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

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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 Science9/2005 Quantum
Systems for Information TechnologyWS 2006/07
Thomas Brenner Peter Maurer
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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
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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
• -gt(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
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Voltage-Controlled Exchange

• For e gt 0
• (0,2)S ground state
• (0,2)T are neglected
• ( 400 meV above)
• For e lt 0
• Discuss (1,1) in S, 3xT
• e ltlt 0
• (1,1) non interdot
• tunneling
• -gt S and T are
• degenerated
• not small
• Interdot tunneling
• -gt Hybridization (1,1)S and (0,2)S
• -gt Energy splitting J(e) for S

QSIT, WS 2006/07 Thomas Brenner Peter Maurer
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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
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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
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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
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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
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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)

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Singlet-triplet spin echo
Pulse sequence
Mixing between S and T0 ? dephasing
QSIT, WS 2006/07 Thomas Brenner Peter Maurer
Refocusing with tsts
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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?

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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 T292 ns
• coherence time T21.2 µs (from exp. fit)
• time 180 ps

x 100
x 7000
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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
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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