Coherent Manipulation of Coupled Electron Spin in
Semiconductor Quantum Dots
Petta J, Johnson A, Taylor J, Laird E, Yacoby A, Lukin M, Marcus C, Hanson M, Gossard A
Science9/2005
Quantum Systems for Information TechnologyWS 2006/07
Thomas Brenner Peter Maurer
2
Overview Q
SIT
, WS
200
6/07
Tho
mas
Bre
nner
& P
eter
Mau
rer
• Setup and Experimental Realization of QD-QUBITS
• Control of Exchange Interaction
• Spin SWAP pulse sequence
• Spin echo sequence – decoherence time enlargement
• Summary
3
Experimental Setup
• GaAs/AlGaAs heterostructure – Grown by molecular beam epitaxy – 2-DEG: 100 nm b.s. and
• Double-well potential VR, VL – Distinguish potential shape – – Connect dots to reservoirs
->(0,2)S below Fermi level (0,2)T above – Pulsing time ~ 1 nsec
• Interdot tunneling VT • Quantum point contact (QPC)
– Measuring # of electrons in the Dot
211102 cm
LR VV
QS
IT, W
S 2
006/
07 T
hom
as B
renn
er &
Pet
er M
aure
r
4
Voltage-Controlled Exchange
• For > 0 : (0,2)S ground state (0,2)T are neglected
(~ 400 eV above)• For < 0 :
Discuss (1,1) in S, 3xT – << 0 :
(1,1) non interdot tunneling -> S and T are degenerated
– not small : Interdot tunneling
-> Hybridization (1,1)S and (0,2)S
-> Energy splitting J() for S
egeneratedd
hybridization
QS
IT, W
S 2
006/
07 T
hom
as B
renn
er &
Pet
er M
aure
r
5
Hyperfine Interaction
• GaAs has spin-3/2 electron couples to GaAs nuclei by hyperfine inter.
random distributed magnetic fields
• Zeeman splitting with two-level system With Basis
• With Large detuning ( ), are
eigenstates
• Bloch sphere S, T0 on z-axis and on x-axis
610T 5 T 1 mBm nuc
0
1 1,1 ,
1
0 1,1 0TS
0nuc
nuc
B
BJH
STST 21 ,21
nucBBgJ ,
,
T 100 eV 2.5 mBBg B
QS
IT, W
S 2
006/
07 T
hom
as B
renn
er &
Pet
er M
aure
r
6
Measuring the Exchange Splitting
• Measuring process is swept from positive (0,2)S to large negativeseparation time S = 200 nsec PS: probability to projected qubit to (0,2)S
by swept to positive
• At large detuning S, T0 are degenerated Hyperfine mixes states
• T+ crosses S atDegenerated two-level
system S-T+ transition takes
place Reduces PS Determines J()
BgJ B
QS
IT, W
S 2
006/
07 T
hom
as B
renn
er &
Pet
er M
aure
r
7
Dephasing of Separated Singlet
• How long can the electrons be separated before losing phase
• Same measuring cycle but varying separation time S
– Pass S-T+ degeneracy fast enough
• Projects back to (0,2)S
• Semiclassical model: – Independent statistical
distributed nuclei Gaussian like decay
Do not obtain Rabi oscillation
QS
IT, W
S 2
006/
07 T
hom
as B
renn
er &
Pet
er M
aure
r
8
Spin SWAP and Rabi Oscillation
• (1,1)S, Pass S-T+ degeneracy as quickly as possible • Adiabatic lowering to small J()is always in a eigenstate
are eigenstates; S goes to ground state
• Increase J() fast exchange occurs splitting S and T0 Rabi oscillation (around z-axis )
Spin SWAP possible
• Readout: inverse process
,
2
4
1
122
1
1:
2
42
42
222
22
B
J
B
J
B
J
B
J
EVBJJ
B
BBJJ
EH
EJ
T
S
QS
IT, W
S 2
006/
07 T
hom
as B
renn
er &
Pet
er M
aure
r
9
Spin SWAP and Rabi Oscillation (II)Q
SIT
, WS
200
6/07
Tho
mas
Bre
nner
& P
eter
Mau
rer
,...5,3, EJ• Singlet Probability shows minima (swapping) at,
obtained with corresponding pulses
• Rabi Oscillations become faster with more positive detuning and lower V ( lower barrier decreases period)
10
Singlet-triplet spin echo Q
SIT
, WS
200
6/07
Tho
mas
Bre
nner
& P
eter
Mau
rer
Pulse sequence: Mixing between S and T0 dephasing
Refocusing with τs=τs‘
11
Singlet State ProbabilityQ
SIT
, WS
200
6/07
Tho
mas
Bre
nner
& P
eter
Mau
rer
Results:
• Singlet Probability „comes back“: Refocusing obviously works
• Information can be stored ~100 times longer (next slide)
• Noise stronger than in other measurements: Due to charge dephasing?
12
Qubit decay time Q
SIT
, WS
200
6/07
Tho
mas
Bre
nner
& P
eter
Mau
rer
• very important for storing quantum information: the longer the better
• in SC-Qubits mainly due to hyperfine interaction of electron spins with about 106 GaAs nuclei
• dephasing time T2*=9±2 ns
• coherence time: T2=1.2 µs (from exp. fit)
• time ~ 180 psSWAP
x 100
x 7000
13
SummaryQ
SIT
, WS
200
6/07
Tho
mas
Bre
nner
& P
eter
Mau
rer
• Qubits made of semiconductor quantum dots based on entangled spins can be fabricated and controlled via exchange interaction
• SWAP operation is demonstrated
• Spin dephasing time T2* ~10 ns; decoherence time after spin echo sequence: ~ 1 µs (increase of factor 100)
• interesting building block for more sophisticated implementation of a quantum algorithm in a solid-state architecture
14
ReferencesQ
SIT
, WS
200
6/07
Tho
mas
Bre
nner
& P
eter
Mau
rer
[1] Petta, J.R. et al.: Coherent Manipulation of Coupled Electron Spins in Semiconductor Quantum Dots, Science, 309, 2180-2184, 2005
[2] Ihn, T.M.: Semiconductor Nanostructures, script to the corresponding lecture at ETH Zurich, 2006
[3] Bodenhausen, Ernst, R.R., Wokaun, A.: Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Oxford, 1987
