Nuclear-induced time evolution of entanglement of two-electron spins in anisotropically coupled quantum dot

TL;DR

This paper investigates how the entanglement of two electron spins in anisotropically coupled quantum dots evolves over time under nuclear spin interactions, revealing critical behavior influenced by exchange interactions and magnetic fields.

Contribution

It introduces a detailed analysis of entanglement dynamics in anisotropic quantum dots, highlighting the critical behavior and decay profiles influenced by exchange interaction differences and external magnetic fields.

Findings

Entanglement decays to a saturation value depending on exchange interaction and magnetic field.

Entanglement exhibits symmetric behavior around a critical exchange interaction value.

Decay profiles shift from linear to power law to Gaussian near the critical point.

Abstract

We study the time evolution of entanglement of two spins in anisotropically coupled quantum dot interacting with the unpolarized nuclear spins environment. We assume that the exchange coupling strength in the z-direction $J_z$ is different from the lateral one $J_l$. We observe that the entanglement decays as a result of the coupling to the nuclear environment and reaches a saturation value, which depends on the value of the exchange interaction difference $J=\| J_l-J_z\|$ between the two spins and the strength of the applied external magnetic field. We find that the entanglement exhibits a critical behavior controlled by the competition between the exchange interaction $J$ and the external magnetic field. The entanglement shows a quasi-symmetric behavior above and below a critical value of the exchange interaction. It becomes more symmetric as the external magnetic field increases. The entanglement reaches a large saturation value, close to unity, when the exchange interaction is far above or below its critical value and a small one as it closely approaches the critical value. Furthermore, we find that the decay rate profile of entanglement is linear when the exchange interaction is much higher or lower than the critical value but converts to a power law and finally to a Gaussian as the critical value is approached from both directions. The dynamics of entanglement is found to be independent of the exchange interaction for isotropically coupled quantum dot.