Spin-Orbit Mediated Control of Spin Qubits

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Spin-Orbit Mediated Control of Spin Qubits

• Christian Flindt, Anders S. Sorensen, Karsten
  Flensberg

Michael Schroer Petta Lab Journal Club 8/28/07
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Overview

• Why is spin-orbit an attractive technique?
• How can we use spin-orbit to implement single and
  two-qubit operations?
• What kind of performance can we expect?
• Summary

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Why Spin orbit? I

• Ways to control electron spin
• ESR-
• Exchange Coupling-
• Spin Orbit -

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Why Spin orbit? II

• ESR - similar problems to NMR qubits
• Localizing a magnetic field is difficult
• Gradient magnetic fields?
• Delft group - limited by induced electric fields
  - ?/2 time of 30 ns
• Exchange Coupling
• No single electron operations
• Highly sensitive to low frequency electrical
  noise
• Slow gating times

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How Spin orbit? I

• Hamiltonian for a single electron in a nanowire
  based quantum dot

• Assume that the potential is harmonic, but may
  be shifted by wiggling the voltages on the gates

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How Spin orbit? II

• Perform unitary transformation with

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How Spin orbit? III

• Now, a trace over x gives a simple form for the
  Hamiltonian

where the trace has rescaled g by a factor of
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Now for the cool stuff...
Two options for using this Hamiltonian for single
spin control
When we meet the condition

• Looks like ESR!
• Sometimes called Electron Dipole Induced Spin
  Resonance (EDSR)

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Option 2
Quickly displace spin by
Let it evolve under this hamiltonian for
Immediately move back to x(0), and the spin has
flipped using just one voltage pulse
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Two Qubit Operations?
Moving one electron creates a force on the other
through the Coulomb interaction
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Two Qubit Operations II
Initially looks like we dont have coupling
between spins
Perturbation theory
with
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Performance
Theoretical device
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Single Spin Performance

• For spin flip operation
• Requires E 6.6 uV/nm
• Gate voltage of 3 mV
• Total time 0.1 ns
• Delft group performed spin flip in 54 ns
• Allows for fast spin echo, as well as fast single
  qubit operations

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Two Qubit Performance

• Gate times 5 ns
• More concerned with noise performance

Spin Orbit coupling much more noise
resistant than exchange coupling
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More two qubit noise performance

• Open circles - t
• Stars - Zeeman Splitting
• Closed Circles - Exchange Coupling

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Is InAs really the best system for this?

• Maybe we could find a material with strong spin
  orbit coupling?
• Or, is a weaker spin orbit coupling actually
  better?
• Remember, rescaling of g!

Luckily, the authors came through for us...
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Questions

• Paper uses bulk properties of Indium Arsenide
• What about multiple sources of spin orbit?
• What two qubit gates can be applied using this
  coupling?
• Does it actually work?

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Ennslin Group example of EDSR
EDSR on a large number of electrons in a large
quantum well
Were able to produce spin flips in 1.8 ns
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Summary

• Spin orbit control of electron spin is fast
• Can control one electron as well as the coupling
  between two electrons

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Discussion