Quantum random walk of the field in an externally driven cavity

Using a 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 48, 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 iSˣ(a-a^) 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 wave function depending on the state of the two-level atom. Measurements of the state of the two-level atom would then generate an effective state of the field. Using a homodyne technique, the state of the quantum random walker can be monitored.