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Adiabatic elimination methods allow the reduction of the space dimensionneeded to describe systems dynamics which exhibits separation of time scale.For open quantum system, it consists in eliminating the fast part assuming ithas almost instantaneously reached its steady-state and obtaining anapproximation of the evolution of the slow part. These methods can be appliedto eliminate a linear subspace within the system Hilbert space, oralternatively to eliminate a fast subsystems in a bipartite quantum system. Inthis work, we extend an adiabatic elimination method used for removing fastdegrees of freedom within a open quantum system (Phys. Rev. A 2020, 101,042102)to eliminate a subsystem from an open bipartite quantum system. As anillustration, we apply our technique to a dispersively coupled two-qubit systemand in the case of the open Rabi model.

Projection based adiabatic elimination of bipartite open quantum systems