Quantum random walk of the field in an externally driven cavity (6 pages)

Mauro Paternostro, Hyunseok Jeong

Keith R. Burnett, Zhi Ma, S. A. Gardiner +1 more

Jozef Košík, Vladimír Bužek

G. S. Agarwal, Pradyumna K. Pathak

Under strong driving, the field inside the cavity undergoes displacement left or right by passing an atom, thus provides possible realization of quantum walks. Using Homodyne technique, the state of the walker can be monitored.

G. S. Agarwal, Pradyumna K. Pathak

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 $i{S}^{x}(a\ensuremath{-}{a}^{\ifmmode\dagger\else\textdagger\fi{}})$ 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.