  We propose a scheme to implement the simplest and best-studied version of
quantum random walk, the discrete Hadamard walk, in one dimension using
coherent macroscopic sample of ultracold atoms, Bose-Einstein condensate (BEC).
Implementation of quantum walk using BEC gives access to the familiar quantum
phenomena on a macroscopic scale. This paper uses rf pulse to implement
Hadamard operation (rotation) and stimulated Raman transition technique as
unitary shift operator. The scheme suggests implementation of Hadamard
operation and unitary shift operator while the BEC is trapped in long Rayleigh
range optical dipole trap. The Hadamard rotation and a unitary shift operator
on BEC prepared in one of the internal state followed by a bit flip operation,
implements one step of the Hadamard walk. To realize a sizable number of steps,
the process is iterated without resorting to intermediate measurement. With
current dipole trap technology it should be possible to implement enough steps
to experimentally highlight the discrete quantum random walk using a BEC
leading to further exploration of quantum random walks and its applications.
