  Quantum heat engine with ideal gas has been well studied, yet the role of
interaction was seldom explored. We construct a quantum Otto heat engine with N
repulsive Bosonic particles in a 1D hard wall box. With the advantage of exact
solution using Bethe Ansatz, we obtain not only the exact numerical result of
efficiency in all interacting strength c, but also analytical results for
strong interaction. We find the efficiency \eta recovers to the one of
non-interacting case $\eta_{\mathrm{non}}=1-(L_{1}/L_{2})^{2}$ for strong
interaction with asympotic behavior
$\eta\sim\eta_{\mathrm{non}}-4(N-1)L_{1}\left(L_{2}-L_{1}\right)/(cL_{2}^{3})$.
Here, $L_{1}$ and $L_{2}$ are two trap sizes during the cycle. Such recovery
reflects the duality between 1D strongly repulsive Bosons and free Fermion. We
observe and explain the appearance of a minimum efficiency at a particular
interacting strength c, and study its dependence on the temperature.
