ABSTRACT
The decay rate γ of an excited dipole molecule inside a waveguide is evaluated for the strongly coupled matter-field case near a cutoff frequency https://www.w3.org/1998/Math/MathML"> ω c https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq7563.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> without using perturbation analysis. Due to the singularity in the density of photon states at the cutoff frequency, we find that γ depends non-analytically on the coupling constant g as https://www.w3.org/1998/Math/MathML"> g 4 / 3 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq7564.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . In contrast to the ordinary evaluation of γ which relies on the Fermi golden rule (itself based on perturbation analysis), γ has an upper bound. As a result, again in contrast to the statement found in the literature, the speed of emitted light from the molecule does not vanish at https://www.w3.org/1998/Math/MathML"> ω c https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq7565.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and is proportional to https://www.w3.org/1998/Math/MathML"> c g 2 / 3 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq7566.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> which is on the order of https://www.w3.org/1998/Math/MathML"> 10 3 ∼ 10 4 m / s https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq7567.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> for typical dipole molecules.
