Exact reduced dynamics for a qubit in a precessing magnetic field and in the contact with a heat-bath

TL;DR

This paper derives an exact reduced dynamics for a qubit in a precessing magnetic field coupled to a heat bath, using block operator matrices, and explores the validity of adiabatic approximation in open quantum systems.

Contribution

It introduces a novel approach based on block operator matrices to obtain exact dynamics and analyzes the adiabatic approximation for an open quantum system.

Findings

Exact reduced dynamics derived for the qubit system.

Standard adiabatic conditions hold in the weak coupling regime.

Explicit example of adiabatic evolution in an open quantum system.

Abstract

The two-level quantum system (qubit) in a precessing magnetic field and in contact with a heat bath is investigated. The exact reduced dynamics for the qubit in question is obtained. We apply the approach based on the block operator matrices theory, in contrast with the standard methods provided by the theory of the open quantum systems. We also present the solution of the Riccati operator equation associated with the Hamiltonian of the system. Next, we study the adiabatic approximation for the system under consideration using quantum fidelity as a way to measure validity of the adiabatic theory. We find that in the weak coupling domain the standard condition that ensures adiabatic behavior of the spin in the magnetic field also guarantees its adiabatic evolution in the open system variant of this model. Therefore, we provide the explicit example of the open quantum system that satisfies the adiabatic approximation firstly formulated for the closed quantum systems.