ~ Jij (t) i · j
HRF ~ Ai(t) cos(i t) xi
Coherence measure coherence time
in 2DEG: T2 > 100 ns (Kikkawa&Awschalom, 1998)
SL SR
Read-out convert spin to charge
then measure charge
Electrical single-shot spin measurement
Convert spin to charge, then measure charge
Loss & DiVincenzo, PRA 1998
Outline(1) one-electron
quantum dots…(3) …fast charge
detection…
(4) ….single spin measurement!(2) …two-level
system…
EZ = gBB
Outline: we need…(1) one-electron
double dots…(3) …fast charge
detection…
(4) ….single spin measurement!(2) …two-level
system…
EZ = gBB
• Electrically measured (contact to 2DEG)
• Electrically controlled (gated tunnel barriers, dot potential)
A quantum dot as a one-electron box
200 nm
A quantum point contact (QPC) as a charge detector
-0.80 -0.85 -0.90 -0.95 -1.000
2
Co
nd
uct
an
ce (
e2 /h)
QPC gate voltage (V)
Field et al, PRL 1993
-1.17 -1.20 -1.23 -1.26 -1.291.0
1.5
2.0
QP
C C
urre
nt (
nA)
Dot plunger voltage (V)
Few-electron double dotTransport through QPC
-0.96
-1.02
-0.15 -0.30
00
10
01
11
2221
12
VL
(V)
V PR(V)
-0.9
-1.1
0 -0.6
00
VL
(V)
V PR(V)
• Double dot can be emptied• QPC can detect all charge transitions
dIQPC/dVL
J.M. Elzerman et al., PRB 67, R161308 (2003)
0 Tesla
Outline: we need…(1) one-electron
double dots…
(2) …two-level system…
EZ = gBB
(3) …fast charge detection…
(4) ….single spin measurement!
Energy level spectroscopy at B = 0
B = 0 T
10
-10
0
VT (mV)-653 -695
VS
D (
mV
)
N=1
dIDOT/dVSD
• E ~ 1.1meV
• EC ~ 2.5meV
Ground and excited state
Ground state
N=0
DRAINSOURCE
200 nm M P R
Q
T
Notransport
-995 -1010VR (mV)
10 T
N=0
-675VT (mV)
N=1
2
-2
0
-657
6 T
VS
D (
mV
)
N=0N=1
0 T
2
-2
0 N=0
VS
D (
mV
)
GS
ES
Single electron Zeeman splitting in B//
B=0 B > 0
gBB
Hanson et al, PRL 91, 196802 (2003)Also: Potok et al, PRL 91, 016802 (2003)
0 5 10 150
0.1
0.2
B// (T)
EZ (
me
V)
|g|=0.44
IQPC
DRAIN
SOURCE
RE
SE
RV
OIR
200 nm M R
Q
T
-VP time
time
IQ
PC
P
0
EF
Excited-state spectroscopy on a nearly-closed quantum dot
•Apply pulse train to gate P
•Measure amplitude of pulse-response with lock-in amplifier
Electron tunneling small pulse response
Elzerman et al, APL 84, 4617, 2004Also: Johnson, cond-mat/04
1
10
-1.13 -1.15
N = 0N = 1
VP (
mV
)
VM (V)
VM (V)-1.135 -1.150
lock
-in s
igna
l (a
rb.u
nits
)
B = 10 T
EZ
eff
f = 385 Hz
Zeeman splitting for N = 1
Bipolar spin filter
0
0
Gate voltage
N=1 N=0VS
D (
mV
)
VS
D (
mV
)
Gate voltage
N=1N=2S
S
T+
T-
T0
T0
Expt: Hanson et al, cond-mat/0311414, Theory: Recher et al, PRL 85,1962, 2000
Outline: we need…(1) one-electron
double dots…
(2) …two-level system…
EZ = gBB
(3) …fast charge detection…
(4) ….single spin measurement!
