Toward a theory of nonlinear stochastic realization

Bibliography: leaves 14-15."October, 1981" "Feedback and Synthesis of Linear and Nonlinear Systems -Proceedings of the Workshop in Bielefeld, West-Germany, June 22-26, 1981, and Rome Italy, June 29-July 3, 1981.""National Science Foundation Grant ECS-7903731" "Air Force Office of Scientific Research grant AFOSR 78-3519"Anders Lindquist, Sanjoy Mitter, Giorgio Picci

Pulsed Generation of Quantum Coherences and Non-classicality in Light-Matter Systems

We show that a pulsed stimulus can be used to generate many-body quantum coherences in light-matter systems of general size. Specifically, we calculate the exact real-time evolution of a driven, generic out-of-equilibrium system comprising an arbitrary number N qubits coupled to a global boson field. A novel form of dynamically-driven quantum coherence emerges for general N and without having to access the empirically challenging strong-coupling regime. Its properties depend on the speed of the changes in the stimulus. Non-classicalities arise within each subsystem that have eluded previous analyses. Our findings show robustness to losses and noise, and have potential functional implications at the systems level for a variety of nanosystems, including collections of N atoms, molecules, spins, or superconducting qubits in cavities -- and possibly even vibration-enhanced light harvesting processes in macromolecules.Comment: 9 pages, 4 figure

Geometry and response of Lindbladians

Markovian reservoir engineering, in which time evolution of a quantum system is governed by a Lindblad master equation, is a powerful technique in studies of quantum phases of matter and quantum information. It can be used to drive a quantum system to a desired (unique) steady state, which can be an exotic phase of matter difficult to stabilize in nature. It can also be used to drive a system to a unitarily-evolving subspace, which can be used to store, protect, and process quantum information. In this paper, we derive a formula for the map corresponding to asymptotic (infinite-time) Lindbladian evolution and use it to study several important features of the unique state and subspace cases. We quantify how subspaces retain information about initial states and show how to use Lindbladians to simulate any quantum channels. We show that the quantum information in all subspaces can be successfully manipulated by small Hamiltonian perturbations, jump operator perturbations, or adiabatic deformations. We provide a Lindblad-induced notion of distance between adiabatically connected subspaces. We derive a Kubo formula governing linear response of subspaces to time-dependent Hamiltonian perturbations and determine cases in which this formula reduces to a Hamiltonian-based Kubo formula. As an application, we show that (for gapped systems) the zero-frequency Hall conductivity is unaffected by many types of Markovian dissipation. Finally, we show that the energy scale governing leakage out of the subspaces, resulting from either Hamiltonian/jump-operator perturbations or corrections to adiabatic evolution, is different from the conventional Lindbladian dissipative gap and, in certain cases, is equivalent to the excitation gap of a related Hamiltonian.Comment: Published version. See related talk at https://sites.google.com/site/victorvalbert/physics/diss_powerpoint.pd