QSIT Student Presentations
Anastasia Varlet ETH - 05/04/12
Quantum Dot Spin QuBits
Quantum Devices for Information Technology
Outline
Anastasia Varlet ETH - 05/04/12
I. Double Quantum Dot
II. The Logical Qubit
III. Experiments
∣S ⟩
∣T 0⟩
∣↑ ↓ ⟩∣↓ ↑ ⟩
I. Double Quantum Dot
Anastasia Varlet ETH - 05/04/12
1. Reminder : Quantum Dot (QD)
AlGaAs/GaAs heterostructure → 2DEG at the interface.
1/14
[1] T. Ihn, Semiconductor Nanostructures (2009), Oxford University Press. [2] Hanson et al.,Coherent manipulation of single spins in SC (2008), Nature 453, 1043
I. Double Quantum Dot
Anastasia Varlet ETH - 05/04/12
1. Reminder : Quantum Dot (QD)S D
PG
Picture from: [3] Ciorga et al.,
Phys. Rev. B 61 (2000)
2/14
Electrically-defined island → top gates on a 2DEG2 tunable parameters : - source and drain bias - plunger gate voltage
I. Double Quantum Dot
Anastasia Varlet ETH - 05/04/12
1. Reminder : Quantum Dot (QD)
PG
Picture from: [3] Ciorga et al.,
Phys. Rev. B 61 (2000)
[4] Hanson et al., Spins in few-electron QDs (2007), Rev. Mod. Phys., Vol. 79, No. 4
2/14
S D
Electrically-defined island → top gates on a 2DEG2 tunable parameters : - source and drain bias - plunger gate voltage
I. Double Quantum Dot
Anastasia Varlet ETH - 05/04/12
1. Reminder : Quantum Dot (QD)
Electrically-defined island → top gates on a 2DEG2 tunable parameters : - source and drain bias - plunger gate voltage PG
Picture from: [3] Ciorga et al.,
Phys. Rev. B 61 (2000)
[4] Hanson et al., Spins in few-electron QDs (2007), Rev. Mod. Phys., Vol. 79, No. 4
2/14
S D
I. Double Quantum Dot
Anastasia Varlet ETH - 05/04/12
2. Double Quantum Dot
[1] T. Ihn, Semiconductor Nanostructures (2009), Oxford University Press.
[4]
VR
VL
Picture from: [5] Petta et al.,
Science 309 (2005)
[5]
3/14
Electrically-defined island → top gates on a 2DEG2 tunable parameters : - source and drain bias - plunger gate voltages
I. Double Quantum Dot
Anastasia Varlet ETH - 05/04/12
3. Two-electron regime
A Quantum Point Contact is used to determine the charge state in the dots.
[1] T. Ihn, Semiconductor Nanostructures (2009), Oxford University Press.
[4]
VR
VL
Picture from: [3] Petta et al.,
Science 309 (2005)
[3]
[3]
4/14
I. Double Quantum Dot
Anastasia Varlet ETH - 05/04/12
3. Two-electron regimeA Quantum Point Contact is used to determine the charge state in the dots.
Picture from: [5] Petta et al.,
Science 309 (2005)
[5]
[3]
5/14
I. Double Quantum Dot
Anastasia Varlet ETH - 05/04/12
3. Two-electron regime[3]
[5]
6/14
[4] Hanson et al., Spins in few-electron QDs (2007),Rev. Mod. Phys., Vol. 79, No. 4∆V
ε = η∆V
I. Double Quantum Dot
Anastasia Varlet ETH - 05/04/12
3. Two-electron regime[3]
[5]
6/14
[4] Hanson et al., Spins in few-electron QDs (2007),Rev. Mod. Phys., Vol. 79, No. 4
→ (1,1) and (0,2) hybridize.
∆V
ε = η∆V
I. Double Quantum Dot
Anastasia Varlet ETH - 05/04/12
3. Two-electron regime[3]
[5]
6/14
[4] Hanson et al., Spins in few-electron QDs (2007),Rev. Mod. Phys., Vol. 79, No. 4
→ (1,1) and (0,2) hybridize.
→ Triplet states are split.
∆V
ε = η∆V
Outline
Anastasia Varlet ETH - 05/04/12
I. Double Quantum Dot
II. The Logical Qubit
III. Experiments
∣S ⟩
∣T 0⟩
∣↑ ↓ ⟩∣↓ ↑ ⟩
II. The Logical QuBit
Anastasia Varlet ETH - 05/04/12
1. Which System ?[3]
[3]
7/14
Picture from: [6] C. Barthel, PhD Thesis (2010)
II. The Logical QuBit
Anastasia Varlet ETH - 05/04/12
1. Which System ?[3]
7/14
[3]
Picture from: [6] C. Barthel, PhD Thesis (2010)
[3]
II. The Logical QuBit
Anastasia Varlet ETH - 05/04/12
1. Which System ?[3]
[3]
7/14
J(ε) J(ε)
∣S ⟩
∣T 0 ⟩
∣↑ ↓ ⟩∣↓ ↑ ⟩
Picture from: [6] C. Barthel, PhD Thesis (2010)
[3]
II. The Logical QuBit
Anastasia Varlet ETH - 05/04/12
1. Which System ?
[3]
7/14
S
T0
∣↑ ↓ ⟩∣↓ ↑ ⟩
∣↑ ↓ ⟩
∣↓ ↑ ⟩
∣S ⟩
∣T 0 ⟩
∣↑ ↓ ⟩∣↓ ↑ ⟩ J(ε)
- ΔBz between the dots.
