QSIT Student Presentations Quantum Dot Spin QuBits Quantum Devices for Information Technology
Outline I. Double Quantum Dot S II. The Logical Qubit T 0 III. Experiments
I. Double Quantum Dot 1. Reminder : Quantum Dot (QD) AlGaAs/GaAs heterostructure 2DEG at the interface. [2] Hanson et al.,coherent manipulation of single spins in SC (2008), Nature 453, 1043 [1] T. Ihn, Semiconductor Nanostructures (2009), Oxford University Press. 1/14
I. Double Quantum Dot 1. Reminder : Quantum Dot (QD) S Electrically-defined island top gates on a 2DEG 2 tunable parameters : - source and drain bias - plunger gate voltage 2/14 D Picture from: Ciorga et al., Phys. Rev. B 61 (2000) PG
I. Double Quantum Dot 1. Reminder : Quantum Dot (QD) S Electrically-defined island top gates on a 2DEG 2 tunable parameters : - source and drain bias - plunger gate voltage D Picture from: Ciorga et al., Phys. Rev. B 61 (2000) PG [4] Hanson et al., Spins in few-electron QDs (2007), Rev. Mod. Phys., Vol. 79, No. 4 2/14
I. Double Quantum Dot 1. Reminder : Quantum Dot (QD) S Electrically-defined island top gates on a 2DEG 2 tunable parameters : - source and drain bias - plunger gate voltage D Picture from: Ciorga et al., Phys. Rev. B 61 (2000) PG [4] Hanson et al., Spins in few-electron QDs (2007), Rev. Mod. Phys., Vol. 79, No. 4 2/14
I. Double Quantum Dot 2. Double Quantum Dot [5] Electrically-defined island top gates on a 2DEG 2 tunable parameters : - source and drain bias - plunger gate voltages Picture from: [5] Petta et al., Science 309 (2005) [4] VL VR [1] T. Ihn, Semiconductor Nanostructures (2009), Oxford University Press. 3/14
I. Double Quantum Dot 3. Two-electron regime A Quantum Point Contact is used to determine the charge state in the dots. [4] Picture from: Petta et al., Science 309 (2005) VL VR [1] T. Ihn, Semiconductor Nanostructures (2009), Oxford University Press. 4/14
I. Double Quantum Dot 3. Two-electron regime [5] A Quantum Point Contact is used to determine the charge state in the dots. Picture from: [5] Petta et al., Science 309 (2005) 5/14
I. Double Quantum Dot 3. Two-electron regime [5] [4] Hanson et al., Spins in few-electron QDs (2007), Rev. Mod. Phys., Vol. 79, No. 4 V ε = η V 6/14
I. Double Quantum Dot 3. Two-electron regime [5] [4] Hanson et al., Spins in few-electron QDs (2007), Rev. Mod. Phys., Vol. 79, No. 4 V ε = η V (1,1) and (0,2) hybridize. 6/14
I. Double Quantum Dot 3. Two-electron regime [5] [4] Hanson et al., Spins in few-electron QDs (2007), Rev. Mod. Phys., Vol. 79, No. 4 V ε = η V (1,1) and (0,2) hybridize. Triplet states are split. 6/14
Outline I. Double Quantum Dot S II. The Logical Qubit T 0 III. Experiments
II. The Logical QuBit 1. Which System? Picture from: [6] C. Barthel, PhD Thesis (2010) 7/14
II. The Logical QuBit 1. Which System? Picture from: [6] C. Barthel, PhD Thesis (2010) 7/14
II. The Logical QuBit 1. Which System? S J(ε) J(ε) T 0 Picture from: [6] C. Barthel, PhD Thesis (2010) 7/14
II. The Logical QuBit 1. Which System? S T0 J(ε) T 0 S ε <<0, J(ε) 0 ΔBz - ΔBz between the dots. - S and T0 are mixed by hyperfine field. Picture from: [6] C. Barthel, PhD Thesis (2010) 7/14
II. The Logical QuBit 2. Singlet-Triplet QuBit S J(ε) T 0 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 Picture from: [6] C. Barthel, PhD Thesis (2010) 8/14
II. The Logical QuBit 3. Manipulation Source [6] T0 S 1. Initialization 9/14
II. The Logical QuBit 3. Manipulation Source [6] T0 S 2. Spin separation Fast sweep rate 9/14
II. The Logical QuBit 3. Manipulation Source [6] T0 S 3. Adiabatic sweep 9/14
II. The Logical QuBit 3. Manipulation Source [6] T0 S 4. Manipulation 9/14
II. The Logical QuBit 3. Manipulation Source [6] T0 S 5. Read-out Determination of the charge state via QPC measurement of Ps 9/14
Outline I. Double Quantum Dot S II. The Logical Qubit T 0 III. Experiments
III. Experiments 1. Coherence How long do two spatially separated electrons retain coherence? Measurement of the dephasing time of S(1,1) (0,2)S τm < T1 ε Determination of the spin state using the calibrated QPC charge sensor Estimation of T2* ~10ns 10/14
III. Experiments 2. Manipulation and SWAP T0 S Source [6] J (ϵ) τ E ℏ If ϕ=π : Swap! ϕ= 11/14
III. Experiments 2. Manipulation and SWAP 180ps J (ϵ) τ E ℏ If ϕ=π : Swap! ϕ= 12/14
Conclusion Source [6] - Coherent control of a logical QuBit - T2* was measured - Rabi Oscillations were observed - SWAP operation-time ~ 180ps. 13/14
Perspective 3 weeks ago... 14/14
End of the presentation Thank you for your attention! And many thanks to Arkady. Questions?
References [1] T. Ihn, Semiconductor Nanostructures (2009), Oxford University Press. [2] Hanson et al.,coherent manipulation of single spins in SC (2008), Nature 453, 1043. 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 3. Spin Echo
Appendix