Interface des maths et systèmes complexes
Small-time control of strongly driven quantum rotors
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Description
We consider a strongly driven quantum rotor, modelled as a Schrödinger
PDE (on the two-dimensional sphere) forced via low modes multiplicative
controls. This system is used in quantum chemistry and quantum
information processing. We present a geometric control strategy for
inducing transitions between particular rotational eigenstates in
arbitrarily small time. Roughly speaking, the first step consists in
sending two impulsions with opposite sign, with a very short time delay.
These opposite kicks permit to recover directions (a.k.a. Lie brackets)
that are not directly accessible.