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(GQR67/AFC7) From Recurrence to Selection: Resolving Directional Ambiguity in Atomic Frequency Comb Memory

JAMES SUTTON

Published Apr 18, 2026• 0 citations
Publisher

Abstract

Atomic frequency comb (AFC) systems provide robust temporal recurrence but do not, in their symmetricform, ensure preservation of directional equivalence. As a result, signal amplitude may be maintained whilesignal identity remains ambiguous.In this work, we examine the structure of the AFC response across three stages. First, baseline measure-ments reveal persistent forward–backward asymmetry despite low disturbance. Second, direct mode-resolvedanalysis shows only weak trends with high variability, indicating that the accessible spectral space does notadmit a stable interpretation. Third, the introduction of selective filtering (“fuzz removal”) produces a quali-tative transition: sharply defined band structure emerges immediately, with spectral weight concentrating intoa restricted set of modes.These results demonstrate that the relevant operation is not the construction of structure, but its revelationthrough suppression of non-persistent components. AFC systems therefore act as recurrence substrates, whilereliable memory behaviour requires a selection layer that enforces persistence under constraint.This establishes a clear distinction between accessibility and stability, and provides a pathway for engi-neering AFC-based memory systems in which structure is controlled through constraint-driven selection ratherthan amplitude preservation alone. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.

