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Communication Dans Un Congrès Année : 2016

Adiabatic elimination for open quantum systems with effective Lindblad master equations

Résumé

We consider an open quantum system described by a Lindblad-type master equation with two time scales. The fast time scale is strongly dissipative and drives the system towards a low-dimensional decoherence-free space. To perform the adiabatic elimination of this fast relaxation, we propose a geometric asymptotic expansion based on the small positive parameter describing the time scale separation. This expansion exploits geometric singular perturbation theory and center-manifold techniques. We conjecture that, at any order, it provides an effective slow Lindblad master equation and a completely positive parameterization of the slow invariant sub-manifold associated to the low-dimensional decoherence-free space. By preserving complete positivity and trace, two important structural properties attached to open quantum dynamics , we obtain a reduced-order model that directly conveys a physical interpretation since it relies on effective Lindbladian descriptions of the slow evolution. At the first order, we derive simple formulae for the effective Lindblad master equation. For a specific type of fast dissipation, we show how any Hamiltonian perturbation yields Lindbladian second-order corrections to the first-order slow evolution governed by the Zeno-Hamiltonian. These results are illustrated on a composite system made of a strongly dissipative harmonic oscillator, the ancilla, weakly coupled to another quantum system.
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Dates et versions

hal-01398460 , version 1 (17-11-2016)

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Rémi Azouit, Alain Sarlette, Pierre Rouchon. Adiabatic elimination for open quantum systems with effective Lindblad master equations. 55th Conference on Decision and Control (CDC 2016), Dec 2016, Las Vegas, NV, United States. ⟨hal-01398460⟩
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