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arXiv · 2110.07049

Analysis of single-excitation states in quantum optics

Jeremy Hoskins·Jason Kaye·Manas Rachh·John Schotland
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Abstract

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 $O(1/t^3)$ 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.

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Jeremy Hoskins, Jason Kaye, Manas Rachh, John Schotland. 2021-10-13. Analysis of single-excitation states in quantum optics. https://arxiv.org/abs/2110.07049

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