Reconstructing the relaxation dynamics induced by an unknown heat bath

TL;DR

This paper introduces a method to reconstruct the unknown heat bath-induced relaxation dynamics in quantum systems using a maximum likelihood approach, enabling better understanding of system-bath interactions despite unknown bath properties.

Contribution

It presents a novel estimation scheme based on steepest-descent and maximum likelihood to reconstruct relaxation dynamics from experimental data with unknown heat bath effects.

Findings

Successfully reconstructs relaxation dynamics from experimental data.

Constrains the quantum state to a curve in state space after reconstruction.

Provides a new tool for analyzing uncontrolled system-bath interactions.

Abstract

In quantum state tomography, one potential source of error is uncontrolled contact of the system with a heat bath whose detailed properties are not known, and whose impact on the system moreover varies between different runs of the experiment. Precisely these variations provide a handle for reconstructing the system's effective relaxation dynamics. I propose a pertinent estimation scheme which is based on a steepest-descent ansatz and maximum likelihood. After reconstructing the relaxation dynamics, the original quantum state of the system can be constrained to a curve in state space.