- S and T0 are mixed by
hyperfine field.
ε <<0, J(ε) ≈ 0
ΔBz
Picture from: [6] C. Barthel, PhD Thesis (2010)
II. The Logical QuBit
Anastasia Varlet ETH - 05/04/12
2. Singlet-Triplet QuBit[3]
8/14
J = exchange energy between singlet and triplet→ rotation around the z-axis.
ΔBZnuc
= difference in B-field seen by the two electrons→ rotation around x-axis
∣S ⟩
∣T 0 ⟩
∣↑ ↓ ⟩∣↓ ↑ ⟩
Picture from: [6] C. Barthel, PhD Thesis (2010)
J(ε)
[3]
II. The Logical QuBit
Anastasia Varlet ETH - 05/04/12
3. Manipulation[3]
9/14
S
T0
1. Initialization
∣↑ ↓ ⟩
∣↓ ↑ ⟩
Source [6]
[3]
II. The Logical QuBit
Anastasia Varlet ETH - 05/04/12
3. Manipulation[3]
9/14
S
T0
2. Spin separationFast sweep rate
∣↑ ↓ ⟩
∣↓ ↑ ⟩
Source [6]
[3]
II. The Logical QuBit
Anastasia Varlet ETH - 05/04/12
3. Manipulation[3]
9/14
S
T0
3. Adiabatic sweep
∣↑ ↓ ⟩
∣↓ ↑ ⟩
Source [6]
[3]
II. The Logical QuBit
Anastasia Varlet ETH - 05/04/12
3. Manipulation[3]
9/14
S
T0
4. Manipulation
∣↑ ↓ ⟩
∣↓ ↑ ⟩
Source [6]
[3]
II. The Logical QuBit
Anastasia Varlet ETH - 05/04/12
3. Manipulation[3]
9/14
S
T0
∣↑ ↓ ⟩
∣↓ ↑ ⟩
5. Read-outDetermination of the charge state via QPC
→ measurement of Ps
Source [6]
Outline
Anastasia Varlet ETH - 05/04/12
I. Double Quantum Dot
II. The Logical Qubit
III. Experiments
∣S ⟩
∣T 0⟩
∣↑ ↓ ⟩∣↓ ↑ ⟩
III. Experiments
Anastasia Varlet ETH - 05/04/12
1. Coherence
10/14
(0,2)S
ε
Determination of the spin state using the calibrated QPC charge sensor → Estimation of T
2*
~10ns
How long do two spatially separated electrons retain coherence ? → Measurement of the dephasing time of S(1,1)
τM < T
1
III. Experiments
Anastasia Varlet ETH - 05/04/12
2. Manipulation and SWAP
11/14
S
T0
∣↑ ↓ ⟩
∣↓ ↑ ⟩
If : Swap !
ϕ=J (ϵ) τE
ℏϕ=π
Source [6]
III. Experiments
Anastasia Varlet ETH - 05/04/12
2. Manipulation and SWAP
12/14
If : Swap !
ϕ=J (ϵ)τE
ℏϕ=π
→ 180ps
Conclusion
Anastasia Varlet ETH - 05/04/1213/14
- Coherent control of a logical QuBit
- T2* was measured
- Rabi Oscillations were observed
- √SWAP operation-time ~ 180ps.
Source [6]
Perspective
Anastasia Varlet ETH - 05/04/1214/14
3 weeks ago...
End of the presentation
Anastasia Varlet ETH - 05/04/12
Thank you for your attention !
And many thanks to Arkady.
Questions ?
References
Anastasia Varlet ETH - 05/04/12
[1] T. Ihn, Semiconductor Nanostructures (2009), Oxford University Press.
[2] Hanson et al.,Coherent manipulation of single spins in SC (2008), Nature 453, 1043 .
[3] Ciorga et al., Phys. Rev. B 61 (2000).
[4] Hanson et al., Spins in few-electron QDs (2007), Rev. Mod. Phys., Vol. 79, No. 4
[5] Petta et al., Coherent Manipulation of coupled electron spins in SC Qds, Science 309 (2005)
[6] C. Barthel PhD Thesis, Control and Fast Measurement of Spin Qubits (2010).
[7] Shulman et al., Demonstration of Entanglement of Electrostatically Coupled S-T QuBits, Science 336 (2012).
III. Experiments
Anastasia Varlet ETH - 05/04/12
3. Spin Echo
Appendix
Anastasia Varlet ETH - 05/04/12