  Many coherence transfer experiments in Nuclear Magnetic Resonance
Spectroscopy, involving network of coupled spins, use temporary spin-decoupling
to produce desired effective Hamiltonians. In this paper, we show that
significant time can be saved in producing an effective Hamiltonian, if
spin-decoupling is avoided. We provide time optimal pulse sequences for
producing an important class of effective Hamiltonians in three spin networks.
These effective Hamiltonians are useful for coherence transfer experiments and
implementation of quantum logic gates in NMR quantum computing. It is
demonstrated that computing these time optimal pulse sequences can be reduced
to geometric problems that involve computing sub-Riemannian geodesics on
Homogeneous spaces.
