• Corpus ID: 238856762

Analysis of single-excitation states in quantum optics

@inproceedings{Hoskins2021AnalysisOS,
  title={Analysis of single-excitation states in quantum optics},
  author={Jeremy G. Hoskins and Jason Kaye and Manas Rachh and John C. Schotland},
  year={2021}
}

• Jeremy G. Hoskins, Jason Kaye, +1 author J. Schotland
• Published 13 October 2021
• Physics, Mathematics

In this paper we analyze the dynamics of single-excitation states, which model the scattering of a single photon from multiple two level atoms. For short times and weak atom-field 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 Wigner-Weisskopf analysis of spontaneous emission. On the other hand, at large times, the atomic field decays like O(1/t3) 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.