In this paper, we consider this photo-isomerization model under the Jaynes-Cummings approximation where there is a maximum of only one excitation (the singleexcited subspace plus the ground state) because the lightmatter coupling strength ℏg c /ω c < 0.1 thus the results do not significantly change when including states with multiple excitations. In this case, the possible Fock states are just |n⟩ ∈ {|0⟩, |1⟩}. Thus, the system Hamiltonian ĤS can be written as ĤS = TR + E g (R)|g, 0⟩⟨g, 0| + E e (R)|e, 0⟩⟨e, 0| (82) + E g (R) + ℏω c |g, 1⟩⟨g, 1| + ℏg c |e, 0⟩⟨g, 1| + |g, 1⟩⟨e, 0| , and the system Lindblad jump operator can be written as