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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 3: Quantenmechanik und Quanteninformation

MP 3.4: Vortrag

Dienstag, 1. März 2016, 18:20–18:40, VMP6 HS B

Quantum control for a Jaynes-Cummings-Hubbard model — •Margret Heinze and Michael Keyl — Zentrum Mathematik, M5, Technischen Universität München, Boltzmannstraße 3, D-85748 Garching

We examine the control of a quantum system consisting of several two-level atoms with each atom interacting with a different mode of an electromagnetic field.

More precisely, the system is a Jaynes-Cummings-Hubbard model where each cavity contains an atom and a bosonic excitation that can tunnel to the neighbouring cavities. The interaction strengths can be time dependently tuned in order to achieve controllability.

We discuss if it is possible that every pure state can be reached from a given reference state (pure-state controllability). This analysis is lifted to the level of operators where each unitary has to be approximated with arbitrarily small error by a time evolution operator for appropriate control functions and finite time (strong controllability).

The challenge of this infinite dimensional control problem is met, by firstly examining the symmetries of the system. A finite dimensional block diagonal decomposition is obtained for the control Hamiltonians that obey an abelian symmetry and due to a cut-off finite dimensional Lie analysis can be applied. By then adding a Hamiltonian that breaks the symmetry pure state and strong controllability are examined, c.f. [Michael Keyl, Robert Zeier, Thomas Schulte-Herbrüggen. "Controlling several atoms in a cavity". New Journal of Physics 16.6 (2014): 065010].