General introduction to optimal control theory and how to control matter at the quantum level
David Tannor gave the Director’s Blackboard Talk at KITP today:
Very nice talk, goes on a bit in the middle talking about the time dependent quantum mechanical picture vs use of phase control.
Very nice finish on mathematics of optimal control theory and the physical picture of how to use variational schemes to implement practical control.
Things I took away from this:
optimal control theory is underway but has a lot of open interesting questions;
there are theoretical techniques for implementing locally optimal control at the molecular level (and better, since similar technique permit high fidelity control of nuclear spins, individually and in ensemble);
the degree of controllability is quantifiable and may be complete for real systems;
(with the caveat that optimization has a divergent path which takes the system to infinite energy and imposing a penalty function my bias the search space)
there are clear technology paths for implementing real control over real systems;
this means phase control over molecular and atomic dynamics, including dissociation and association, at the individual atom and ensemble level, with high yield;
it may also be possible to control quantum coherence of mesoscopic pieces of material for interestingly long times;
it really all boils down to whether commutators of perturbed hamiltonians span the space of n*n hermitian matrices… or whether the Lie algebra is irreducable;
there are nice classical analogies on ergodicity, recurrence and disconnected compact phase spaces;
I would worry a bit about asymptotic states, non-local optimization, and whether additional perturbations of the hamiltonians can complete the system – ie if you have a system that is not completely controllable, can you impose a deliberate perturbation which changes it to a similar but completely controllable system;
long term goal – put some stuff into a cavity in a machine, tell the machine what you want the stuff to become, inject some energy in carefully sculpted and timed pulses, and with some reasonable efficiency get exactly what you want out, down to the atom or even the spin of the nucleus within the atom;
you can use this, in principle, eventually, to do cool stuff, like clean controlled chemistry, controlled coherence, and preparing qubits;
oh, and this is totally fucking awesome!