Quantum and classical correlations in electron-nuclear spin echo

Abstract

The quantum properties of dynamic correlations in a system of an electron spin surrounded by nuclear spins under the conditions of free induction decay and electron spin echo have been studied. Analytical results for the time evolution of mutual information, classical part of correlations, and quantum part characterized by quantum discord have been obtained within the central-spin model in the high-temperature approximation. The same formulas describe discord in both free induction decay and spin echo although the time and magnetic field dependences are different because of difference in the parameters entering into the formulas. Changes in discord in the presence of the nuclear polarization βI in addition to the electron polarization βS have been calculated. It has been shown that the method of reduction of the density matrix to a two-spin electron-nuclear system provides a qualitatively correct description of pair correlations playing the main role at βS ≈ βI and small times. At large times, such correlations decay and multispin correlations ensuring nonzero mutual information and zero quantum discord become dominant.