• VA = 0.8nV/Hz1/2 (white)
• IA = 0.4 pA/Hz1/2 @ 40 kHz (~ f )
• CL = 1.5 nF
• Operating BW: 40 kHz
• Shot-noise limit: 40 MHz
IQPC
DRAIN
SOURCE
RE
SE
RV
OIR
200 nm M P R
Q
T
Fast charge detection
Observation of individual tunnel events
IQPC
DRAIN
SOURCE
RE
SE
RV
OIR
200 nm M P R
Q
T
• VSD = 1 mV
• IQPC ~ 30 nA• ∆IQPC ~ 0.3 nA
• Shortest steps ~ 8 µs
Vandersypen et al, APL, to appear (see cond-mat/0407121)
Pulse-induced tunneling
responseto pulse
IQ
PC (
nA)
Time(ms)
0 0.5 1.0 1.5
responseto electrontunneling
0.0
0.4
0.8
-0.4
Outline: we need…(1) one-electron
double dots…
(2) …two-level system…
EZ = gBB
(3) …fast charge detection…
(4) ….single spin measurement!
Spin read-out principle:convert spin to charge
N = 1
N = 1 N = 1N = 0
SPIN UP
SPIN DOWN
time
charge
0
time
charge
0
-e
-1
-e
Spin read-out procedureinject & wait
empty QD
Vp
uls
e
read-out spinempty QD
IQ
PC
Inspiration: Fujisawa et al., Nature 419, 279, 2002
Spin read-out resultsinject & wait
empty QD
Vp
uls
e
read-out spinempty QD
IQ
PC
“SPIN UP” “SPIN DOWN”
Time (ms)Time (ms)
0 1.00.5
IQ
PC (
nA)
0
1
2
1.5 0 1.00.5 1.5
Elzerman et al., Nature 430, 431, 2004
Verification spin read-out
Waiting time (ms)
Spi
n do
wn
frac
tion
0.0 0.5 1.0 1.5 12
0.1
0.2
0.3
Measurement of T1
B = 8 TT1 ~ 0.85 ms
B = 10 TT1 ~ 0.55 ms
B = 14 TT1 ~ 0.12 ms
• Surprisingly long T1
• T1 goes up at low B
Elzerman et al., Nature 430, 431, 2004
Single-shot read-out fidelity
visibility = 1-- 0.65
Future improvements:
• : lower Tel
• : faster charge detection
spin:
“down”
“up”
outcome:
=0.28
0.72
0.93=0.07
Threshold (nA)
0.0
1.0
0.8
0.6
0.4
0.2
0.6 1.0 0.8
65%
• Pr[ escapes]
• Pr[miss step] + Pr[ relaxes]
Outlook
Initialization 1 electron, low T, high B0
Read-out convert spin to charge
then measure charge
ESR pulsed microwave magnetic field
SWAP exchange interaction
H0 ~ i zi
HJ ~ Jij (t) i · j
HRF ~ Ai(t) cos(i t) xi
Coherence measure coherence time
T1 is long; T2 = ??
SL SR
EZ = gBB
EZ = gBB
J(t) J(t)
Single Electron Spin Resonance
x
z
S
yB1
S’
B0
fres
fLarmor
B1 = 1 mT fRabi~ 5 MHz
250 nm
IAC
B1B0
250 μm
L, R =10 MHzT2 =100 ns
300 fAFor 1.1 mT (~ -10dBm) Peak is only 300 fA
Detection of Continuous Wave ESREngel & Loss, PRL 86, 4648 (`01)
ISDS
D
L R
ESR induced current peak
Electron transport under CW microwaves
VG (V)-4245 -4290-0.396
0.431
V SD (
mV)
N=0N=1
dI/dVSD( S) 0.025-0.01
gate voltage (V) -1.023-1.029
I (pA)
0.8
0.0
from -60dBm to -40dBm
hf
hf
Photon Assisted TunnelingPumping
Electric field dominates signal!
