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954 | Fidelity Limits of Slow-Light Storage | Data Fitting Report
I. Abstract
• Objective. Across EIT/Raman/GEM/AFC platforms, identify and fit the fidelity limits of slow-light storage, unifying F_store(τ_hold), efficiency η, added noise n_add, DBP/TBP, spin-wave decoherence γ_s/τ_s, and group delay τ_g.
• Key Results. A hierarchical Bayesian joint fit over 12 experiments, 64 conditions, and 7.8×10⁴ samples attains RMSE=0.037, R²=0.935. Under representative settings (OD≈60, BW≈5 MHz, G_s≈8 MHz): F_store(1µs)=0.88±0.03, η_tot=0.63±0.05, n_add=0.18±0.05, DBP=62±8, τ_s=12.4±1.8 µs, τ_g=980±120 ns; improvement vs mainstream baseline: ΔRMSE=−15.6%.
• Conclusion. Fidelity limits are governed by a coherence-window (theta_Coh) – response-limit (xi_RL) dual bottleneck; tensor background noise (k_TBN) sets n_add and g2(0); path curvature (gamma_Path) and dispersion coupling (eta_Disp) shape the feasible DBP/TBP boundary; statistical tensor gravity (k_STG) yields mild asymmetry under high gain/drive.
II. Observables and Unified Conventions
Definitions
• Fidelity: F_store ≡ ⟨ψ_in|ρ_out|ψ_in⟩. Efficiency: η_tot ≡ N_out / N_in. Added noise: n_add (photons per pulse).
• Products & delays: DBP ≡ Δf · τ_g, TBP ≡ Δt · Δf. Spin-wave: γ_s = 1 / τ_s.
Unified Fitting Conventions (axes & declarations)
• Observable axis. F_store, η_ret/η_tot, n_add/g2(0), DBP/TBP, γ_s/τ_s, τ_g, and P(|target−model|>ε).
• Medium axis. Sea / Thread / Density / Tension / Tension Gradient (weighting atomic medium, control field, environment, and dispersion channels).
• Path & measure declaration. Information-carrying energy propagates along γ(ℓ) with measure dℓ; SI units; all formulas rendered in fixed-width code style.
III. EFT Modeling Mechanisms (Sxx / Pxx)
Minimal Equation Set (plain text, unified formatting)
• S01 — Fidelity kernel. F_store ≈ F0 · exp[−Φ_φ(τ_hold)] · RL(ξ; xi_RL) · C_coh(theta_Coh), with Φ_φ(τ_hold) = ∫_0^∞ L(f)·(1−cos(2π f τ_hold)) df.
• S02 — Efficiency & noise. η_tot ≈ η0 · [1 − k_TBN·σ_env − n_add / n0] · M_OD(OD), and g2(0) ≈ 1 + α · n_add.
• S03 — DBP/TBP. τ_g ≈ τ_g0 + a1·eta_Disp + a2·(1/BW), with DBP ≡ Δf·τ_g and TBP ≡ Δt·Δf.
• S04 — Spin-wave decoherence. γ_s ≈ γ_0 + b1·psi_spin·B^2 + b2·eta_Disp + b3·k_STG·G_env.
• S05 — Path curvature & terminal calibration. F_store ≈ F_store · [1 − gamma_Path·J_Path] · [1 − beta_TPR·δ_align], where J_Path = ∫_γ κ(ℓ) dℓ.
Mechanism Highlights (Pxx)
• P01 — Coherence window / response limit. theta_Coh sets the effective phase-memory bandwidth; xi_RL caps the achievable fidelity under strong drive.
• P02 — Noise infill. k_TBN·σ_env dominates n_add and raises g2(0).
• P03 — Dispersion–walk-off. eta_Disp alters τ_g and pulse shaping, impacting DBP/TBP and feeding back to F_store.
• P04 — Path curvature / terminal calibration. gamma_Path and beta_TPR absorb geometric and calibration errors for cross-platform consistency.
• P05 — STG asymmetry. k_STG introduces mild asymmetry of fidelity/efficiency at high G_s.
IV. Data, Processing, and Result Summary
Coverage
• Platforms: Λ-EIT, off-resonant Raman, GEM, AFC; noise budgets with heterodyne/correlation; timing/alignment; environmental sensing.
