Séminaire du LPTMS : Steven Tomsovic (Washington State University)

One of the principal goals of controlling classically chaotic dynamical systems is known as targeting, which is the very weakly perturbative process of using the system’s extreme sensitivity to initial conditions in order to arrive at a predetermined target state.  It is shown that a generalization to chaotic quantum systems is possible in the semiclassical regime, but requires tailored perturbations whose effects must undo the dynamical spreading of the evolving quantum state.  For simplicity, the procedure described here is first applied to a simple paradigm of chaos that has been realized in quantum simulations with ultracold atoms, the quantum kicked rotor, to illustrate the method, and investigate its accuracy.  Starting with a minimum uncertainty wave packet, it is shown that coherent targeting leads to vanishing errors as $\hbar \rightarrow 0$.  An approximate, simpler method is also shown, illustrating the flexibility of the concept.  Finally, quantum targeting is illustrated for initial coherent states in the Bose-Hubbard model in a chaotic regime.