to describe cavity loss. This jump operator is an approximation of the rigorously derived jump operators that describe jumps between the energy eigenstates of the system and include thermal effects. Regardless, the dynamics of the rigorously derived jump operators are typically well approximated by those of the phenomenological one for polariton systems. Using one of the single photon mode cavity QED Hamiltonians in Sec. 2 as the system Hamiltonian ĤS and the jump operator LS in Eq. 186 to describe cavity loss, the Lindblad master equation for single mode polariton systems with cavity loss is as follows