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

Paolo Forni 1 Alain Sarlette 2 Thibault Capelle 3 Emmanuel Flurin 3 Samuel Deléglise 3 Pierre Rouchon 2
2 QUANTIC - QUANTum Information Circuits
ENS Paris - École normale supérieure - Paris, MINES ParisTech - École nationale supérieure des mines de Paris, SU - Sorbonne Université, Inria de Paris
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 mic rowave 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.
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Submitted on : Thursday, December 6, 2018 - 1:15:37 PM
Last modification on : Wednesday, May 15, 2019 - 3:55:45 AM
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  • HAL Id : hal-01946773, version 1


Paolo Forni, Alain Sarlette, Thibault Capelle, Emmanuel Flurin, Samuel Deléglise, et al.. Adiabatic elimination for multi-partite open quantum systems with non-trivial zero-order dynamics. CDC 2018 - 57th IEEE Conference on Decision and Control, Dec 2018, Miami, United States. ⟨hal-01946773⟩



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