  It was reported that, if and only if the specific heat, correlation length,
and dynamical exponents $\alpha, \nu$ and $z$, fulfill the condition
$\alpha-z\nu>0$, the phase transitions can enable a quantum heat engine to
approach Carnot efficiency at finite power. We start our analysis via a
different approach in which the effects of interaction and fluctuations on the
Hamiltonian of a trapped dilute Bose gas belonging to the same universality as
$XY$ model. Based on models of quantum Otto heat engines, we find the general
expression of the efficiency which includes the correction due to interaction
and fluctuations at the critical point, and show that, near the
Bose-Einstein-condensation point with $\alpha-z\nu<0$, energy fluctuations
could enable attaintment of the Carnot efficiency with nonvanishing power. Such
quantum heat engines can also be realized by changing the shape of the trap
confining the ideal and weakly interacting Bose gas during the adiabatic
processes of the cycle. These quantum heat engines working with the trapped
Bose gases, which are based on techniques of cooling Bose condensates and could
be realizable at present technology.
