  A Brownian information engine is a device extracting a mechanical work from a
single heat bath by exploiting the information on the state of a Brownian
particle immersed in the bath. As for engines, it is important to find the
optimal operating condition that yields the maximum extracted work or power.
The optimal condition for a Brownian information engine with a finite cycle
time $\tau$ has been rarely studied because of the difficulty in finding the
nonequilibrium steady state. In this study, we introduce a model for the
Brownian information engine and develop an analytic formalism for its steady
state distribution for any $\tau$. We find that the extracted work per engine
cycle is maximum when $\tau$ approaches infinity, while the power is maximum
when $\tau$ approaches zero.
