Analysis of singleexcitation states in quantum optics
Abstract
In this paper we analyze the dynamics of singleexcitation states, which model the scattering of a single photon from multiple two level atoms. For short times and weak atomfield couplings we show that the atomic amplitudes are given by a sum of decaying exponentials, where the decay rates and Lamb shifts are given by the poles of a certain analytic function. This result is a refinement of the "pole approximation" appearing in the standard WignerWeisskopf analysis of spontaneous emission. On the other hand, at large times, the atomic field decays like $O(1/t^3)$ with a known constant expressed in terms of the coupling parameter and the resonant frequency of the atoms. Moreover, we show that for stronger coupling, the solutions also feature a collection of oscillatory exponentials which dominate the behavior at long times. Finally, we extend the analysis to the continuum limit in which atoms are distributed according to a given density.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.07049
 Bibcode:
 2021arXiv211007049H
 Keywords:

 Mathematical Physics;
 Physics  Optics
 EPrint:
 22 pages, 4 figures