Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model

TL;DR

This paper provides an analytical framework for understanding the effectiveness and limits of dynamical decoupling in quantum systems coupled to structured bosonic environments, including infinite-mode baths.

Contribution

It introduces a new Trotter theorem for multiple Hamiltonians and derives bounds for the convergence speed of dynamical decoupling in complex quantum environments.

Findings

Bounds accurately predict decoupling efficiency

Analytical results extend to infinite-mode boson baths

Comparison with numerical data confirms theoretical predictions

Abstract

Dynamical decoupling is a technique aimed at suppressing the interaction between a quantum system and its environment by applying frequent unitary operations on the system alone. In the present paper, we analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment initially prepared in a thermal state. We find sufficient conditions under which dynamical decoupling works for such systems, and, most importantly, we find bounds for the convergence speed of the procedure. Our analysis is based on a new Trotter theorem for multiple Hamiltonians and involves a rigorous treatment of the evolution of mixed quantum states via unbounded Hamiltonians. A comparison with numerical experiments shows that our bounds reproduce the correct scaling in various relevant system parameters. Furthermore, our analytical treatment allows for quantifying the decoupling efficiency for boson baths with infinitely many modes, in which case a numerical treatment is unavailable.