  The Landau-Zener formula provides an analytical expression for the final
excitation of a quantum system after passage of an avoided crossing of two
energy levels. If the two levels correspond to a ground state, and to an
excited state which is subject to radiative decay, the probability of exciting
the system by adiabatic passage of the level crossing is reduced. In this
article we use a stochastic master equation to study the level crossing
dynamics when the system is subject to continuous probing of the emitted
radiation. The measurement backaction on the system associated with the
fluctuating homodyne detection record alters the level crossing dynamics,
leading to significant excitation in spite of decay and imperfect transfer.
