Quantum Control (11w5030)

Arriving in Banff, Alberta Sunday, April 3 and departing Friday April 8, 2011


Herschel Rabitz (Princeton University)

(University of Windsor)

Holger Teismann (Acadia University)

(BCAM - Basque Center for Applied Mathematics)


We envision the following broad themes to be covered at the workshop, with each topic given roughly one day.

* Controllability. approximate and exact, finite- and infinite-dimensional, linear and nonlinear, PDE techniques and Lie-algebraic methods, discretization and approximation

* Optimal, adaptive and feedback control. algorithms, numerics, applications, control landscapes, role of measurement

* Open quantum systems. quantum control in the presence of the environment, environment control, mitigation of decoherence, master equations, (non-)Markovian dissipation, entanglement, stochastic Schr�dinger equations

* Beyond Hartree-Fock and Gross-Pitaevskii equations. quantum control of strongly-correlated systems, many particle quantum systems

* Strong fields and ultra-short pulses. high harmonic generation, control of attosecond processes, high-power nonlinear Schr�dinger equation

Each theme will be introduced/surveyed in one or two one-hour talks by senior experts in the field; the rest of each day will be divided between shorter talks and/or poster presentations by junior researchers, round-table discussions, and time for collaboration and impromptu presentations.

We feel that the proposed workshop is more than timely as the field is, while fast moving, in the process of consolidation and integration. Physicists, chemists, engineers, mathematicians, theorists and experimentalists, are increasingly collaborating on quantum control problems. This is evidenced by the success of a few recent workshops exhibiting a similar diversity of themes and backgrounds. As an example, we mention a workshop held in Vienna in February 2009 [2], which produced the following list of open problems that complement the list of topics given above

* Control landscapes: how do control landscapes depend on the target functional and constraints?

* The inner workings: what are the physical mechanisms that allow or prevent control? are there any models that can be (semi-) explicitly solved? what does the control process look like in a semi-classical (WKB) limit and/or Wigner representation?

* System identification: (how) can pulse-shaping and optimization schemes be modified to determine the system Hamiltonian?

* Controllability: optimal-time control, how does (exact) controllability depend on the drift and control operators?

* Nonlinearity: can it be used to improve controllability?

* Algorithms: how to deal with huge state spaces and non-convexity?

* Finite-dimensional vs. infinite-dimensional: what is the appropriate model?

* Molecular dynamics and many-particle quantum systems: need for improved (i.e. beyond Hartree and Hartree-Fock) approximation techniques (MCTDHF etc) for the many-particle Schr�dinger equation.

The various communities (mathematicians, chemists, physicists, engineers, etc) working in the field will be well represented in the workshop. Our plan to provide review talks as well as opportunities for in-depth discussions/informal tutorials lends itself naturally for training of junior researchers.

[2] Workshop "Quantum Control", Wolfgang Pauli Institute, Vienna, Feb. 23 - 27, 2009. Organizers: C. Bardos and H. Teismann. http://www.wpi.ac.at/event_view.php?id_activity=113