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Overview

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 Science 9/2005 Quantum Systems for Information Technology WS 2006/07 Thomas Brenner Peter Maurer. Overview.

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Overview

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  1. Coherent Manipulation of Coupled Electron Spin in Semiconductor Quantum DotsPetta J, Johnson A, Taylor J, Laird E, Yacoby A, Lukin M, Marcus C, Hanson M, Gossard A Science9/2005 Quantum Systems for Information TechnologyWS 2006/07Thomas BrennerPeter Maurer

  2. Overview • Setup and Experimental Realization of QD-QUBITS • Control of Exchange Interaction • Spin SWAP pulse sequence • Spin echo sequence – decoherence time enlargement • Summary QSIT, WS 2006/07 Thomas Brenner & Peter Maurer

  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 QSIT, WS 2006/07 Thomas Brenner & Peter Maurer

  4. Voltage-Controlled Exchange • For e > 0 : (0,2)S ground state (0,2)T are neglected (~ 400 meV above) • For e < 0 : Discuss (1,1) in S, 3xT • e << 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(e) for S QSIT, WS 2006/07 Thomas Brenner & Peter Maurer

  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 QSIT, WS 2006/07 Thomas Brenner & Peter Maurer

  6. Measuring the Exchange Splitting • Measuring process e is swept from positive (0,2)S to large negative separation time tS = 200 nsec • PS: probability to projected qubit to (0,2)S by swept to positive e • At large detuning S, T0 are degenerated Hyperfine mixes states • T+ crosses S at • Degenerated two-level system S-T+ transition takes place Reduces PS Determines J(e) QSIT, WS 2006/07 Thomas Brenner & Peter Maurer

  7. Dephasing of Separated Singlet • How long can the electrons be separated before losing phase • Same measuring cycle but varying separation time tS • 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 QSIT, WS 2006/07 Thomas Brenner & Peter Maurer

  8. Spin SWAP and Rabi Oscillation • (1,1)S, Pass S-T+ degeneracy as quickly as possible • Adiabatic lowering to small J(e)is always in a eigenstate  are eigenstates; S goes to ground state  • Increase J(e) fast  exchange occurs  splitting S and T0  Rabi oscillation (around z-axis )  Spin SWAP possible • Readout: inverse process QSIT, WS 2006/07 Thomas Brenner & Peter Maurer

  9. Spin SWAP and Rabi Oscillation (II) QSIT, WS 2006/07 Thomas Brenner & Peter Maurer • 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 Pulse sequence: Mixing between S and T0 dephasing QSIT, WS 2006/07 Thomas Brenner & Peter Maurer Refocusing with τs=τs‘

  11. Singlet State Probability QSIT, WS 2006/07 Thomas Brenner & Peter Maurer • 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 • 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 QSIT, WS 2006/07 Thomas Brenner & Peter Maurer • dephasing time T2*=9±2 ns • coherence time: T2=1.2 µs (from exp. fit) • time ~ 180 ps x 100 x 7000

  13. Summary • 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 QSIT, WS 2006/07 Thomas Brenner & Peter Maurer

  14. References [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 QSIT, WS 2006/07 Thomas Brenner & Peter Maurer

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