Open Quantum System Dynamics from a Measurement Perspective: Applications to Coherent Particle Transport and to Quantum~Brownian Motion

TL;DR

This paper uses measurement theory to analyze open quantum systems, applying it to quantum dot transport and quantum Brownian motion, revealing new insights into decoherence mechanisms and the role of information transfer.

Contribution

It introduces a measurement-based framework for open quantum system dynamics and applies it to two distinct problems, offering new perspectives on decoherence and quantum transport.

Findings

Decoherence in quantum dots can be controlled via adiabatic schemes.

Quantum contribution to position diffusion is an artifact of the Markovian approximation.

Phase averaging is the dominant decoherence mechanism in collisional quantum Brownian motion.

Abstract

We employ the theoretical framework of positive operator valued measures, to study Markovian open quantum systems. In particular, we discuss how a quantum system influences its environment. Using the theory of indirect measurements, we then draw conclusions about the information we could hypothetically obtain about the system by observing the environment. Although the environment is not actually observed, we can use these results to describe the change of the quantum system due to its interaction with the environment. We apply this technique to two different problems. In the first part, we study the coherently driven dynamics of a particle on a rail of quantum dots. This tunnelling between adjacent quantum dots can be controlled externally. We employ an adiabatic scheme similar to stimulated Raman adiabatic passage, to transfer the particle between different quantum dots. We compare two fundamentally different sources of decoherence. In the second part, we study the dynamics of a free quantum particle, which experiences random collisions with gas particles. Previous studies on this topic applied scattering theory to momentum eigenstates. We present a supplementary approach, where we develop a rigorous measurement interpretation of the collision process to derive a master equation. Finally, we study the collisional decoherence process in terms of the Wigner function. We restrict ourselves to one spatial dimension. Nevertheless, we find some interesting new insight, including that the previously celebrated quantum contribution to position diffusion is not real, but a consequence of the Markovian approximation. Further, we discover that the leading decoherence process is due to phase averaging, rather than induced by the information transfer between the colliding particles.