On the excitability of two-level atoms by spectrally encoded single-photon wave packets in quantum networks

TL;DR

This paper investigates how spectrally encoded single-photon wave packets interact with two-level atoms, revealing how encoding affects excitation and informing design rules for quantum network links.

Contribution

It introduces a formal analysis of spectral phase encoding effects on atom-photon interactions and derives performance bounds for quantum network implementations.

Findings

Spectral phase encoding broadens photon wave packets and weakens atomic excitation.

Atomic response depends on spectral overlap, code length, and phase errors.

Provides design guidelines for scalable and secure quantum networks.

Abstract

We analyze the time-dependent interaction between a two-level atom and a spectrally encoded single-photon wave packet using the Heisenberg-Langevin equations and derive the atomic excitation probability. Spectral phase encoding broadens the photon wave packet in the time domain and reduces its peak intensity, leading to markedly weaker atomic excitation than for an unencoded photon. We formalize this behavior via an overlap bound with the time-reversed spontaneous emission mode and show how excitation depends on code length, bandwidth, and phase errors. Interpreted at the quantum network level, atoms behave as phase-sensitive, and mode-selective receivers whose response scales with a spectral-overlap functional that captures decoding fidelity, detuning, and multiuser interference. From this, we extract design rules and performance bounds for encoded links, quantifying trade-offs among code length, addressability, cross-talk, and identifying tolerances for decoding error. These results clarify how spectrally encoded photons couple to quantum nodes and provide guidelines for efficient, scalable, and secure quantum networking.