  We study the quantum interference between the excitation pathways in a
three-level $\Lambda$-type atom interacting with two short laser pulse trains
  under the conditions of electromagnetically induced transparency. The
probability amplitude equations which describe the interaction of a three-level
$\Lambda$-type atom with two laser pulse trains are numerically solved. We
derive analytical expressions for the population of the upper excited state
  for resonant laser pulse trains with a rectangular temporal profile. By
varying the parameters of the laser pulse trains such as area of a single
pulse, detuning, repetition period, and number of individual pulses, we analyze
the quantum interference between the excitation pathways in terms of the upper
excited state population.
