Consequently, choosing the initial cavity state as in eq. 8 for λ c ̸ = 0 will result in ⟨Ψ 0 |n c |Ψ 0 ⟩ > 0 which indicates the presence of virtual photons that can drive the isomerization. In contrast, the choice in eq. 9 ensures that initially there are no photons in the cavity even for finite cavity-system coupling strengths. In Fig. we show the location of the initial wavepackets for the two possible choices of the initial cavity state. As shown below, the presence or absence of virtual photons makes a significant difference in terms of the extent of modulation of the isomerization due to cavity-system coupling. In what follows we refer to the choice of eq. 8 and eq. 9 as the virtual and zero photon cases respectively. The time evolved quantum state Ψ(q, x c ; t) is obtained by numerically solving the Schrödinger equation using the split-operator method with a step size of ∆t = 4 au (∼ 0.1 fs), with a sufficiently fine grid over the range [-2.0, 2.0] and [-320.0, 320.0] for the reactive and the photon coordinates respectively. The quantum isomerization probability is calculated as