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Frontiers in Optics

Quantum random walk of the field in an externally driven cavity

G. S. Agarwal, Pradyumna K. Pathak

Published Jan 1, 2005• 1 citation
Publisher

Abstract

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.
DOI
10.1364/fio.2005.fwm4

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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.
The quincunx, or Galton board, has a long history as a tool for demonstrating and investigating random walk processes, but a quantum quincunx (QQ) for demonstrating a coined quantum walk (QW) is yet to be realized experimentally. We propose a variant of the QQ in cavity quantum electrodynamics, designed to eliminate the onerous requirement of directly flipping the coin. Instead, we propose driving the cavity in such a way that cavity field displacements are minimized and the coin is effectively flipped via this indirect process. An effect of this indirect flipping is that the walker's location is no longer confined to a single circle in the planar phase space, but we show that the phase distribution nonetheless shows quadratic enhancement of phase diffusion for the quantum versus classical walk despite this small complication. Thus our scheme leads to coined QW behaviour in cavity quantum electrodynamics without the need to flip the coin directly.