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

TL;DR

The work addresses the excitation of a two-level atom by spectrally encoded single-photon wave packets in quantum networks. It develops a Heisenberg-Langevin framework and an overlap bound with the time-reversed spontaneous-emission mode, showing that spectral phase encoding broadens the photon in time and lowers peak excitation, while decoding can recover strong coupling. A spectral-overlap functional $\mathcal{M}[\phi,\Delta]$ is derived to quantify decoding fidelity, detuning, and multiuser interference, leading to concrete design rules for encoded links, including bandwidth matching, code-length tradeoffs, phase-noise budgets, and cross-talk limits. The results provide a practical, unitary approach to multiplexed, secure quantum networking, enabling mode-selective receivers and scalable, low-interference atom–photon interfaces.

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.

Figures (7)

• Figure 1: A schematic of the interaction between a two-level atom and a photon wave packet.
• Figure 2: The excitation probability $P_e(t)$ of a two-level atom that interacts with a rectangular shape of a single-photon wave packet as a function of $\gamma t$.
• Figure 3: The excitation probability $P_e(t)$ of a two-level atom which interacts with an encoded rectangular shape of photon wave packet as a function of $\gamma t$ for the various code length $N_0$ (blue curves) compared to the uncoded case (red curves). a) $N_0=3$ b) $N_0=5$ c) $N_0=7$ d) $N_0$=31 and e) $N_0=63$.
• Figure 4: Intensity of the uncoded (orange) and encoded (blue) single-photon wave packet. In this figure, $N_0=31$.
• Figure 5: The excitation probability $P_e(t)$ of a two-level atom by an encoded photon wave packet considering three different sequences of the random phase (0 and $\pi$) for the code length $N_0=63$ in the binary spectral encoding.