  We consider the resonant tunneling through a multi-level system. It is
demonstrated that the resonant current displays quantum interference effects
due to a possibility of tunneling through different levels. We show that the
interference effects are strongly modulated by a relative phase of states
carrying the current. This makes it possible to use these effects for measuring
the phase difference between resonant states in quantum dots. We extend our
model for a description of magnetotransport through the Zeeman doublets. It is
shown that, due to spin-flip transitions, the quantum interference effects
generate a distinct peak in the shot-noise power spectrum at the frequency of
Zeeman splitting. This mechanism explains modulation in the tunneling current
at the Larmor frequency observed in scanning tunneling microscope experiments
and can be utilized for a single spin measurement.
