Multiple Nuclear Polarization States in a Double Quantum Dot

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Multiple Nuclear Polarization Statesin a Double
Quantum Dot

• Collaboration between theory and experiment

Theory Jeroen Danon, Yuli Nazarov Experiment Ivo
Vink, Katja Nowack, Frank Koppens,Lieven
Vandersypen
Delft University of Technology, The Netherlands
March 12th 2009
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Overview

• Electron Spins in Quantum Dots, Hyperfine
  Interaction
• Electron Spin Resonance, Coherent Spin Rotations
• Some Surprising Data
• Overhauser Effect? No.
• So what is going on?
• Results
• Conclusions

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Electron Spins in Quantum Dots

• confinement even single (!) electrons
• initialization Atature et al., Science ('06)
• manipulation Petta et al., Science
  ('05) Koppens et al., Nature ('06)
• read-out Hanson et al., PRL ('05)

BUT Hyperfine interaction
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ESR in DQD Coherent Spin Rotations
scan (?,B0)
on resonance current
resonance
off-resonance no current
Icps
B0
stripline with oscillating current creates
oscillating B-field
vary length of ESR pulse
B1
Koppens et al., Nature ('06)
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ESR in DQD Surprise!
just change sweep direction!
x
tune to resonance and wait

• Resonance "dragged" over large rangeas if
  something cancels B0
• Multi-stability at resonance (4 stable states)

The usual suspects nuclear spins ESR nuclear
polarization some Overhauser-like effect?
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ESR and Overhauser Effect
Overhauser use Electron Spin Resonance to
polarize your nuclei
Idea
Mechanism 1. equilibrium is disturbed by ESR 2.
HF is one of the restoring forces
Reasoning also applies to quantum dots JD
Nazarov, PRL ('08)

• nuclear spin pumping
• bistabilities

• too weak
• "wrong" sign

Direction of pumping electrons high ? low
energy nuclei opposite of electrons
here B0 gt ?, need dPnuc/dt gt 0
in example dPnuc/dt lt 0
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What is going on?
Complications compared to single "closed" dot 1.
decay path available 2. accompanying E-field ?
E-field assisted flip-flops possible 3. gets
broadened by PAT
Important effect flip-flops loose preference for
reduction of Zeeman energy
if reasoning above is relevant, need other
asymmetry to determine sign
Overhauser wrong sign of polarization this
slide no sign of polarization
expect "right" sign strong enough?
Dominating mechanism, assuming saturated
ESR compare weak driving Rudner Levitov, PRL
('07) 1. E-field assisted hyperfine flip-flops 2.
tunneling to outgoing lead takes care of energy
differences 3. internal spin relaxation causes
(small) spin asymmetry
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Approach
Master equation and second order Fermi's Golden
Rule
1. transform problem to rotating frame
2. find quasistationary occupation probabilities
relexation decay
we add
and solve master equation to find
and calculate the current as
3. calculate 2nd order HF transition rates
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Results
asymmetric rates
Nuclear spin pumping
symmetric rates
Current

100 mT
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Results
Double Dot combine current and pumping
up to nine (!) stable points
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Conclusions

• ESR related nuclear spin dynamics in a DQD
• motivated by unexpected results
• investigated possible pumping mechanisms ?
  identified dominating mechanism
• calculated current and pumping curves for double
  dot setup
• found up to nine stable points
• four different values for the current could fit
  the data!
• suppressed fluctuations
• More info on arXiv0902.2653