### Adiabatic elimination for multi-partite open quantum systems with non-trivial zero-order dynamicsAdiabatic elimination for multi-partite open quantum systems with non-trivial zero-order dynamics

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 Author Forni, Paolo ♦ Sarlette, Alain ♦ Capelle, Thibault ♦ Flurin, Emmanuel ♦ Deléglise, Samuel ♦ Rouchon, Pierre Source Hyper Articles en Ligne (HAL) Content type Text File Format PDF Language English
 Subject Keyword math ♦ phys ♦ Mathematics [math]/Dynamical Systems [math.DS] ♦ Physics [physics]/Quantum Physics [quant-ph] Abstract We provide model reduction formulas for open quantum systems consisting of a target component which weakly interacts with a strongly dissipative environment. The time-scale separation between the uncoupled dynamics and the interaction allows to employ tools from center manifold theory and geometric singular perturbation theory to eliminate the variables associated to the environment (adiabatic elimination) with high-order accuracy. An important specificity is to preserve the quantum structure: reduced dynamics in (p ositive) Lindblad form and coordinate mappings in Kraus form. We provide formulas of the reduced dynamics. Themain contributions of this paper are (i) to show how the decomposition of the environment into $K$ components enables its efficient treatment, avoiding the quantum curse of dimension; and (ii) to extend the results to the case where the target component is subject to Hamiltonian evolution at the fast time-scale. We apply our theory to a microwave superconducting quantum resonator subject to material losses, and we show that our reduced-order model can explain the transmission spectrum observed in a recent pump probe experiment. Educational Use Research Learning Resource Type Proceeding