A new approach for open quantum systems based on a phonon number representation of a harmonic oscillator bath

TL;DR

This paper introduces a computationally efficient method for simulating open quantum systems using a phonon number representation, enabling large system analysis with accurate results.

Contribution

It presents a novel phonon number-based approach that reduces computational cost compared to hierarchical equations of motion for open quantum systems.

Findings

Accurately reproduces exact results for a quantum damped harmonic oscillator.

Enables analysis of large-dimensional systems with reduced computational resources.

Provides a link to the total wave function through new boson operators.

Abstract

To investigate a system coupled to a harmonic oscillator bath, we propose a new approach based on a phonon number representation of the bath. Compared to the method of the hierarchical equations of motion, the new approach is computationally much less expensive in a sense that a reduced density matrix is obtained by calculating the time evolution of vectors, instead of matrices, which enables one to deal with large dimensional systems. As a benchmark test, we consider a quantum damped harmonic oscillator, and show that the exact results can be well reproduced. In addition to the reduced density matrix, our approach also provides a link to the total wave function by introducing new boson operators.