where ∆ρ pl II = ρ pl II (t + δt) -ρ pl II (t). From time t to t + δt, all the polariton states that lose population form group A, while all the polariton states that gain population form group B. Here we only need to calculate the switching probability when the current active state |E I ⟩ belongs to A, and the destination state belongs to B. All other types of state switches, for example, |E I ⟩ and |E J ⟩ belong to the same subgroup, or |E I ⟩ belong to B and |E J ⟩ belongs to A, are not allowed, and the switching probabilities are set to 0 based on the algorithm. The non-adiabatic transition, i.e. stochastic switches from the currently occupied state |E I ⟩ to another state |E K ⟩, occurs if the following condition is satisfied