2018/03/21 by Paolo E. Forni, Forni, Paolo, Alain Sarlette +9 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Electromagnetic Simulation and Numerical Methods #FOS: Physical sciences #Model Reduction and Neural Networks #Numerical methods for differential equations #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1803.07810
openalex publication_date 2018/03/21 · openalex created_date 2022/09/19 · openalex updated_date 2026/07/28
We provide model reduction formulas for open quantum systems consisting of a\ntarget component which weakly interacts with a strongly dissipative\nenvironment. The time-scale separation between the uncoupled dynamics and the\ninteraction allows to employ tools from center manifold theory and geometric\nsingular perturbation theory to eliminate the variables associated to the\nenvironment (adiabatic elimination) with high-order accuracy. An important\nspecificity is to preserve the quantum structure: reduced dynamics in\n(positive) Lindblad form and coordinate mappings in Kraus form. We provide\nformulas of the reduced dynamics. The main contributions of this paper are (i)\nto show how the decomposition of the environment into K components enables\nits efficient treatment, avoiding the quantum curse of dimension; and (ii) to\nextend the results to the case where the target component is subject to\nHamiltonian evolution at the fast time-scale. We apply our theory to a\nmicrowave superconducting quantum resonator subject to material losses, and we\nshow that our reduced-order model can explain the transmission spectrum\nobserved in a recent pump probe experiment.\n