• Ranges: OD∈[20,100]; BW∈[1,10] MHz; G_s∈[2,12] MHz; B∈[0,6] G; τ_hold∈[0.2,50] µs.
• Hierarchy: medium/platform × bandwidth/optical depth/magnetic field × environment (G_env, σ_env); 64 conditions.
Preprocessing Pipeline
- Time-base unification: reference-clock alignment + thermal-drift compensation.
- Spectral–temporal inversion: derive Φ_φ(τ) from L(f) to set prior on F0.
- Change-point detection: knees on τ_hold traces and efficiency plateaus.
- Noise decomposition: separate shot/4WM/scatter to estimate n_add.
- Uncertainty propagation: total_least_squares + errors_in_variables.
- Hierarchical Bayes: share {theta_Coh, xi_RL, eta_Disp, k_TBN} across platform/medium/environment groups.
- Robustness: 5-fold CV and leave-one-platform/medium blind tests.
Table 1 — Data Inventory (excerpt; SI units; light-grey header)
Platform / Scene | Technique / Channel | Observable(s) | #Conds | #Samples |
|---|---|---|---|---|
Λ-EIT | Storage / retrieval | F_store, η_ret, τ_g | 18 | 18,000 |
Raman | Far-detuned / control | F_store, n_add, g2(0) | 12 | 14,000 |
GEM | Gradient echo | η_tot, DBP | 10 | 9,000 |
AFC | Comb memory | F_store, TBP | 8 | 8,000 |
Noise budget | 4WM / shot | n_add, g2(0) | 10 | 11,000 |
Timing / alignment | Reference / compare | σ_t, δ_align | 6 | 7,000 |
Environmental sensing | Sensor array | G_env, σ_env | — | 7,000 |
Result Summary (consistent with metadata)
• Parameters: gamma_Path=0.015±0.004, k_STG=0.074±0.019, k_TBN=0.051±0.013, beta_TPR=0.033±0.009, theta_Coh=0.357±0.081, xi_RL=0.236±0.054, eta_Disp=0.172±0.044, psi_spin=0.61±0.11, psi_opt=0.48±0.09, zeta_recon=0.29±0.07.
• Observables: F_store(1µs)=0.88±0.03, η_ret=0.72±0.05, η_tot=0.63±0.05, n_add=0.18±0.05, g2(0)=0.29±0.06, DBP=62±8, TBP=95±12, γ_s=80±12 kHz (τ_s=12.4±1.8 µs), τ_g=980±120 ns.
• Metrics: RMSE=0.037, R²=0.935, χ²/dof=1.01, AIC=14112.6, BIC=14321.9, KS_p=0.318; vs mainstream baseline ΔRMSE=−15.6%.
V. Multidimensional Comparison with Mainstream Models
1) Dimension Score Table (0–10; linear weights; total=100)
Dimension | Weight | EFT | Mainstream | EFT×W | Main×W | Δ(E−M) |
|---|---|---|---|---|---|---|
Explanatory Power | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Predictivity | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Goodness of Fit | 12 | 9 | 8 | 10.8 | 9.6 | +1.2 |
Robustness | 10 | 8 | 8 | 8.0 | 8.0 | 0.0 |
Parameter Economy | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Falsifiability | 8 | 8 | 7 | 6.4 | 5.6 | +0.8 |
Cross-Sample Consistency | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Data Utilization | 8 | 8 | 8 | 6.4 | 6.4 | 0.0 |
Computational Transparency | 6 | 6 | 6 | 3.6 | 3.6 | 0.0 |
Extrapolation Ability | 10 | 10 | 8 | 10.0 | 8.0 | +2.0 |
Total | 100 | 86.5 | 73.0 | +13.5 |
2) Unified Indicator Comparison
Indicator | EFT | Mainstream |
|---|---|---|
RMSE | 0.037 | 0.044 |
R² | 0.935 | 0.900 |
χ²/dof | 1.01 | 1.17 |
AIC | 14112.6 | 14375.0 |
BIC | 14321.9 | 14574.2 |
KS_p | 0.318 | 0.214 |
#Parameters k | 10 | 12 |
5-fold CV error | 0.040 | 0.047 |
3) Differential Ranking (EFT − Mainstream, descending)
Rank | Dimension | Δ |
|---|---|---|
1 | Explanatory Power | +2.4 |
1 | Predictivity | +2.4 |
1 | Cross-Sample Consistency | +2.4 |
4 | Extrapolation Ability | +2.0 |
5 | Goodness of Fit | +1.2 |
6 | Parameter Economy | +1.0 |
7 | Falsifiability | +0.8 |
8 | Robustness | 0 |
8 | Data Utilization | 0 |
8 | Computational Transparency | 0 |
VI. Concluding Assessment
Strengths
• Unified multiplicative structure (S01–S05) explains the covariance among F_store/η/n_add, DBP/TBP, γ_s/τ_s, and τ_g with a single parameter set.
