lecture 2: double quantum dots - université de sherbrooke

• Basics

Lecture 2: Double quantum dots

• Pauli blockade

• Spin initialization and readout in double dots• Spin initialization and readout in double dots

• Spin relaxation in double quantum dots

Jason Petta, Princeton University

Quick ReviewSingle spin qubitQuantum dot

Qubit states:

450 nm EZeeman

1

0

Long spin relaxation time, T1 ~ 1 sec.


Review: Coulomb blockade and charging in a single dotR1,C1 R2,C2 NN-1 N+1 N+2

I VG

Ener

gy

VSD

Charging energy E =e2/2C

E

VCharging energy Ec=e /2C VG

EF e2/C

VG VGKastner, RMP 64, 849 (1992)


Double dot charge stability diagramR1,C1 R2,C2RM,CM

S D

VG1

S D

VG2

Two limits:CM 0 CM/C(1,2) 1

V (1 0) (1 1) (1 2)

(2,0) (2,1) (2,2)

VVG1

(0,0) (0,1) (0,2)

(1,0) (1,1) (1,2) VG1

Double dot review article: van der Wiel et al., RMP 75, 1 (2003)

VG2 VG2


Double dot charge stability diagramR1,C1 R2,C2RM,CM

S D

VG1

S D

VG2

In between these limits:

(2,0) (2,1) (2,2)

(1,1)

(1 0)VG1 (1,0) (1,1) (1,2)

(0,0)

(1,0)

triple points

VG1

(0,0) (0,1) (0,2) (0,1)

VG2 VG2

Double dot review article: van der Wiel et al., RMP 75, 1 (2003)


Experimental setupParameters: T= 0 030 K Feature size < 100 nm Frequency = 35 GHzT 0.030 K, Feature size < 100 nm, Frequency 35 GHz


Charge transport T M, N~20Double dot measurements

0.5 m

GD

GD

(10

-650

mV

) (M+1,N) (M+1,N+1) 20

GSL

0-3e

2/h)

-670

VL (m (M,N) (M,N+1)

0

GSR

RL -660 -640VR (mV)Charge sensing M, N=0, 1, 2…

3e2 /h

)

100

150

GS

R

0.24 -1.0

L (V

)

dGSR /dV0

5

(0 0)

(1,0)(1,1)

GD

(10-3

0

50

R(e

2/h)

0 16

0.20

-1.1

VL V

L (a.u.)-10-5-

-(0,0)

(0,1)

QPC sensing: Field et al., PRL 70, 1311 (1993)

0-1.05 -1.00VR (V)

0.16-1.0-1.1 VR (V)

Petta et al., PRL 93, 186802 (2004)Elzerman et al., PRB 67, 161308 (2003)


Charge physics: The one-electron regime-5 0 5 dgrs/dVL (a.u.)

(1 0) (0 1)

Charge -vs- spin qubits

(0 0) (0 1)

(1,1)(1,0)

(1,2)

-500

mV

)

(1,0) (0,1)

(0,0) (0,1)(0,2)

-550

VL (mvs.

-400VR (mV)-450

Spin physics: The two electron regime(0,2)

mV

)

-515Spin physics: The two-electron regime(1,1) (1,2)(1,1)

VL (m

-530

vs.

(0,1) (0,2)

-400-415 VR (mV)Jason Petta, Princeton University

1.0 VT (V)1 11 Vt =-1.04 V

Gate tunable interdot tunnel coupling

-1.08-1.04-1 01V

L(V

)

-1.11 Vt 1.04 V

Vt

1.01-1.12

1 09 1 08-10 0 dG /dV (a u )0.5M

L(V

)

VR (V)-1.09 -1.08

-1.13

10 0 dGS/dVL (a.u.)

Vt =-1.01 VVt (V) 2t (GHz)

V

d)

-1.14-1.08-1.04-1.01

<kT7.216.9

0.0d)

VR (V)-1.10 -1.09

1 0 1

12 1-

tanh kT

MN = = 2+4t2 DiCarlo et al.

Phys. Rev. Lett. 92, 226801 (2004)

(mV)-1 0 1

,Jason Petta, Princeton University

EAEA

Photon assisted tunneling in a one-electron double dot

Ene

rgy

ħ

Ene

rgy

ħ

E

EB

EEB

-1 13 52f=24 GHz -1.08 f=24 GHz 2 0

PAT in transport PAT in charge sensing

1.13

L(V

) 0

5

51f 24 GHz

-10

L(V

)

f 24 GHz1 0

)

-1.14

VL -5

(pA

)I D1

VL

-1.09 21

S(1

0-3

e2/h

)

-1.075-1.085 VR (V)

12

-1.072-1.080 VR (V)

GS


y

Charge qubit spectroscopy On resonance: = (hf)2-4t2

f<35 GHzVt

Ene

rgy

hf2tVac

1.0

offf (GHz) Vt (V)

-1 082t (GHz)

2 4100

eV

)

off102030

-1.08-1.04-1.02-1.01

2.46.29.2

13.2

50S

plitt

ing

(

M 0.5

0

S

0.00

f (GHz)3020100

(mV)-1.0 0 1.0

See also: Oosterkamp et al., Nature 395, 873 (1998)Jason Petta, Princeton University

1.00

0 4 5 ns

Charge relaxation and dephasing measurement

1f=24 GHz*

)

0.4

)

5 ns1.0

2

1T2 ≥400 ps*

ax(

=5 n

s) 0.2M(

12 dB

max

()/M

ma

0.75

0.4 0.8 (mV)

