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

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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 (positive) Lindblad form and coordinate mappings in Kraus form. We provide formulas of the reduced dynamics. The main 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.
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SINGULAR PERTURBATION

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MLA
Forni, Paolo et al. “Adiabatic Elimination for Multi-partite Open Quantum Systems with Non-trivial Zero-order Dynamics.” 2018 IEEE CONFERENCE ON DECISION AND CONTROL (CDC). IEEE, 2018. 6614–6619. Print.
APA
Forni, P., Sarlette, A., Capelle, T., Flurin, E., Deleglise, S., & Rouchon, P. (2018). Adiabatic elimination for multi-partite open quantum systems with non-trivial zero-order dynamics. 2018 IEEE CONFERENCE ON DECISION AND CONTROL (CDC) (pp. 6614–6619). Presented at the 57th IEEE Conference on Decision and Control (CDC), IEEE.
Chicago author-date
Forni, Paolo, Alain Sarlette, Thibault Capelle, Emmanuel Flurin, Samuel Deleglise, and Pierre Rouchon. 2018. “Adiabatic Elimination for Multi-partite Open Quantum Systems with Non-trivial Zero-order Dynamics.” In 2018 IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 6614–6619. IEEE.
Chicago author-date (all authors)
Forni, Paolo, Alain Sarlette, Thibault Capelle, Emmanuel Flurin, Samuel Deleglise, and Pierre Rouchon. 2018. “Adiabatic Elimination for Multi-partite Open Quantum Systems with Non-trivial Zero-order Dynamics.” In 2018 IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 6614–6619. IEEE.
Vancouver
1.
Forni P, Sarlette A, Capelle T, Flurin E, Deleglise S, Rouchon P. Adiabatic elimination for multi-partite open quantum systems with non-trivial zero-order dynamics. 2018 IEEE CONFERENCE ON DECISION AND CONTROL (CDC). IEEE; 2018. p. 6614–9.
IEEE
[1]
P. Forni, A. Sarlette, T. Capelle, E. Flurin, S. Deleglise, and P. Rouchon, “Adiabatic elimination for multi-partite open quantum systems with non-trivial zero-order dynamics,” in 2018 IEEE CONFERENCE ON DECISION AND CONTROL (CDC), Miami Beach, FL, 2018, pp. 6614–6619.
@inproceedings{8604912,
  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 (positive) Lindblad form and coordinate mappings in Kraus form. We provide formulas of the reduced dynamics. The main 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.}},
  author       = {{Forni, Paolo and Sarlette, Alain and Capelle, Thibault and Flurin, Emmanuel and Deleglise, Samuel and Rouchon, Pierre}},
  booktitle    = {{2018 IEEE CONFERENCE ON DECISION AND CONTROL (CDC)}},
  isbn         = {{9781538613955}},
  issn         = {{0743-1546}},
  keywords     = {{SINGULAR PERTURBATION}},
  language     = {{eng}},
  location     = {{Miami Beach, FL}},
  pages        = {{6614--6619}},
  publisher    = {{IEEE}},
  title        = {{Adiabatic elimination for multi-partite open quantum systems with non-trivial zero-order dynamics}},
  url          = {{http://dx.doi.org/10.1109/CDC.2018.8619205}},
  year         = {{2018}},
}

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