Note the term N µ 0 can be removed by the translation qc → qc + 2 ℏωc A 0 • N µ 0 using a displacement operator for q c . With this simplification, the expression of the collective Rabi-splitting for the many-molecule case can be obtained by defining a collective molecular coordinate R B = 1 √ N J R J which couples to the qc with a collective coupling scaled by √ N . At the resonant condition of ω c = ω 0 , the Rabi splitting ℏΩ R in the collective coupling regime can be expressed as