Quantum heat engine based on trapped Bose gases: Its maximum efficiency can approach the Carnot value at finite power

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.