Würzburg 2018 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 3: Thermodynamics and Field Theory

MP 3.3: Vortrag

Dienstag, 20. März 2018, 17:45–18:05, Z6 - SR 1.012

Path algebras and the controllability of atom-cavity systems — •Michael Keyl — FU Berlin

In this talk we study controllability of a d-level atom interacting with the electromagnetic field in a cavity. The system is modelled by an ordered graph Γ. The vertices of Γ describe the energy levels and the edges allowed transitions. To each edge of Γ we associate a harmonic oscillator representing one mode of the electromagnetic field. The dynamics of the system (drift) is given by a natural generalization of the Jaynes-Cummings Hamiltonian. If we add in addition sufficient control over the atom, the overall system (atom and em-field) becomes strongly controllable, i.e. each unitary on the system Hilbert space can be approximated with arbitrary precision in the strong topology by control unitaries. A key role in the proof is played by a topological *-algebra which is (roughly speaking) a representation of the path algebra of Γ. It contains crucial structural information about the control problem, and is therefore an important tool for the implementation of control tasks like preparing a particular state from the ground state.