Controlling Arbitrary Observables in Correlated Many-body Systems

TL;DR

This paper develops a theoretical framework for controlling arbitrary observables in strongly correlated many-body systems, deriving equations of motion and constraints, and discussing practical implementation and limitations.

Contribution

It introduces a non-linear, field-free control equation for arbitrary observables in many-body systems, with rigorous controllability constraints and solution examples.

Findings

Derived a non-linear control equation for observables

Identified physical constraints limiting controllability

Discussed experimental feasibility of control fields

Abstract

Here we present an expanded analysis of a model for the manipulation and control of observables in a strongly correlated, many-body system, which was first presented in [McCaul et al., eprint: arXiv:1911.05006]. A field-free, non-linear equation of motion for controlling the expectation value of an essentially arbitrary observable is derived, together with rigorous constraints that determine the limits of controllability. We show that these constraints arise from the physically reasonable assumptions that the system will undergo unitary time evolution, and has enough degrees of freedom for the electrons to be mobile. Furthermore, we give examples of multiple solutions to generating target observable trajectories when the constraints are violated. Ehrenfest theorems are used to further refine the model, and provide a check on the validity of numerical simulations. Finally, the experimental feasibility of implementing the control fields generated by this model is discussed.