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Section: New Results

Quantum Adiabatic Elimination: extension to rotating systems

Participants: Paolo Forni, Timothée Launay, Alain Sarlette and Pierre Rouchon

Adiabatic elimination is a technique to eliminate fast converging variables of a large system, while retaining their impact on slower dynamics of interest. Its most extreme form is a standard procedure when neglecting the dynamics of e.g. actuators or measurement devices in dynamical systems. In quantum systems it is particularly relevant to eliminate subsystems in tensor product structure. However, a major constraint is to obtain a reduced system in quantum form (Lindblad equations), preserving positivity and the unit trace. After having set up the framework for quantum adiabatic elimination to arbitrary order as a series expansion during the thesis of Rémi Azouit, we had worked out first- and second-order Lindblad equations only. With Paolo Forni, we have been pursuing the development of explicit formulas for higher-order cases. In [26], we present an extension of the technique for the case where the slowly decaying subsystem of interest, is subject to fast Hamiltonian dynamics. This appears e.g. in systems with significant detunings, where a description in rotating frame would lead to time-dependent equations if one does not want to neglect fast oscillating terms.