  We have performed an extensive analysis of a single particle stochastic heat
engine constructed by manipulating a Brownian particle in a time dependent
harmonic potential. The cycle consists of two isothermal steps at different
temperatures and two adiabatic steps similar to that of a Carnot engine. The
engine shows qualitative differences in inertial and overdamped regimes. All
the thermodynamic quantities, including efficiency, exhibit strong fluctuations
in a time periodic steady state. The fluctuations of stochastic efficiency
dominate over the mean values even in the quasistatic regime. Interestingly,
our system acts as an engine provided the temperature difference between the
two reservoirs is greater than a finite critical value which in turn depends on
the cycle time and other system parameters. This is supported by our analytical
results carried out in the quasistatic regime. Our system works more reliably
as an engine for large cycle times. By studying various model systems we
observe that the operational characteristics are model dependent. Our results
clearly rules out any universal relation between efficiency at maximum power
and temperature of the baths. We have also verified fluctuation relations for
heat engines in time periodic steady state.