DOI
10.5281/zenodo.19643941

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Atomic frequency comb (AFC) systems provide robust temporal recurrence but do not, in their symmetricform, ensure preservation of directional equivalence. As a result, signal amplitude may be maintained whilesignal identity remains ambiguous.In this work, we examine the structure of the AFC response across three stages. First, baseline measure-ments reveal persistent forward–backward asymmetry despite low disturbance. Second, direct mode-resolvedanalysis shows only weak trends with high variability, indicating that the accessible spectral space does notadmit a stable interpretation. Third, the introduction of selective filtering (“fuzz removal”) produces a quali-tative transition: sharply defined band structure emerges immediately, with spectral weight concentrating intoa restricted set of modes.These results demonstrate that the relevant operation is not the construction of structure, but its revelationthrough suppression of non-persistent components. AFC systems therefore act as recurrence substrates, whilereliable memory behaviour requires a selection layer that enforces persistence under constraint.This establishes a clear distinction between accessibility and stability, and provides a pathway for engi-neering AFC-based memory systems in which structure is controlled through constraint-driven selection ratherthan amplitude preservation alone. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.
Atomic frequency comb (AFC) systems provide a robust mechanism for temporal recurrence through collective rephasing of spectrally distributed excitations. However, recurrence alone does not guarantee preservation of signal identity: multiple accessible modes may persist with comparable amplitude while remaining dynamically ambiguous. This work introduces a spectral admissibility framework in which stable structure emerges through selection rather than recurrence alone. Each spectral mode is assigned a survival-weighted contribution of the form w_n = S_n e^{-Λ_n}, where S_n represents spectral support and Λ_n encodes suppression arising from dephasing, mismatch, and inter-mode competition. Within this formulation, recurrence generates a high-dimensional accessible set of configurations, while selection determines which configurations persist under constraint. Empirical analysis shows that raw AFC spectra exhibit diffuse multi-mode occupancy, whereas the introduction of suppression mechanisms produces a qualitative transition to sharply defined structure. This demonstrates that filtering does not construct spectral organisation, but reveals it by eliminating non-persistent components. The underlying spectral field is therefore structured prior to selection, with stable configurations emerging through constraint-driven survival. The results establish a two-layer architecture for spectral systems: recurrence defines accessibility, and admissibility enforces persistence. This provides a unified perspective on AFC memory behaviour and suggests a general design principle for coherence-based photonic systems, in which stable operation is achieved through alignment between accessibility and persistence rather than amplitude preservation alone.
High signal integrity in quantum memory systems is often assumed to be recoverable throughdownstream optimisation. Here, using a model of atomic frequency comb (AFC) dynamics, weshow that signal integrity is instead determined at formation. Across a broad parameter space,the system exhibits a transient regime in which signal amplitude remains close to a clean referencewhile directional asymmetry emerges between forward and backward evolution (AB̸ = BA). Thisdefines an echological regime, characterised by low signal disturbance and loss of path equivalence.Time-resolved analysis reveals a universal transition from an early structured regime to a noise-dominated state, with the transition time largely independent of comb parameters. Apparent late-time stability is shown to arise from loss of accessible structure rather than recovery of the originalsignal. Comparison of observables further demonstrates that convergence in raw intensity canmask divergence in more sensitive representations, indicating that stability is strongly observable-dependent.These results imply that AFC systems, in their symmetric form, act as recurrence substratesrather than complete memory devices. Reliable memory requires an additional selection or filter-ing layer capable of suppressing ambiguous components and restoring directional asymmetry in acontrolled manner. More generally, the findings establish that signal integrity is not produced bycorrection, but emerges when system parameters are aligned with a constrained operating regimeat formation. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.
Abstract: Atomic frequency comb (AFC) memories employ periodic spectral absorptionstructures that produce delayed photon echoes through collective rephasing of atomic excitations.Recent modelling studies have examined robustness limits of cavity-enhanced rare-earth AFCsystems from a geometric tolerance perspective, identifying dimensionless stability criteria foradmissible operating regions. Here we present a complementary dynamical framework that linksthe spectral comb structure directly to the temporal impulse response of the medium.Starting from a frequency-domain description of the comb absorption profile, we reconstructthe complex transfer function and show that periodic spectral geometry generates a temporallyrecurrent impulse response with peaks separated by 1/Δ, where Δ is the comb spacing. Convolu-tion with arbitrary input pulses reproduces the characteristic AFC echo dynamics and enablesdirect evaluation of retrieval efficiency. Numerical simulations recover three key AFC properties:deterministic echo timing 𝑡echo = 1/Δ, efficiency scaling governed by comb finesse 𝐹 = Δ/𝛾,and the influence of cavity bandwidth on retrieval efficiency.The results provide a unified description connecting spectral comb geometry, impulse responserecurrence, and echo formation in AFC memories. This perspective complements previoustolerance analyses by revealing the dynamical origin of echo recurrence and offers a compactframework for analysing and designing comb-based quantum memories. Full programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.
Abstract: We present a regime-resolved modelling study of cavity-enhanced Eu3+:Y2SiO5atomic frequency comb (AFC) quantum memories that quantifies bandwidth robustness acrosscontrast and comb-bandwidth parameter space. Using Kramers–Kronig–consistent susceptibilityreconstruction and frequency-domain cavity transfer modelling with representative integrated-device parameters, we construct contrast–bandwidth response atlases for wide- and narrow-cavityregimes. While first-order dispersion cancellation between spectral pit and AFC structures canbe achieved, robustness is shown to be governed by higher-order susceptibility curvature undercavity phase feedback. For representative configurations, cavity narrowing reduces admissibleoperating volume by approximately 35–40%, despite comparable peak echo amplitude. Theatlas methodology provides a quantitative tolerance-analysis framework for integrated rare-earthphotonic memories. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.
Cavity-enhanced rare-earth-ion-doped atomic frequency comb (AFC) memoriesexhibit robustness limits not fully captured by peak efficiency or first-order dispersion analysis.We identify a dimensionless ridge-drift ratio that governs tolerance collapse in contrast–bandwidthparameter space. Using a Kramers–Kronig-consistent susceptibility reconstruction and cavitytransfer model representative of rare-earth-ion crystal platforms, we show that survival probabilityfollows a logistic boundary controlled by the ratio of ridge displacement to local admissiblebandwidth width. This collapse law persists across threshold definitions and cavity finesseregimes and is independent of dominance-exchange branch crossings. The results provide aquantitative tolerance condition for robust design of integrated rare-earth photonic quantummemory devices. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.
Noncommuting generators of evolution impose ordering constraints on dynamical systems,restricting the set of admissible transitions. We introduce an Accessibility–Ordering Invariant(AOI) that captures this admissible ordering structure.Three manifestations of ordering geometry are examined in this work. First, ordered trans-port dynamics in graphene systems generate phase ladders in observables governed by a Flo-quet ordering relation. Second, newly identified Schr¨odinger–Heisenberg divisibility fracture inopen quantum dynamics produces ridge manifolds that obey the same ladder condition. Third,atomic-frequency-comb quantum memories exhibit spectral comb structures whose Fourier dualgenerates temporal ladder recurrence.These systems therefore realize a common ordering geometry expressed in conjugate phasecoordinates. In compact form the resulting ladder relations reduce toΓΛ ≈ nπ, tn = n∆ , n ∈ Z,revealing the dual appearance of phase ladders and Dirac-comb temporalis. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.