Two-level atom excitation probability for single- and $N$-photon wavepackets

TL;DR

This paper analyzes how the excitation probability of a two-level atom varies with different photon wavepackets, providing analytical expressions for large photon numbers and considering various pulse shapes and states.

Contribution

It introduces analytical formulas for the excitation probability of a two-level atom driven by N-photon wavepackets, accounting for pulse shape and losses, extending understanding beyond single-photon cases.

Findings

Derived scaling laws for excitation probability with large N

Provided analytical expressions for different pulse shapes

Analyzed effects of external losses and quantum states

Abstract

We study how the transient excitation probability of a two-level atom by a quantized field depends on the temporal profile of the incident pulse, in the presence of external losses, for both coherent and Fock states, and in two complementary limits: when the pulse contains only one photon (on average), and when the number of photons $N$ is large. For the latter case we derive analytical expressions for the scaling of the excitation probability with $N$ that can be easily evaluated for any pulse shape.