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

TL;DR

This paper models spin decay in chaotic quantum dots using a voltage probe approach, linking spin-flip noise to entanglement suppression and deriving statistical and experimental relations for spin-related quantum transport phenomena.

Contribution

It introduces a novel application of the voltage probe model to quantify spin decay and entanglement loss in chaotic quantum dots, including statistical distributions and experimental correlations.

Findings

Critical spin decay rate gamma_c determines entanglement cessation.

Distribution of gamma_c depends on time-reversal symmetry presence.

A direct relation between entanglement rate and spin-resolved shot noise is established.

Abstract

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 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 gamma greater than a critical value gamma_c, the entanglement production rate vanishes identically. The statistical distribution P(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 gamma_c this distribution is proportional to gamma_c^(-1+beta/2), depending on the presence (beta=1) or absence (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.