  Achieving the Carnot efficiency at finite power is a challenging problem in
heat engines due to the trade-off relation between efficiency and power that
holds for general heat engines. It is pointed out that the Carnot efficiency at
finite power may be achievable in the vanishing limit of the relaxation times
of a system without breaking the trade-off relation. However, any explicit
model of heat engines that realizes this scenario for arbitrary temperature
difference has not been proposed. Here, we investigate an underdamped Brownian
Carnot cycle where the finite-time adiabatic processes connecting the
isothermal processes are tactically adopted. We show that in the vanishing
limit of the relaxation times in the above cycle, the compatibility of the
Carnot efficiency and finite power is achievable for arbitrary temperature
difference. This is theoretically explained based on the trade-off relation
derived for our cycle, which is also confirmed by numerical simulations.
