Controlling Many-Body Quantum Chaos: Optimal Coherent Targeting
Abstract
Quantum simulators based on complex many-body quantum systems have the potential to address difficult scientific, engineering, andcomputational problems. However, even if a quantum system is isolated and pro-tected from environmental perturbations, non-equilibrium quantum dynamics is commonly subject to rapid thermalization. This equilibration process goes along with the scrambling of quantum information, i.e., its spreading into the vast number of degrees of freedom of the many-body system. Hence, steering and stabiliz-ing such complex quantum dynamics, a prerequisite for performing controlled quantum operations, is relevant, both for numerical andexperimental quantum simulations.This control of interacting quantum systems is a particularly challenging problem, if their classical counter-parts exhibit highly chaotic motion as, e.g., for ultracold atom-based quantum simulators or certain realiza-tions of quantum computing schemes. The presence of such quantum chaotic dynamics leading to instability and equilibration is most often conceptualized as the ultimate enemy of quantum device control: For chaotic classical many-body dynamics small initial deviations increaseexponentially fast, which is reflected in the instability of the corresponding many-body quantum system. However, what if that chaos could be harnessed instead as a resource for control? The main idea of the pro-posal is to take maximal advantage of this exponential sensitivity in the underlying classical chaotic dynamics. Inspired by classical targeting, which is the very weakly perturbativeprocess of using the system s extreme sensitivity to initial conditions in order to rapidly arrive at a predetermined target state,we propose to develop a novel robust many-body quantum control technique to efficiently deal with unstable complex quantum dy-namics. Our proposal aims at developing novel means to counteract unwanted effects of chaos and instead to guide, control and protect (entangled) many-body states. Our proposed method is # by construction # rather general and will serve as a conceptual platform for a broad range of applications in various branches of quan-tum control science. These comprise ultracold atom quantum simulators, Rydberg atom arrays, optimized pathways for chemical reactions and certain platforms for quantum computing, to name a few.After our recentencouraging preliminary single-particle studies, the major step is now to bring the technique into the realm of many-body quantum simulators and to enable the realization of optimal coherent chaotic quantum targeting for many-body systems. This requires two essential stages: To provide a proof of principle for targeting in a high-dimensional many-body Hilbert space, and to convert this into an experimentally ame-nable protocol.Our research proposed comprises various research thrusts:- We plant to implement the targeting concept for bosonic, quantum chaotic many-body systems, i.e. for the Bose-Hubbard model which is a paradigmatic model for complex dynamics and platform for quantum simula-tors. - We will identify experimental protocols that accomplish controlled targeting for ultracold atom quantum simulators, in particular for atoms in optical lattices. - We plan to include many-body quantum interference and entanglement into coherent targeting. - We will investigate the generalization of controlling quantum chaos to fermionic or spin systems.The general approach to be followed, combining techniques at the interface between classical nonlinear dy-namics, machine learning and many-body quantum physics, is based on powerful semiclassical and quantum path integral methods that have been developed by us during the last years. We will test approximate analyti-cal predictions by means of full numerical many-body quantum calculations.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Apr 11, 2024
- Source ID
- N629092412053
Entities
People
- Klaus Richter
Organizations
- Office of Naval Research
- United States Navy
- University of Regensburg