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Coherent Manipulation of Coupled Electron Spin in Semiconductor Quantum Dots

This article discusses the setup, experimental realization, and control of quantum dots for information technology. It explores the exchange interaction, spin SWAP pulse sequence, spin echo sequence, and decoherence time enlargement. The study concludes that semiconductor quantum dots can be controlled via exchange interaction and have potential for implementing quantum algorithms in solid-state architectures.

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Coherent Manipulation of Coupled Electron Spin in Semiconductor Quantum Dots

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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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