1. 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. A seven-spin NMR quantum computer
Vandersypen et al., Nature 414, 883 (2001)
Vandersypen & Chuang, RMP, Oct 2004. F
13C
12C
C5H5 CO Fe 1 3 5 4 2 6 7
15 = 3 x 5

3. Quantum computing with electron spins
Loss & DiVincenzo, PRA 1998 Vandersypen et al., Proc. MQC02 (quant-ph/ ) SL SR
Initialization electron, low T, high B0
H0 ~ S wi szi
Read-out convert spin to charge
then measure charge
Read-out convert spin to charge
then measure charge
ESR pulsed microwave magnetic field
HRF ~ S Ai(t) cos(wi t) sxi
SWAP exchange interaction
HJ ~ S Jij (t) si · sj
Coherence measure coherence time
in 2DEG: T2 > 100 ns (Kikkawa&Awschalom, 1998)

4. Electrical single-shot spin measurement
Convert spin to charge, then measure charge
Loss & DiVincenzo, PRA 1998

5. Outline  (1) one-electron quantum dots… (3) …fast charge detection…
(4) ….single spin
measurement!
(2) …two-level system… 
EZ = gmBB 

6. Outline: we need…  (1) one-electron double dots…
(3) …fast charge detection…
(4) ….single spin
measurement!
(2) …two-level system… 
EZ = gmBB 

7. A quantum dot as a one-electron box
Electrically measured (contact to 2DEG)
Electrically controlled (gated tunnel barriers, dot potential)

8. A quantum point contact (QPC) as a charge detector
Field et al, PRL 1993

9. Few-electron double dot Transport through QPC
J.M. Elzerman et al., PRB 67, R (2003)
-0.96
-1.02
-0.15
-0.30 00 10 01 11 22 21 12 V L
(V) PR
dIQPC/dVL
0 Tesla
-1.1 00 V L
(V)
-0.9 V PR
(V)
-0.6
Double dot can be emptied
QPC can detect all charge transitions

10. Outline: we need…  (1) one-electron double dots…
(3) …fast charge detection…
(4) ….single spin
measurement!
(2) …two-level system… 
EZ = gmBB 

11. Energy level spectroscopy at B = 010
dIDOT/dVSD
DRAIN
SOURCE G
200 nm M P R Q T
VSD (mV)
N=1
N=0
Ground and excited state
No transport
Ground state
B = 0 T
-10
-653
-695
VT (mV)
E ~ 1.1meV
EC ~ 2.5meV

12. Single electron Zeeman splitting in B//2 -2
N=0
VSD (mV) GS ES
Hanson et al, PRL 91, (2003) Also: Potok et al, PRL 91, (2003)  
B=0
B > 0
gmBB
-675
VT (mV)
N=1 2 -2
-657
6 T
VSD (mV)
N=0
-995
-1010
VR (mV)
10 T
N=0 5 10 15
0.1
0.2
B// (T)
DEZ (meV)
|g|=0.44

13. Excited-state spectroscopy on a nearly-closed quantum dot
Elzerman et al, APL 84, 4617, 2004 Also: Johnson, cond-mat/04 T
DRAIN t t
IQPC
-VP
time
RESERVOIR Q
DIQPC
time
200 nm M P R
SOURCE G EF
Make sure scale bar is correct! G
Apply pulse train to gate P
Measure amplitude of pulse-response with lock-in amplifier
Electron tunneling  small pulse response

14. Zeeman splitting for N = 110
DEZ
lock-in signal
(arb.units)
VP (mV)
B = 10 T
N = 1
N = 0
-1.135
VM (V)
-1.150
f = 385 Hz 1
-1.13
VM (V)
-1.15
Make sure scale bar is correct!
Geff G

15. Bipolar spin filter N=1 N=0 N=1 N=2 VSD (mV) Gate voltage VSD (mV)
VSD (mV)
N=1
N=0
Gate voltage
VSD (mV)
Gate voltage
N=1
N=2 S T+ T- T0
Expt: Hanson et al, cond-mat/ , Theory: Recher et al, PRL 85,1962, 2000

16. Outline: we need…  (1) one-electron double dots…
(3) …fast charge detection…
(4) ….single spin
measurement!
(2) …two-level system… 
EZ = gmBB 

