Analytical solution of the time evolution of an entangled electron spin pair in a double quantum dot nanostructure

TL;DR

This paper provides an exact analytical solution for the time evolution of an entangled electron spin pair in a double quantum dot, incorporating relaxation and decoherence effects, offering a new approach to complex quantum system analysis.

Contribution

It introduces a systematic method to analytically solve coupled differential equations for quantum systems, reducing reliance on numerical simulations.

Findings

Exact analytical solution for spin dynamics in quantum dots

Inclusion of relaxation and decoherence effects

Applicable to a broad class of complex quantum systems

Abstract

Using master equations we present an analytical solution of the time evolution of an entangled electron spin pair which can occupy 36 different quantum states in a double quantum dot nanostructure. This solution is exact given a few realistic assumptions and takes into account relaxation and decoherence rates of the electron spins as phenomenological parameters. Our systematic method of solving a large set of coupled differential equations is straightforward and can be used to obtain analytical predictions of the quantum evolution of a large class of complex quantum systems, for which until now commonly numerical solutions have been sought.