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Section: New Results

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

Participants: Paolo Forni, Alain Sarlette, Pierre Rouchon

We pursue the work initiated in our group during the thesis of Rémi Azouit, where we apply center manifold theory in order to reduce the model of a quantum system to its slowly contracting dynamics. Such model reduction is ubiquitous in models of coupled quantum systems where part of the system relaxes quickly towards an equilibrium situation, and acts as an environment for a system of interest. The extension presented in this work is the answer to a question by experimental physicists at Laboratoire Kastler Brossel (LKB), where they apply a strong drive which, in an 'intuitive model', would saturate so-called two-level-system impurities and thereby imply a particular behavior of frequency shift and dissipation on the target system (slow dynamics) as a function of drive characteristics. A good model for this situation involves, beyond a strongly dissipative environment, also a fast non-dissipative dynamics on the slowly contracting subsystem. Adding the latter into the model reduction was the purpose of this result. We analyze the experimental results and show that the model reduction allows us to explain the observed trends. This result led to a publication in collaboration with physicists Thibault Capelle, Emmanuel Flurin and Samule Deleglise from LKB [20].

Further extensions of adiabatic elimination formulas have been worked out during this year and will hopefully be part of next year's publications.