Apply microwaves
Pulsed ESR scheme
Read out spin state
electric field component no longer hinders ESR detection
ESR in a Si-FET channelM. Xiao et al. Nature 430, 435 (‘04)
Summary
Tunable few-electron double dotElzerman et al., PRB 67, R161308, 2003
00Spin qubit ideas
Vandersypen et al, Proc. MQC02,quant-ph/0207059Engel et al. PRL (to appear)
DC or LOCK-IN SINGLE-SHOT
Zeeman splittingHanson et al, PRL 91, 196802, 2003
Fast charge detection
Single-shot spin read-out
T1 ~ 0.85 ms (8 T)Excited states using QPCElzerman et al, APL 84, 4617, 2004
Elzerman et al, Nature 430, 431, 2004
Vandersypen et al, APL to appear, cond-mat/0407121
http://qt.tn.tudelft.nl/research/spinqubits
Hanson et al, cond-mat/0311414
Bipolar spin filter
Tunable double dot designCiorga ’99
Open design
Field ’93Sprinzak ’01
QPC for charge detection
200 nm
T
ML RPL PR
QPC-R
IDOT
IQPCIQPC
QPC-L
GaAs/AlGaAs heterostructure2DEG 90 nm deepns = 2.9 x 1011 cm-2
Few-electron double dotTransport through dots
-0.96
-1.02
-0.15 -0.30
00
10
01
11
2221
12
VL
(V)
V PR(V)
1 pA
2 pA
70 pA
Peak height
J.M. Elzerman et al., PRB 67, R161308 (2003)
Tunnel process is stochastic
0.0 0.5 1.0 1.5
0.0
0.5
1.0
0.0 0.5 1.0 1.5
0.0
0.5
1.0
IQ
PC (
nA)
Time(ms) Time(ms)
inout
out
Histograms tunnel timeI
QP
C [
a.u.
]
~ (60 s)-1
0.0 0.5 1.0 1.5-1
0
1
2
3
IQ
PC (
a.u
.)
Time (ms)
~ (230 s)-1
Increase tunnelbarrier
0.0 0.5 1.0 1.5-1
0
1
2
3
Time (ms)
More spin-down traces
Time (ms)
0 1.5
IQ
PC (
nA)
0
1
2
1.00.5
treadtwait
thold
Read-out characterization
spin:
“down”
“up”
outcome:
Characterization: = Pr [“down” if ]
0.6 1.0Threshold (nA)
0.80.0
1.0
0.8
0.6
0.4
0.2
Time (ms)
0 1.00.5 1.5
IQ
PC (
nA)
0
1
2
Waiting time (ms)
Spi
n do
wn
frac
tion
0.0 0.5 1.0 1.5 12
0.1
0.2
0.3
p ) exp(- t / T1) +
Characterization: = Pr [“up” if ]
Threshold (nA)
0.0
1.0
0.8
0.6
0.4
0.2
0.0 0.5 1.0 1.5 2.0
Time (ms)
0
1
IQ
PC (
nA)
2 = Pr [ miss step ]
=1/T1
1/T1 +
11 + T1
1 = Pr [ flips before tunneling ] 12
1
0.6 1.0 0.8
Finding the spin read-out regime
gl = gd
Alternative spin read-out schemes (2)
needgl gd
gl exchange enhanced
(2 DEG, Englert et al, von Klitzing et al)
EF
Etriplet > Esinglet
(Tarucha et al,
Loss et al)
N=2
Vandersypen et al, Proc. MQC02, see quant-ph/0207059
Alternative spin read-out schemes
| = (| - |) + (| + |) = |S + |T0
Engel et al, PRL, to appear (cond-mat/0309023)See also: Ono et al, Science, 2002
Weakly coupled dots
-900
-867
-1100-1108 -800
-100
0
Left gate (mV)QPC gate (mV)
Rig
ht g
ate
(mV
)
dIQPC/dVPR
B// = 6 Tesla40
00
11
10
01
20
2131
30
1202
2232
1303
2333
42
1404
2434
Strongly coupled dots
-967
-933
-1167-1000 -700
-116
7
dIQPC/dVPR
B// = 6 Tesla
Left gate (mV)QPC gate (mV)
Rig
ht g
ate
(mV
)
00
= 15 s
300
18090
45
VM (V)
lock
-in s
igna
l (ar
b.un
its)
-1.12 -1.13
VM (V)-1.07 -1.40V
R (
V)
-0.76
-0.96
f = 4.17 kHz
0
1
2
345678
7 6 5 4 32
Electron response reveals tunnel rate
dip
heig
ht (
%)
0
100
3700 (s)
•Electron response (dip) disappears for high frequencies (small )
•Dip half-developed when
•Top: barrier to drain closed
•Right: barrier to reservoir closed
•Middle: both closed
N = 1N = 2 N = 1N = 2
-1.160 -1.175VM (V)-1.160 -1.175VM (V)1
10
VP (
mV
)
S
S
eff
EST
f = 385 Hz f = 1.538 kHz
Singlet-triplet and Zeeman for N = 2
1
10
VP (
mV
)