which is propotional to 𝑘 -1 ‖ when 𝑘 ‖ ≪ 𝑘 ⊥ , and the associated loss rate is Γ ′ 10 = 1/𝜏 ‖ (which corresponding to the photon decay of |1 k ⟩ → |0 k ⟩). Note that 𝜏 ‖ differs from the cavity lifetime 𝜏 c introduced previously. Specifically, 𝜏 ‖ accounts for loss in the in-plane direction, 𝜏 c describes the loss channel only due to the escaping of the photon with a direction that is perpendicular to the mirror surface 𝑘 ⊥ , and was introduced through the Ĥloss term and was assumed to be identical for all cavity modes 𝜔 k (independent of 𝑘 ‖ ). A reasonable estimation for 𝒟 is provided as follows. As mentioned before, the typical values for the VSC experiments are 𝑁 ≈ 10 6 ∼ 10 12 , and the effective density is 𝑁/𝒱 ≈ 10 20 cm -3 . Using 𝒱 = ℒ • 𝒟 2 , and the typical value for the mirror distance ℒ = 1 𝜇m, we have 𝒟 ≈ 10 -1 ∼ 10 𝜇m (or 10 2 ∼ 10 5 nm), and the range of 𝒟/𝑐 ≈ 1 ∼ 100 fs. For example, when 𝒟 ∼ 300 nm, 𝒟/𝑐 ∼ 10 -15 s -1 = 1 fs. On the other hand, 𝜏 c usually varies from 100 fs to 5 ps in typical VSC experiments.