Optimal Control of Quantum Systems
We consider the optimal control problem of transferring population
between states of a quantum system where the coupling proceeds only
via intermediate states that are subject to decay. We pose the
question whether it is generally possible to carry out this transfer.
For a single intermediate decaying state, we recover the Stimulated
Raman Adiabatic Passage (STIRAP) process for which we present
analytic solutions in the finite time case. The solutions yield
perfect state transfer only in the limit of infinite time. We also
present analytic solutions for the case of transfer that has to
proceed via two consecutive intermediate decaying states. We show
that in this case, for finite power the optimal control does not
approach perfect state transfer even in the infinite time limit.
We generalize our findings to characterize the topologies of paths
that can be achieved by coherent control.