The Bose-Fermi duality in quantum Otto heat engine with trapped repulsive Bosons

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.