  A Brownian particle moving in a staircase-like potential with feedback
control offers a way to implement Maxwell's demon. An experimental
demonstration of such a system using sinusoidal periodic potential carried out
by Toyabe et al. has shown that information about the particle's position can
be converted to useful work. In this paper, we carry out a numerical study of a
similar system using Brownian dynamics simulation. A Brownian particle moving
in a periodic potential under the action of a constant driving force is made to
move against the drive by measuring the position of the particle and effecting
feedback control by altering potential. The work is extracted during the
potential change and from the movement of the particle against the external
drive. These work extractions come at the cost of information gathered during
the measurement. Efficiency and work extracted per cycle of this information
engine are optimized by varying control parameters as well as feedback
protocols. Both these quantities are found to crucially depend on the amplitude
of the periodic potential as well as the width of the region over which the
particle is searched for during the measurement phase. For the case when
potential flip ($i.e.$, changing the phase of the potential by $180$ degrees)
is used as the feedback mechanism, we argue that the square potential offers a
more efficient information-to-work conversion. The control over the numerical
parameters and averaging over large number of trial runs allow one to study the
non-equilibrium work relations with feedback for this process with precision.
It is seen that the generalized integral fluctuation theorem for error free
measurements holds to within the accuracy of the simulation.