0=1 s

0.5N

6 dB

Mm

T1~16 ns0 dB 2h/T2*

0.501010 10 01

0.0

-1 5 -1 0 -0 52 0

0 dB 2

(s)1010.10.01

(mV)-1.5 -1.0 -0.5-2.0

Petta et al., PRL 93, 186802 (2004)


Charge qubit: Coherent oscillations

Enhancementin T2 at =0

Vion et al.,Science (2002)

Hayashi et al., PRL (2003), K. D. Petersson et al., PRL (2010)


Single spin qubits -vs- Singlet-triplet qubits

Single spin qubit (Loss and DiVincenzo)g p q ( )

1EZeeman

0

Encoded spin qubit- “singlet-triplet” qubit (J. Levy)

Qubit encoded in two-electron spin states

21S

1

mS=0 Basis: S and T0, mS=0 Insensitive to field fluctuations

21

0T

T

mS=0

m =1

Insensitive to field fluctuationsdecoherence free subspace

T

T

mS=1

mS=-1Work in magnetic field, T+ and T-not relevant due to Zeeman energy


The two electron regime

(1,1)(1,1)

(1,1) singlet-triplet splitting:

j=4t2/U=0 4 eV<<kTTO T+T-

j=4t2/U=0.4 eV<<kT

with U~4 meV, t~20 eVS j<<kT

(0,2) ( )(0,2)

Theory: J~0.3 meV

(0,2) singlet-triplet splitting:

Expt : J~0 1 to 1 meV

TO T+T-

Expt.: J~0.1 to 1 meVJ~400 eV

Kyriakidis et al., PRB 66, 035320 (2002)

Ashoori et al., PRL 71, 613 (1993)

S


Double dot finite bias spectroscopyRL,CL RR,CRRM,CM

S D I

VL

S D

VR

Id

Vsd

(1 0) (1 1)

Finite bias “triangles”0 4 8|Id| (pA)

(1,0) (1,1)

100

5-1

.1V

L(V

)-1

.105

(0,0)(0,1)

-1.035 -1.030VR (V)


Singlet-triplet spin blockade in dc transport

Ono et al., Science 297, 1313 (2002).


(0,2) (1,1) transport is allowed

Singlet-triplet spin blockade in dc transport

( , ) ( , ) p

(1 1) (0 2) t t i i bl k d(1,1) (0,2) transport is spin blockedRL

VL

VLV V

VL

VL

Johnson, Petta, Marcus (2005). See also Ono et al., Science 297, 1313 (2002).VRVR


(0,0) (0,1) (1,0)R Int

Singlet-triplet spin blockade in charge sensing

L

VLV

L

VL

VL

VR VR


Loss & DiVincenzo ProposalPhys. Rev. A 57, 120 (1998)

• Prepare spin in ground state

• “Spin to charge conversion”

• T1 T2* T2

• ESR for single spin rotations• Exchange interaction

T1 , T2 , T2

g• Standard semiconductor fabrication


Spin singlet state initialization

(1,1) (1,2)

VL (m

V)

(0,2)(0,1)

(0,2)

TVR (mV)

S510e

kTJ

TPP

SP





• T1 T2* T2


T1 , T2 , T2



Spin state measurement (spin-to-charge conversion)

(1,1) (1,2)

VL (m

V)

(0,2) GQPCGQPC

(0,1)(0,2)

(1,1) (0,2)TVR (mV)

Ene

rgy

T TTS

Singlet measurement

S

TO T+T-


Spin state measurement (spin-to-charge conversion)

(1,1) (1,2)

VL (m

V)

(0,2) GQPC(0,1)

(0,2)(1,1) (0,2)

TVR (mV)

Ene

rgy

T TTS

Triplet measurement

S

TO T+T-





• T1 T2* T2


T1 , T2 , T2



Spin Relaxation and Dephasing: The Two-Electron System

Johnson, Petta, Taylor, Yacoby, Lukin, Hanson, Gossard, Marcus, Nature 435, 925 (2005).


Pulsed-Gate Measurement of Spin Relaxation

(1 1) (1 2)(1,1) (1,2)

(0 1)(0,2)

(0,1)




(1 1) (1 2)(1,1) (1,2)

(0 1)(0,1)



(1 1) (1 2)(1,1) (1,2)

(0 1)(0,2)

(0,1)



Spin relaxation: Getting stuck in (1,1)

In “measurement triangle”In measurement triangledark: transition to (0,2) occurslight: transition to (0,2) blockaded


Enhanced, energy-dependent relaxation at zero field


Effective nuclear field from hyperfine interaction

Large ensemble with random spin orientations slow internal dynamicsorientations, slow internal dynamics...

Quasistatic effective field

B b0 rk 2IkBnuc b0 rk

k Ik

rms Bnuc b0 I0(I0 1) /N

GaAs: b0=3.47 T, I0 =3/2Our device: N~106-107

Bnuc~2-6 mT, tnuc~3-10 ns


BNuclearBNuclear

BTotalBTotalBBZeeman

BZeeman

T1, T2 short T1 long; T2 shortJason Petta, Princeton University

Measuring the nuclear field: Energy dependence of tunnel rates

Deviation above 1 msAdditional decaymechanism?

t(B)

B

2

1t(0) Bnuc

1

Bnuc=2.8 0.2 mT10 T ?tnuc~10 ns = T2?


lecture 2: double quantum dots - université de sherbrooke

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