Campuses:

Singular perturbations and Lindblad-Kossakowski differential<br/><br/>equations

Monday, March 2, 2009 - 9:50am - 10:20am
EE/CS 3-180
Pierre Rouchon (Mines-ParisTech)
In this joint work with Mazyar Mirrahimi,
we consider an ensemble of quantum systems described by a density matrix,
solution of a Lindblad-Kossakowski differential equation. We focus on the
special
case where the decoherence is only due to a highly unstable excited
state and where the spontaneously emitted photons are measured by a
photo-detector. We propose a systematic method to eliminate the
fast and asymptotically stable dynamics associated to the excited
state in order to obtain another differential equation for the slow
part. We show that this slow differential equation is still of
Lindblad-Kossakowski type, that the decoherence terms and the
measured output depend explicitly on the amplitudes of
quasi-resonant applied field, i.e., the control. Beside a rigorous
proof of the slow/fast (adiabatic) reduction based on singular
perturbation theory, we also provide a physical interpretation
of the result in the context of coherence population trapping via
dark states and decoherence-free subspaces. Numerical simulations
illustrate the accuracy of the proposed approximation for a 5-level
systems.
MSC Code: 
34D15