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