  We propose a non-Hermitian generalization of stimulated Raman adiabatic
passage (STIRAP), which allows one to increase speed and fidelity of the
adiabatic passage. This is done by adding balanced imaginary (gain/loss) terms
in the diagonal (bare energy) terms of the Hamiltonian and choosing them such
that they cancel exactly the nonadiabatic couplings, providing in this way an
effective shortcut to adiabaticity. Remarkably, for a STIRAP using delayed
Gaussian-shaped pulses in the counter-intuitive scheme the imaginary terms of
the Hamiltonian turn out to be time independent. A possible physical
realization of non-Hermitian STIRAP, based on light transfer in three
evanescently-coupled optical waveguides, is proposed.