17. Fast charge detection G VA = 0.8nV/Hz1/2 (white)
DRAIN
VA = 0.8nV/Hz1/2 (white)
IA = kHz (~ f )
CL = 1.5 nF
Operating BW: 40 kHz
Shot-noise limit: 40 MHz
RESERVOIR
IQPC Q G
200 nm M P R
SOURCE

18. Observation of individual tunnel events
Vandersypen et al, APL, to appear (see cond-mat/ ) T
DRAIN
RESERVOIR
IQPC Q G
200 nm M P R
SOURCE
VSD = 1 mV
IQPC ~ 30 nA
∆IQPC ~ 0.3 nA
Shortest steps ~ 8 µs

19. Pulse-induced tunneling
response
to electron
tunneling
0.8
response
to pulse
DIQPC (nA)
0.4
0.0
-0.4
0.5
1.0
1.5
Time (ms)

20. Outline: we need…  (1) one-electron double dots…
(3) …fast charge detection…
(4) ….single spin
measurement!
(2) …two-level system… 
EZ = gmBB 

21. Spin read-out principle: convert spin to charge
SPIN UP -e
N = 1
time
charge
SPIN DOWN -e
time
N = 1
N = 0
N = 1
~G-1

22. Spin read-out procedure
inject & wait
read-out spin
empty QD
empty QD
Vpulse
DIQPC
Inspiration: Fujisawa et al., Nature 419, 279, 2002

23. Spin read-out results Vpulse DIQPC DIQPC (nA) Time (ms) Time (ms) 2
Elzerman et al., Nature 430, 431, 2004
inject & wait
read-out spin
empty QD
empty QD
Vpulse
DIQPC 2
“SPIN UP”
“SPIN DOWN”
DIQPC (nA) 1
0.5
1.0
1.5
0.5
1.0
1.5
Time (ms)
Time (ms)

24. Verification spin read-out
Spin down fraction
oc09-710
-1230 W3
0 W12
G9-2340 G G G
B 10T (?)
Waiting time (ms)

25. Measurement of T1 Surprisingly long T1 T1 goes up at low B B = 8 T
T1 ~ 0.85 ms
Measurement of T1
B = 10 T
T1 ~ 0.55 ms
Surprisingly long T1
T1 goes up at low B
B = 14 T
T1 ~ 0.12 ms
Elzerman et al., Nature 430, 431, 2004

26. Single-shot read-out fidelity
1.0
spin:
outcome:
0.8
0.93 
“up”
0.6 a
1-b
a=0.07
65%
0.4
b=0.28
0.2 
“down”
0.0
0.72
0.6
0.8
1.0
visibility = 1-a-b  0.65
Threshold (nA)
a = Pr[ escapes]
b = Pr[miss step] Pr[ relaxes]
Future improvements:
a: lower Tel
b: faster charge detection

27. Outlook SL SR Initialization 1 electron, low T, high B0 H0 ~ S wi szi
Read-out convert spin to charge
then measure charge
ESR pulsed microwave magnetic field
HRF ~ S Ai(t) cos(wi t) sxi
SWAP exchange interaction
HJ ~ S Jij (t) si · sj
Coherence measure coherence time
T1 is long; T2 = ??

28. Single Electron Spin Resonancez S y B1 S’ B0
fres
fLarmor W W
250 μm x
250 nm
IAC B1 B0
B1 = 1 mT  fRabi~ 5 MHz

29. Detection of Continuous Wave ESR
Engel & Loss, PRL 86, 4648 (`01)
ISD mS mD GL GR
ESR induced current peak
GL, GR =10 MHz
T2 =100 ns
For 1.1 mT (~ -10dBm) Peak is only 300 fA
300 fA

30. Electron transport under CW microwaves
gate voltage (V)
-1.023
-1.029
I (pA)
0.8
0.0
from -60dBm to -40dBm hf hf
Photon Assisted Tunneling Pumping
Electric field dominates signal!

