Adiabatic theorem for bipartite quantum systems in weak coupling limit

TL;DR

This paper investigates the adiabatic behavior of bipartite quantum systems under weak coupling, deriving formulas involving operator-valued phases, with applications to quantum control of qubits and spin systems.

Contribution

It provides a new adiabatic approximation framework for bipartite quantum systems in the weak coupling limit, including operator-valued geometric and dynamical phases.

Findings

Derived adiabatic transport formulas with operator-valued phases.

Applied results to control of atomic qubits and spin chains.

Demonstrated relevance for quantum control and open quantum systems.

Abstract

We study the adiabatic approximation of the dynamics of a bipartite quantum system with respect to one of the components, when the coupling between its two components is perturbative. We show that the density matrix of the considered component is described by adiabatic transport formulae exhibiting operator-valued geometric and dynamical phases. The present results can be used to study the quantum control of the dynamics of qubits and of open quantum systems where the two components are the system and its environment. We treat two examples, the control of an atomic qubit interacting with another one and the control of a spin in the middle of a Heisenberg spin chain.