Quantum dynamics under coherent and incoherent effects of a spin bath in the Keldysh formalism: application to a spin swapping operation

TL;DR

This paper develops a Keldysh formalism to analyze the quantum dynamics of an open spin system, revealing effects of environment fluctuations on spin swapping that are missed by traditional approximations.

Contribution

It introduces a novel application of the Keldysh formalism to spin dynamics, capturing non-Markovian effects and environment-induced frequency shifts in spin swapping.

Findings

Fast environmental fluctuations decrease swapping frequency.

Full bath memory alters the swapping dynamics.

Analytical solutions reveal short-time quadratic behavior.

Abstract

We develop the Keldysh formalism for the polarization dynamics of an open spin system. We apply it to the swapping between two qubit states in a model describing an NMR cross-polarization experiment. The environment is a set of interacting spins. For fast fluctuations in the environment, the analytical solution shows effects missed by the secular approximation of the Quantum Master Equation for the density matrix: a frequency decrease depending on the system-environment escape rate and the quantum quadratic short time behavior. Considering full memory of the bath correlations yields a progressive change of the swapping frequency.