Optimal building block of multipartite quantum battery in the driven-dissipative charging

To take quantum advantage of collective effects in many-body system, we design an elementary block for building a quantum battery with the optimal number of atoms in a common thermal bath, which is charged collectively by a harmonic driving. Free energy is a novel tool to quantify usable energy in an open system, which includes non-preserved entropy impacts on the stored energy besides the internal energy. The interesting finding is that the free energy variation in the steady state increases non-monotonically, and reaches the maximal value at the optimal number of atoms. It ascribes to the decreasing of the internal energy and the entropy per atom with the increasing of the atoms. In particular, the elementary block with the optimal number of atoms can relax to the optimal steady state with the weak damping of the internal energy due to the strong collective driving. By comparing to each atom parallel charging independently, the optimal battery cell produces lower heat flow to the thermal bath induced by the entropy, which can not be neglected in the dissipative system. The existence of the optimal battery cell provide a guideline for designing a realizable charging scheme.