Quantum Dot Spin QuBits - Quantum Device Lab · I. Double Quantum Dot Anastasia Varlet ETH - 05/04/12 3. Two-electron regime A Quantum Point Contact is used to determine the charge

QSIT Student Presentations

Anastasia Varlet ETH - 05/04/12

Quantum Dot Spin QuBits

Quantum Devices for Information Technology

Outline


I. Double Quantum Dot

II. The Logical Qubit

III. Experiments

∣S ⟩

∣T 0⟩

∣↑ ↓ ⟩∣↓ ↑ ⟩



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



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




PG


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




Electrically-defined island → top gates on a 2DEG2 tunable parameters : - source and drain bias - plunger gate voltage PG


Phys. Rev. B 61 (2000)


2/14

S D



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



3. Two-electron regime

A Quantum Point Contact is used to determine the charge state in the dots.


[4]

VR

VL


Science 309 (2005)

[3]

[3]

4/14



3. Two-electron regimeA Quantum Point Contact is used to determine the charge state in the dots.


Science 309 (2005)

[5]

[3]

5/14



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




[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




[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




III. Experiments

∣S ⟩

∣T 0⟩

∣↑ ↓ ⟩∣↓ ↑ ⟩

II. The Logical QuBit


1. Which System ?[3]

[3]

7/14

Picture from: [6] C. Barthel, PhD Thesis (2010)




7/14

[3]


[3]




[3]

7/14

J(ε) J(ε)

∣S ⟩

∣T 0 ⟩

∣↑ ↓ ⟩∣↓ ↑ ⟩


[3]



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




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 ⟩

∣↑ ↓ ⟩∣↓ ↑ ⟩


J(ε)

[3]



3. Manipulation[3]

9/14

S

T0

1. Initialization

∣↑ ↓ ⟩

∣↓ ↑ ⟩

Source [6]

[3]



3. Manipulation[3]

9/14

S

T0

2. Spin separationFast sweep rate

∣↑ ↓ ⟩

∣↓ ↑ ⟩

Source [6]

[3]



3. Manipulation[3]

9/14

S

T0

3. Adiabatic sweep

∣↑ ↓ ⟩

∣↓ ↑ ⟩

Source [6]

[3]



3. Manipulation[3]

9/14

S

T0

4. Manipulation

∣↑ ↓ ⟩

∣↓ ↑ ⟩

Source [6]

[3]



3. Manipulation[3]

9/14

S

T0

∣↑ ↓ ⟩

∣↓ ↑ ⟩

5. Read-outDetermination of the charge state via QPC

→ measurement of Ps

Source [6]

Outline




III. Experiments

∣S ⟩

∣T 0⟩

∣↑ ↓ ⟩∣↓ ↑ ⟩

III. Experiments


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


2. Manipulation and SWAP

11/14

S

T0

∣↑ ↓ ⟩

∣↓ ↑ ⟩

If : Swap !

ϕ=J (ϵ) τE

ℏϕ=π

Source [6]

III. Experiments


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


Thank you for your attention !

And many thanks to Arkady.

Questions ?

References



[2] Hanson et al.,Coherent manipulation of single spins in SC (2008), Nature 453, 1043 .

[3] Ciorga et al., Phys. Rev. B 61 (2000).


[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


3. Spin Echo

Appendix


Quantum Dot Spin QuBits - Quantum Device Lab · I. Double Quantum Dot Anastasia Varlet ETH - 05/04/12 3. Two-electron regime A Quantum Point Contact is used to determine the charge

Documents