  Using resonant interaction between atoms and the field in a high quality
cavity, we show how to realize quantum random walks as proposed by Aharonov et
al [Phys. Rev. A {\bf48}, 1687 (1993)]. The atoms are driven strongly by a
classical field. Under conditions of strong driving we could realize an
effective interaction of the form $ iS^{x}(a-a^{\dag})$ in terms of the spin
operator associated with the two level atom and the field operators. This
effective interaction generates displacement in the field's wavefunction
depending on the state of the two level atom. Measurements of the state of the
two level atom would then generate effective state of the field. Using a
homodyne technique, the state of the quantum random walker can be monitored.
