single-shot read-out of one electron spin
DESCRIPTION
Single-shot read-out of one electron spin. QIP Workshop Newton Institute, Cambridge 27-30 Sep. 2004. Lieven Vandersypen Jeroen Elzerman Ronald Hanson Laurens Willems van Beveren Frank Koppens Ivo Vink Wouter Naber Leo Kouwenhoven. 2. 1. F. F. 6. 3. F. 12 C. 13 C. 7. 13 C. F. - PowerPoint PPT PresentationTRANSCRIPT
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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
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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
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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
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Electrical single-shot spin measurement
Convert spin to charge, then measure charge
Loss & DiVincenzo, PRA 1998
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Outline(1) one-electron
quantum dots…(3) …fast charge
detection…
(4) ….single spin measurement!(2) …two-level
system…
EZ = gBB
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Outline: we need…(1) one-electron
double dots…(3) …fast charge
detection…
(4) ….single spin measurement!(2) …two-level
system…
EZ = gBB
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• Electrically measured (contact to 2DEG)
• Electrically controlled (gated tunnel barriers, dot potential)
A quantum dot as a one-electron box
200 nm
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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)
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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
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Outline: we need…(1) one-electron
double dots…
(2) …two-level system…
EZ = gBB
(3) …fast charge detection…
(4) ….single spin measurement!
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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
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-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
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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
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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
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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
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Outline: we need…(1) one-electron
double dots…
(2) …two-level system…
EZ = gBB
(3) …fast charge detection…
(4) ….single spin measurement!
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• 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
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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)
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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
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Outline: we need…(1) one-electron
double dots…
(2) …two-level system…
EZ = gBB
(3) …fast charge detection…
(4) ….single spin measurement!
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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
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Spin read-out procedureinject & wait
empty QD
Vp
uls
e
read-out spinempty QD
IQ
PC
Inspiration: Fujisawa et al., Nature 419, 279, 2002
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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
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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
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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
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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]
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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)
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Single Electron Spin Resonance
x
z
S
yB1
S’
B0
fres
fLarmor
B1 = 1 mT fRabi~ 5 MHz
250 nm
IAC
B1B0
250 μm
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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
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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!
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Apply microwaves
Pulsed ESR scheme
Read out spin state
electric field component no longer hinders ESR detection
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ESR in a Si-FET channelM. Xiao et al. Nature 430, 435 (‘04)
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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
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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
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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)
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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
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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)
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More spin-down traces
Time (ms)
0 1.5
IQ
PC (
nA)
0
1
2
1.00.5
treadtwait
thold
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Read-out characterization
spin:
“down”
“up”
outcome:
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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) +
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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
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Finding the spin read-out regime
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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
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Alternative spin read-out schemes
| = (| - |) + (| + |) = |S + |T0
Engel et al, PRL, to appear (cond-mat/0309023)See also: Ono et al, Science, 2002
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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
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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
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= 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
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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
)