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arxiv: 2605.19442 · v1 · pith:LCIYLD6Rnew · submitted 2026-05-19 · 🪐 quant-ph

Exact dynamics of a single-photon emitter in front of a mirror

Mateusz Duda , Thomas Hartwell , Daniel Hodgson , Gin Jose , Pieter Kok , Almut Beige This is my paper

Pith reviewed 2026-05-20 06:03 UTC · model grok-4.3

classification 🪐 quant-ph
keywords single-photon emitternon-Markovian dynamicsone-dimensional waveguidemirror interfacephoton wave packetquantum opticsexact dynamicsMarkovian limit
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The pith

A single-photon emitter near a mirror exhibits non-Markovian dynamics with non-exponential decay that approaches exponential only after times much longer than the round-trip delay.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper solves the Schrödinger equation for a single-photon emitter in a one-dimensional waveguide terminated by a partially transparent mirror. Using a local-photon approach, it establishes that the emitter's excited-state population decays in a non-exponential manner due to the delayed feedback from reflected photons. The decay profile only begins to look exponential after a time much larger than the emitter-mirror round-trip time and recovers the familiar exponential form in the Markovian limit that neglects this delay entirely. The work also derives how the mirror changes the spatial and spectral shape of the outgoing photon wave packet.

Core claim

The evolution of the emitter is non-Markovian, characterized by a non-exponential decay profile. The decay can resemble an exponential after a time that is much larger than the emitter-mirror round-trip time and becomes exponential in the Markovian limit, where the round-trip time between the emitter and the mirror is neglected. The spatial and spectral profile of the emitted photon wave packet is derived and shown to be altered by the environment.

What carries the argument

The local-photon approach to solving the Schrödinger equation for the emitter plus one-dimensional waveguide with a partially transparent mirror interface.

If this is right

  • The spatial and spectral profile of the emitted photon wave packet depends on the distance to the mirror and its reflectivity.
  • Non-Markovian features remain visible until times much larger than the round-trip time between emitter and mirror.
  • In the Markovian limit that neglects the round-trip time, the decay reduces to a simple exponential form.
  • These exact dynamics are required for accurate modeling of nanophotonic structures used in quantum sensors and quantum computers.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The derived non-exponential regime could be exploited to shape the temporal profile of emitted photons for specific quantum-information tasks.
  • The local-photon method might be extended to treat multiple emitters or partially reflective structures with more complex geometries.

Load-bearing premise

The one-dimensional waveguide model with a partially transparent mirror interface fully captures the relevant physics without additional loss channels or higher-dimensional effects.

What would settle it

Time-resolved measurement of the excited-state population of a single-photon emitter placed at a controlled distance from a mirror, checking whether the initial decay curve deviates from exponential before settling into exponential behavior at later times.

Figures

Figures reproduced from arXiv: 2605.19442 by Almut Beige, Daniel Hodgson, Gin Jose, Mateusz Duda, Pieter Kok, Thomas Hartwell.

Figure 1
Figure 1. Figure 1: FIG. 1. Diagram of a two-level quantum emitter near a [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Reabsorption processes contributing to the Dyson [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Two-level emitter excitation probability as a function [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Approximate two-level emitter excitation probabil [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Transition frequency shift ∆ [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Spectral envelope of the emitted photon wave packet, [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Schematic of a possible experimental realization of [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Reabsorption processes contributing to the Dyson series term [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. The emitter–mirror system within the space-discretized quantum trajectory model. The spatial region of interest is [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Comparison between the results of our analytical model (dashed red curves) and numerical quantum trajectory [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
read the original abstract

Single-photon emitters in nanophotonic structures are a key building block for many photonic devices with quantum technology applications, like quantum sensors and quantum computers. In this paper, we determine the exact dynamics of a single-photon emitter in a one-dimensional waveguide terminated by a partially-transparent mirror interface, by solving the Schrodinger equation via a local-photon approach. In general, the evolution of the emitter is non-Markovian, characterized by a non-exponential decay profile. The decay can resemble an exponential after a time that is much larger than the emitter-mirror round-trip time and becomes exponential in the Markovian limit, where the round-trip time between the emitter and the mirror is neglected. We also derive the spatial and spectral profile of the emitted photon wave packet and demonstrate how its properties are altered by the environment.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript claims to solve the time-dependent Schrödinger equation exactly for a single-photon emitter in a one-dimensional waveguide terminated by a partially transparent mirror, using a local-photon approach that reduces the problem to a delay differential equation. This yields non-Markovian dynamics with a non-exponential decay profile for the emitter amplitude; the decay approximates exponential behavior after times much larger than the emitter-mirror round-trip time and recovers exact exponential decay in the Markovian limit of vanishing delay. The spatial and spectral profiles of the emitted photon wave packet are also derived, showing modifications induced by the mirror environment.

Significance. If the central derivation holds, the work is significant for quantum nanophotonics: it supplies a parameter-free, exact analytical description of non-Markovian single-photon emission in a structured environment and explicitly demonstrates the crossover to Markovian dynamics via the finite round-trip time. The reduction to a solvable delay differential equation and the recovery of known limits constitute clear strengths that enable falsifiable predictions for experiments.

minor comments (2)
  1. Notation for the round-trip time should be introduced once and used consistently in the text, equations, and any figures that plot time-dependent quantities.
  2. The abstract would benefit from a single sentence clarifying that the model is closed (no additional loss channels) to help readers immediately gauge the scope of the exact solution.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript, including recognition of the exact non-Markovian solution via the delay differential equation, the demonstration of the Markovian crossover, and the derived photon wave-packet profiles. We are pleased that the work is viewed as significant for quantum nanophotonics and that the recommendation is for minor revision. Below we address the report point by point; since no specific major comments were raised, we note that we will incorporate minor clarifications and improvements in the revised version.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper obtains the emitter dynamics by direct solution of the time-dependent Schrödinger equation in a closed 1D waveguide model using the local-photon approach. This reduces to a delay differential equation whose non-exponential solution follows from the finite emitter-mirror round-trip time; the Markovian limit is recovered by sending the delay to zero. No fitted parameters, self-referential definitions, or load-bearing self-citations are required for the central non-Markovian result. The spatial and spectral profiles of the emitted photon are likewise obtained from the same first-principles solution without renaming or smuggling prior ansatzes.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The derivation rests on standard quantum mechanics and the local-photon representation; no free parameters or new entities are mentioned.

axioms (1)
  • domain assumption The system is described by the time-dependent Schrödinger equation in a one-dimensional waveguide with a partially transparent mirror boundary.
    Invoked to justify the exact solution approach.

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    r VR 2π a† R(k)σ − + r V ∗ R 2π aR(k)σ+ # dk+ Z 0 −∞

    Model In the quantum trajectory model, we discretize the region around the emitter into a series of spatial boxes of width ∆tin time, as shown in Fig. 10. This allows us to simulate the time evolution in discrete time steps ∆t. We start from thek-space Hamiltonian for a two-level emitter coupled to an infinite one-dimensional waveguide: H=ω eσ+σ− + Z ∞ 0 ...

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    11 (solid black curves), with a comparison to the results of our analytical model (dashed red curves)

    Comparison of results The results of the quantum trajectory simulations are presented in Fig. 11 (solid black curves), with a comparison to the results of our analytical model (dashed red curves). For the comparison, we use some of the parameter sets that were used in Fig. 3 to cover a range of different reflection coefficients, emitter–mirror separations...

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