Section: New Results

Towards generic adiabatic elimination for bipartite open quantum systems

Participants: R. Azouit, A. Sarlette, P. Rouchon (and F. Chittaro, visitor in 2016)

The paper [12] is the main paper summarizing the results of the PhD thesis of R.Azouit. We give a theoretical method, with a directly applicable recipe for the physicists who would want to use it, and with examples worked out on applications that experimentalists (e.g. in the partner group at Yale U.) are actually considering nowadays.

We consider a composite open quantum system consisting of a fast subsystem coupled to a slow one. Using the timescale separation, we develop an adiabatic elimination technique to derive at any order the reduced model describing the slow subsystem. The method, based on an asymptotic expansion and geometric singular perturbation theory, ensures the physical interpretation of the reduced second-order model by giving the reduced dynamics in a Lindblad form and the state reduction in Kraus map form. We give explicit second-order formulas for Hamiltonian or cascade coupling between the two subsystems. These formulas can be used to engineer, via a careful choice of the fast subsystem, the Hamiltonian and Lindbald operators governing the dissipative dynamics of the slow subsystem.