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

)