Relaxation times in an open interacting two-qubit system

TL;DR

This paper investigates how environmental interactions influence entanglement decay in a two-qubit system, revealing critical slowing down and non-monotonic behaviors, with a simple model including Markovian and non-Markovian effects.

Contribution

It introduces a straightforward model for two interacting qubits in a thermal environment, analyzing relaxation dynamics and effects of temperature, magnetic field, and environment memory.

Findings

Critical slowing down of entangled state relaxation near zero temperature.

Unusual non-monotonic temperature dependence of relaxation rates.

Resonant cusp-like structures in relaxation rates as a function of environment memory-time.

Abstract

In a two-qubit system the coupling with an environment affects considerably the entanglement dynamics, and usually leads to the loss of entanglement within a finite time. Since entanglement is a key feature in the application of such systems to quantum information processing, it is highly desirable to find a way to prolonging its lifetime. We present a simple model of an interacting two-qubit system in the presence of a thermal Markovian environment. The qubits are modeled as interacting spin-$\half$ particles in a magnetic field and the environment is limited to inducing single spin-flip events. A simple scheme allows us to calculate the relaxation rates for all processes. We show that the relaxation dynamics of the most entangled state exhibit critical slowing down as a function of the magnetic field, where the relaxation rate changes from exponentially small values to finite values in the zero-temperature limit. We study the effect of temperature and magnetic field on all the other relaxation rates and find that they exhibit unusual properties, such as non-monotonic dependence on temperature and a discontinuity as a function of magnetic field. In addition, a simple scheme to include non-Markovian effects is presented and applied to the two-qubit model. We find that the relaxation rates exhibit a sharp, cusp-like resonant structure as a function of the environment memory-time, and that for long memory-times all the different relaxation rates merge into a single one.