Quantum Control of Infinite Dimensional Many-Body Systems

TL;DR

This paper explores how the Quantum Recurrence Theorem can be used to overcome irreversibility in controlling infinite dimensional quantum systems with discrete-spectrum Hamiltonians, enabling better state manipulation.

Contribution

It demonstrates that irreversibility in such quantum systems can be mitigated using recurrence properties, expanding control possibilities for infinite dimensional systems.

Findings

Irreversibility can be overcome using the Quantum Recurrence Theorem.

Control of individual states in infinite-dimensional systems is feasible.

Potential applications include controlling coupled harmonic oscillators.

Abstract

A major challenge to the control of infinite dimensional quantum systems is the irreversibility which is often present in the system dynamics. Here we consider systems with discrete-spectrum Hamiltonians operating over a Schwartz space domain, and show that by utilizing the implications of the Quantum Recurrence Theorem this irreversibility may be overcome, in the case of individual states more generally, but also in certain specified cases over larger subsets of the Hilbert space. We discuss briefly the possibility of using these results in the control of infinite dimensional coupled harmonic oscillators, and also draw attention to some of the issues and open questions arising from this and related work.