Spontaneous light emission by atomic hydrogen: Fermi's golden rule without cheating

Abstract

Focusing on the 2p − 1s transition in atomic Hydrogen, we investigate through first order perturbation theory the time evolution of the survival probability of an electron initially taken to be in the excited (2p) state. We examine both the results yielded by the standard dipole approximation for the coupling between the atom and the electromagnetic field -for which we propose a cutoff-independent regularisation-and those yielded by the exact coupling function. In both cases, Fermi's golden rule is shown to be an excellent approximation for the system at hand: we found its maximal deviation from the exact behaviour of the system to be of order 10 −8 /10 −7 . Our treatment also yields a rigorous prescription for the choice of the optimal cutoff frequency in the dipole approximation. With our cutoff, the predictions of the dipole approximation are almost indistinguishable at all times from the exact dynamics of the system.

Conditions for anti-Zeno-effect observation in free-space atomic radiative decay

“…where η J = 1 + 2J for magnetic transitions, and η J = −1 + 2J for electric transitions with J starts at 1 for a dipole transition (l e − l g = 1), at 2 for a quadrupole transition (l e − l g = 2) and so on; µ = 2 (n g + n e − 1); D Jr are dimensionless constants involving the Clebsch-Gordan coefficients of the transition under consideration; and ω X is the non-relativistic cutoff frequency that emerges naturally from calculations [19,20] and reads [13]:…”

Role of Rabi oscillations in radiative states due to the fully absorbing smaller plasmonic nanoparticles

“…This model represents a dipole approximation of two-level emitters in the weak vacuumcoupling regime, and the Fermi golden rule can be used to relate the decay rates to the density of optical states. 49,50 This widely used conventional description of the selfinteraction in (4) includes an implicit rotating wave approximation (jΔ total jk j ( ω). Note that this real part of self-energy provides us the energy split between the two modes of the strongly coupled oscillators j and k, and corresponding Rabi frequency, in this approximation, 46,51…”

Radiative decay of an emitter due to non-Markovian interactions with dissipating matter

“…Without any significant loss of accuracy, the initial state of the excited particle can also be constructed in the form of n − 1 polarizable point dipoles using a balance of forces. The weak coupling with vacuum allows an evaluation of the interactions using classical fields in the dipole approximation [45][46][47]. The absolute values of self-energy of these representative oscillators provides the probability of excitation of the mutually interacting two-level components.…”