31. Pulsed ESR scheme Apply microwaves Read out spin state
electric field component no longer hinders ESR detection

32. ESR in a Si-FET channel
M. Xiao et al. Nature 430, 435 (‘04)

33. Summary Spin qubit ideas Tunable few-electron double dot
Spin qubit ideas 00
Vandersypen et al, Proc. MQC02,quant-ph/
Engel et al. PRL (to appear)
Tunable few-electron double dot
Elzerman et al., PRB 67, R161308, 2003
DC or LOCK-IN
SINGLE-SHOT
Zeeman splitting
Fast charge detection
Hanson et al,
PRL 91, , 2003
Vandersypen et al, APL to appear, cond-mat/
Bipolar spin filter
Single-shot spin read-out T1 ~ 0.85 ms (8 T)
Hanson et al,
cond-mat/
Excited states using QPC
Elzerman et al, Nature 430, 431, 2004
Elzerman et al,
APL 84, 4617, 2004

35. Tunable double dot design
Ciorga ’99
Open design
IDOT
QPC-L
QPC-R
IQPC
IQPC
Field ’93 Sprinzak ’01 PL PR L M R
QPC for charge detection
GaAs/AlGaAs heterostructure
2DEG 90 nm deep
ns = 2.9 x 1011 cm-2

36. Few-electron double dot Transport through dots
J.M. Elzerman et al., PRB 67, R (2003)
-0.96
-1.02
-0.15
-0.30 00 10 01 11 22 21 12 V L
(V) PR
Peak height
 1 pA
2 pA
70 pA

37. Tunnel process is stochastic
out
DIQPC (nA)
out in
Time (ms)
Time (ms)

38. Histograms tunnel time
G ~ (60 ms)-1
G ~ (230 ms)-1
Increase tunnel barrier
DI QPC [a.u.]

39. More spin-down traces twait tread DIQPC (nA) thold Time (ms) 2 1 1.0
0.5
tread
twait
thold 2
DIQPC (nA) 1
1.5
Time (ms)

40. Read-out characterization
spin:
outcome:
1-a 
“up” a b 
“down”
1-b

41. Characterization: a = Pr [“down” if ]
p (1- b - a) exp(- t / T1) + a
Spin down fraction
1.0
0.8
Waiting time (ms) a
0.6
0.4
Time (ms)
1.0
0.5
1.5
DIQPC (nA) 1 2
0.2
0.0
0.6
0.8
1.0
Threshold (nA)

42. Characterization: b = Pr [“up” if ]
b1 = Pr [ flips before tunneling ]
1-b = (1-b1)(1-b2) + ab1
1/T1 1 =
1/T1 + G
1 + G T1
1.0
1-b2
0.8
b2 = Pr [ miss step ]
0.6 a
1-b
0.4 1
DIQPC (nA)
0.2
0.0
0.6
0.8
1.0
Threshold (nA)
Time (ms)

43. Finding the spin read-out regime

44. Alternative spin read-out schemes (2)
gl = gd EF
need
gl  gd
gl exchange enhanced
(2 DEG, Englert et al, von Klitzing et al)
Etriplet > Esinglet
(Tarucha et al, Loss et al)
N=2
Vandersypen et al, Proc. MQC02, see quant-ph/

45. Alternative spin read-out schemes
| = (| - |) + (| + |)
= |S |T0
Engel et al, PRL, to appear (cond-mat/ ) See also: Ono et al, Science, 2002

46. Weakly coupled dots B// = 6 Tesla dIQPC/dVPR Right gate (mV)
-1000
dIQPC/dVPR 30 40 20 10
B// = 6 Tesla 00 31 21 11 42 01 32
Right gate (mV) 22 12 02 33 23 13 03 34 24 14 04
-867
-900
Left gate (mV)
-1100
QPC gate (mV)
-1108
-800

47. Strongly coupled dots B// = 6 Tesla dIQPC/dVPR Right gate (mV)
-1167
dIQPC/dVPR
B// = 6 Tesla
Right gate (mV) 00
-933
-967
Left gate (mV)
-1167
QPC gate (mV)
-1000
-700

48. Electron response reveals tunnel rate
dip height (%)
100
370
t (ms)
VM (V)
-1.07
-1.40
VR (V)
-0.76
-0.96
f = 4.17 kHz 1 2 3 4 5 6 7 8
t = 15 ms 45
lock-in signal (arb.units) 90
180
300
-1.12
VM (V)
-1.13
oc24766B
-430 W3
0 W12 G
B 10T (?)
Electron response (dip) disappears for high frequencies (small t)
Dip half-developed when Gt  p
Top: barrier to drain closed
Right: barrier to reservoir closed
Middle: both closed

49. Singlet-triplet and Zeeman for N = 210
DEST 10
VP (mV)
VP (mV)
N = 2
N = 1
N = 2
N = 1
f = 385 Hz
f = kHz 1 1
-1.160
VM (V)
-1.175
-1.160
VM (V)
-1.175
(smooth 3)
oc28-781
-430 W3
0 W12 G G G
B 10T (?) G
Geff S S