Quantum Control of Many-Body Systems by the Density

TL;DR

This paper presents a method derived from time-dependent density-functional theory for controlling many-body quantum systems by manipulating their density, enabling efficient and stable control even in large, complex systems.

Contribution

The authors extend a recent density-based control method to higher dimensions and demonstrate its effectiveness and stability through detailed numerical examples.

Findings

Method is efficient and stable for large, rapid density changes.

Applicable to large interacting systems due to its basis in density-functional theory.

Flexible control achieved through simple density interpretation.

Abstract

In this work we focus on a recently introduced method [1] to construct the external potential $v$ that, for a given initial state, produces a prescribed time-dependent density in an interacting quantum many-body system. We show how this method can also be used to perform flexible and efficient quantum control. The simple interpretation of the density (the amount of electrons per volume) allows us to use our physical intuition to consider interesting control problems and to easily restrict the search space in optimization problems. The method's origin in time-dependent density-functional theory makes studies of large systems possible. We further discuss the generalization of the method to higher dimensions and its numerical implementation in great detail. We also present several examples to illustrate the flexibility, and to confirm that the scheme is efficient and stable even for large and rapid density variations irrespective of the initial state and interactions.