Abstract

The theory offers a novel possibility to estimate immediately an atomic or molecular coupling constant G by observing a drastic change of the form of spontaneous emission spectrum of a two-level motionless atom (molecule) placed in to a damped cavity with one resonant mode in it, as its passive linewidth passes the value 2G. More specifically the spectrum turns abruptly from a doublet (or more precisely a hidden triplet form) into a singlet at this point. For the first time the theory provides in this case a very simple and exact analytical solution of the proper Schrodinger equation, treating the problem as a radiative decay of the coupled system "atom + mode resonance field" and drawing the analogy to the two proton radioactivity theory.¹ The spectrum is sought for as the energy eigenvalues of the interacting system, the latter being the observable perturbed frequencies of the radiation field that go out of the cavity. The cavity temperature has been taken to be zero. The wave function and energy eigenvalues have been found by means of the known dream functions formalism² but supplemented with the new algorithm in operating with the causal ζ-functions.³ The decay of the mode field A(t) in the empty cavity due to leaking of photons at the rate Γ_c out of the cavity through its partly penetrable mirrors has been adopted to obey the law A(t) = A_o exp (−i(ω_a − i Γ_c)t), where ω_a is the atomic frequency. This law implies that the unperturbed mode field in the cavity is presented by a packet of field oscillators with the Lorentz-shaped profile of width Γ_c centred at ω_a. In such a manner we have adopted the interaction Hamiltonian in the form ${\text{H}}^{\mathrm{int}}=\text{G}\left({\Sigma }_{\text{k}}{\text{f}}_{\text{k}}\left({\text{C}}_{\text{k}}^{+}{\delta }^{-}+{\text{C}}_{\text{k}}{\delta }^{+}\right)\right)$. The sum is taken over all oscillators entering the packet; G is a coupling constant for ω_k = ω_a; ω_k is the Kth oscillator's frequency; ${\text{C}}_{\text{k}}^{+},{\text{C}}_{\text{k}}$ are photons operators; δ^± are pseudospin operators; the formfactor f_k accounts for the Lorentz profile.

© 1994 IEEE