Approximations employed in spontaneous emission theory

ALBERT ROSE

Xiao-Ping Feng, Kikuo Ujihara

A quantum theory of spontaneous emission from an initially excited two-level atom in a one-dimensional optical cavity with output coupling from both sides is developed. Orthonormal mode functions with a continuous spectrum are employed, which are derived by imposing a periodic boundary condition on the whole space with a period much larger than the cavity length. The delay differential equation of the atomic state of Cook and Milonni [Phys. Rev. A 35, 5081 (1987)] is re-derived in a strict manner, where the reflectivity of the cavity mirrors is included naturally in the mode functions. An approximate solution at a single-resonant-mode limit shows the results of ``vacuum'' Rabi oscillation in an underdamped cavity and enhanced spontaneous emission rate in an overdamped cavity. For the latter case, it is found that in the optical range the spontaneous emission rate is enhanced by a factor F (finesse of the cavity).

Leonid A. Shelepin

Ravinder Rupchand Puri

The role of vacuum fluctuations and radiation reaction in the process of spontaneous emission is examined with particular reference to the Heisenberg picture of quantum electrodynamics. In this picture the radiation reaction is found to be responsible for spontaneous emission if the equations are ordered normally. However, in the case of nonnormally ordered equations there appears to be an explicit contribution to the observable effects from vacuum fluctuations as well. We point out that this contribution from the vacuum field is an artifact of the approximation methods employed for eliminating the free-field variables from the nonnormally ordered equations These approximations are the same as those used in the master-equation approach, in which spontaneous emission appears to be due solely to the vacuum fluctuations. We show that the vacuum field does not contribute explicitly in any ordering if it is eliminated nonperturbatively and the approximation methods are invoked only after its elimination from the equations of motion.

Yiying Yan, Zhiguo Lü

We study the spontaneous emission spectra of a few-level giant atom strongly coupled to a one-dimensional waveguide by employing variational and analytical approaches, which are beyond the rotating-wave approximation and the Markovian approximation. We show that the interference effects due to the multiple coupling points result in dark lines in spontaneous emission spectra of either two-level or three-level giant atoms regardless of whether there is a bound state or not. We illustrate that the generation of dark lines depends on the distance between the coupling points and their number. In the absence of a bound state, the dark lines can be used to suppress emission at a certain frequency in the spectrum. In the presence of a bound state, the total intensity of the emission spectrum can be significantly suppressed. The present results offer the possibility of control over the spontaneous emission with the dark lines due to the destructive interference in giant atoms. Published by the American Physical Society 2024

G.E. Notkin, Sergey G. Rautian, A. A. Feoktistov