• DOI:10.1103/PhysRevB.73.115329
• Corpus ID: 119100501

Voltage probe model of spin decay in a chaotic quantum dot with applications to spin-flip noise and entanglement production

@article{Michaelis2005VoltagePM,
  title={Voltage probe model of spin decay in a chaotic quantum dot with applications to spin-flip noise and entanglement production},
  author={Bj{\"o}rn Michaelis and C. W. J. Beenakker},
  journal={Physical Review B},
  year={2005},
  volume={73},
  pages={115329}
}

• B. Michaelis, C. Beenakker
• Published 19 December 2005
• Physics
• Physical Review B

The voltage probe model is a model of incoherent scattering in quantum transport. Here we use this model to study the effect of spin-flip scattering on electrical conduction through a quantum dot with chaotic dynamics. The spin decay rate $\ensuremath{\gamma}$ is quantified by the correlation of spin-up and spin-down current fluctuations (spin-flip noise). The resulting decoherence reduces the ability of the quantum dot to produce spin-entangled electron-hole pairs. For $\ensuremath{\gamma}$ greater than a critical value ${\ensuremath{\gamma}}_{c}$, the entanglement production rate vanishes identically. The statistical distribution $P({\ensuremath{\gamma}}_{c})$ of the critical decay rate in an ensemble of chaotic quantum dots is calculated using the methods of random-matrix theory. For small ${\ensuremath{\gamma}}_{c}$ this distribution is $\ensuremath{\propto}{\ensuremath{\gamma}}_{c}^{\ensuremath{-}1+\ensuremath{\beta}∕2}$, depending on the presence $(\ensuremath{\beta}=1)$ or absence $(\ensuremath{\beta}=2)$ of time-reversal symmetry. To make contact with experimental observables, we derive a one-to-one relationship between the entanglement production rate and the spin-resolved shot noise, under the assumption that the density matrix is isotropic in the spin degrees of freedom. Unlike the Bell inequality, this relationship holds for both pure and mixed states. In the tunneling regime, the electron-hole pairs are entangled if and only if the correlator of parallel spin currents is at least twice larger than the correlator of antiparallel spin currents.