Time evolution of an entangled initial state in coupled quantum dots with Coulomb correlations

Abstract

We proved that for arbitrary mixed state the concurrence and the entanglement are determined by the average value of electron’s pair correlation functions particular combinations. We analyzed the dynamics of the initial two-electronic state in two interacting single-level quantum dots (QDs) with Coulomb correlations, weakly tunnel coupled with an electronic reservoir. We obtained correlation functions of all orders for electrons in the QDs by decoupling high-order correlations between localized and band electrons in the reservoir. Analysis of the pair correlation functions time evolution allows to follow the changes of the concurrence and the entanglement during the relaxation and transient processes. We investigated dependence of the concurrence on the value of Coulomb interaction and energy levels spacing and found its monotonic behavior. The most interesting physical effect is that more entangled state than the initial one can be formed during the charge relaxation due to the Coulomb correlations. We also demonstrated that behavior of the two-electronic entangled state pair correlation functions in coupled QDs points to the fulfillment of the Hund’s rule for the strong Coulomb interaction. We revealed the appearance of dynamical inverse occupation of the QDs energy levels during the relaxation processes. Our results open up further perspectives in solid state quantum information based on the controllable dynamics of the entangled electronic states.