Validity of the single-particle approach for electron transport in quantum wires assisted by surface acoustic waves

We study by means of time-dependent numerical simulations the quantum entanglement stemming from the Coulomb interaction between two electrons trapped in the minima of the piezoelectric potential generated by surface acoustic waves. We find that for particles captured in low-energy bound states the quantum correlations turn out to be negligible, thus validating a single-particle approach to the dynamics of such systems. At long times, for high-energy electrons, a substantial entanglement appears, which is an indicator of a mostly correlated dynamics.