  Optomechanical cooling is a prerequisite for many exotic applications
promised by modern quantum technology and it is crucial to achieve it in short
times, in order to minimize the undesirable effects of the environment. We
formulate cavity optomechanical cooling as a minimum-time optimal control
problem on anti-de Sitter space of appropriate dimension and use the Legendre
pseudospectral optimization method to find the minimum time and the
corresponding optimal control, for various values of the maximum coupling rate
between the cavity field and the mechanical resonator. The present framework
can also be applied to create optomechanical entanglement in minimum time and
to improve the efficiency of an optomechanical quantum heat engine.
