WavePacket: A Matlab package for numerical quantum dynamics. II: Open quantum systems, optimal control, and model reduction

TL;DR

WavePacket is a versatile open-source Matlab package for simulating quantum dynamics, now extended to include open systems, optimal control, and model reduction techniques, supporting advanced research and educational needs in quantum physics and chemistry.

Contribution

This paper introduces new features in WavePacket for modeling open quantum systems, implementing optimal control algorithms, and applying model reduction methods, enhancing its capabilities beyond previous versions.

Findings

Successfully models open quantum systems with dissipation and dephasing.

Implements rapid monotonic convergence methods for quantum control.

Demonstrates effective dimension reduction using controllability/observability and H2-optimal techniques.

Abstract

WavePacket is an open-source program package for numeric simulations in quantum dynamics. It can solve time-independent or time-dependent linear Schr\"odinger and Liouville-von Neumann-equations in one or more dimensions. Also coupled equations can be treated, which allows, e.g., to simulate molecular quantum dynamics beyond the Born-Oppenheimer approximation. Optionally accounting for the interaction with external electric fields within the semi-classical dipole approximation, WavePacket can be used to simulate experiments involving tailored light pulses in photo-induced physics or chemistry. Being highly versatile and offering visualization of quantum dynamics 'on the fly', WavePacket is well suited for teaching or research projects in atomic, molecular and optical physics as well as in physical or theoretical chemistry. Building on the previous Part I which dealt with closed quantum systems and discrete variable representations, the present Part II focuses on the dynamics of open quantum systems, with Lindblad operators modeling dissipation and dephasing. This part also describes the WavePacket function for optimal control of quantum dynamics, building on rapid monotonically convergent iteration methods. Furthermore, two different approaches to dimension reduction implemented in WavePacket are documented here. In the first one, a balancing transformation based on the concepts of controllability and observability Gramians is used to identify states that are neither well controllable nor well observable. Those states are either truncated or averaged out. In the other approach, the H2-error for a given reduced dimensionality is minimized by H2 optimal model reduction techniques, utilizing a bilinear iterative rational Krylov algorithm.