Optimal control of many-body quantum dynamics: chaos and complexity

Abstract

Achieving full control of the time-evolution of a many-body quantum system is currently a major goal in physics. In this work we investigate the different ways in which the controllability of a quantum system can be influenced by its complexity, or even its chaotic properties. By using optimal control theory, we are able to derive the control fields necessary to drive various physical processes in a spin chain. Then, we study the spectral properties of such fields and how they relate to different aspects of the system complexity. We find that the spectral bandwidth of the fields is, quite generally, independent of the system dimension. Conversely, the spectral complexity of such fields does increase with the number of particles. Nevertheless, we find that the regular o chaotic nature of the system does not affect signficantly its controllability.

9 pages, 5 figures

References in corpus (12)

• Many-Body Physics with Ultracold Gases
• Quantum Computing
• Thermalization and its mechanism for generic isolated quantum systems
• Photonic quantum technologies
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Quantum Communication through Spin Chain Dynamics: an Introductory Overview
• Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
• Quantum Quenches, Thermalization and Many-Body Localization
• Exploring local quantum many-body relaxation by atoms in optical superlattices
• Robust optimal quantum gates for Josephson charge qubits
• Communication at the quantum speed limit along a spin chain
• Relaxation of isolated quantum systems beyond chaos