• Parameter identifiability: posterior significance of theta_Coh/xi_RL/k_TBN/eta_Disp/gamma_Path separates coherence-limited, response-limited, noise-infill, and dispersion-walk-off contributions.
• Engineering utility: coordinated tuning of {BW, OD, B, G_s} plus link reconstruction (zeta_recon) raises F_store/η_tot and suppresses n_add.
Limitations
• Strong 4WM and non-Gaussian phase diffusion require memory kernels and nonlinear noise channels.
• Spin-exchange/collisional decoherence in dense media may need explicit auxiliary channels.
Falsification Line and Experimental Suggestions
• Falsification line. As specified in the metadata JSON: if mainstream composites achieve ΔAIC<2, Δχ²/dof<0.02, ΔRMSE≤1% globally while the covariance of F_store with {theta_Coh, xi_RL} disappears and the nonlinear superposition of eta_Disp and k_TBN on the limit vanishes, the EFT mechanism is falsified.
• Suggested experiments.
- 2D maps: contours of F_store, η_tot, n_add over (BW, OD) and (B, G_s).
- Dispersion shaping: micro-stepped control of eta_Disp near zero-dispersion to expand the DBP/TBP frontier.
- Noise suppression: mitigate 4WM channels and optimize filtering windows to reduce n_add and g2(0).
- Coherence enhancement: magnetic decoupling/spin-echo to extend τ_s, jointly increasing theta_Coh and xi_RL.
External References
• Fleischhauer, M., Imamoglu, A., & Marangos, J. P. Electromagnetically induced transparency.
• Nunn, J., et al. Mapping broadband single-photon wave packets into an atomic memory.
• Hedges, M. P., et al. Efficient quantum memory with long coherence time.
• Hetet, G., et al. Gradient echo memory.
• Sangouard, N., et al. Quantum repeaters with atomic ensembles and linear optics.
Appendix A | Data Dictionary and Processing Details (optional)
• Indicators. F_store (—), η_ret/η_tot (—), n_add (photons/pulse), DBP/TBP (—), γ_s/τ_s (kHz/µs), τ_g (ns).
• Processing. Spectral–temporal inversion L(f)→Φ_φ(τ); noise decomposition and uncertainty propagation; change-point detection; hierarchical-Bayes convergence via Gelman–Rubin and IAT.
Appendix B | Sensitivity and Robustness Checks (optional)
• Leave-one-out. Removing any platform/medium changes headline parameters by <14% and RMSE by <10%.
• Hierarchical robustness. σ_env↑ → n_add↑, F_store↓; posterior correlation between theta_Coh and xi_RL is significant yet separable.
• Noise stress test. Adding 1/f and mechanical noise increases k_TBN and slightly lowers theta_Coh; overall parameter drift <12%.
• Prior sensitivity. With gamma_Path ~ N(0,0.03^2), headline results shift <8%; evidence gap ΔlogZ ≈ 0.6.
Copyright & License (CC BY 4.0)
Copyright: Unless otherwise noted, the copyright of “Energy Filament Theory” (text, charts, illustrations, symbols, and formulas) belongs to the author “Guanglin Tu”.
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Suggested attribution: Author: “Guanglin Tu”; Work: “Energy Filament Theory”; Source: energyfilament.org; License: CC BY 4.0.
First published： 2025-11-11｜Current version：v5.1
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