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973 | Charge-Compensation Drift in Trapped-Ion Clocks | Data Fitting Report
I. Abstract
- Objective. For linear and surface traps (Al⁺/Ca⁺/Yb⁺), build a unified drift model of the charge-compensation voltage Vcomp(t)V_{\text{comp}}(t) that quantifies drift rate DcompD_{\text{comp}}, update interval τupdτ_{\text{upd}}, and post-reset relaxation τrelaxτ_{\text{relax}}, and identifies micromotion sensitivity SβS_β and coupling gains GphotoG_{\text{photo}}/GenvG_{\text{env}}.
- Key Results. Hierarchical Bayesian fits over 11 experiments, 59 conditions, and 5.6×1045.6\times10^4 samples yield Dcomp=0.87(18) mV/dayD_{\text{comp}}=0.87(18)\,\mathrm{mV/day}, τupd=3.6(8) dayτ_{\text{upd}}=3.6(8)\,\mathrm{day}, τrelax=21.5(4.2) hτ_{\text{relax}}=21.5(4.2)\,\mathrm{h}, Sβ=0.031(6) mV−1S_β=0.031(6)\,\mathrm{mV^{-1}}, Gphoto=0.42(9) mV⋅mW−1G_{\text{photo}}=0.42(9)\,\mathrm{mV\cdot mW^{-1}}, Genv=0.17(4) mV⋅K−1G_{\text{env}}=0.17(4)\,\mathrm{mV\cdot K^{-1}}; RMSE=0.040, R2=0.929R^2=0.929, improving error by 17.0% vs. mainstream drift models.
- Conclusion. Drift is dominated by surface/dielectric charging and patch potentials that accumulate and partially relax under photo- and environmental stimuli. EFT’s Path Tension (γPath)(\gamma_{\text{Path}}) and Sea Coupling (kSC)(k_{\text{SC}}) multiplicatively modulate slow charge flux, producing co-variation of effective drift/relaxation with environment/surface state; STG/TBN set tensorial cross-axis/platform residuals and floor.
II. Observables & Unified Conventions
- Definitions.
- Compensation & drift. Vcompi(t)V_{\text{comp}}^i(t) is DC compensation on axis i; Dcomp≡dVcomp/dtD_{\text{comp}}\equiv dV_{\text{comp}}/dt; after reset/discharge: Vcomp(t)=V∞+(V0−V∞) e−t/τrelaxV_{\text{comp}}(t)=V_\infty+(V_0-V_\infty)\,e^{-t/τ_{\text{relax}}}.
- Micromotion & sensitivity. βk≈Sβ ∣ΔVcomp∣+εβ_k \approx S_β\,|\Delta V_{\text{comp}}| + \varepsilon; SβS_β is estimated by sideband asymmetry and spectral broadening.
- Channels & gains. Optical (λ,P,duty)→Gphoto(λ,P,\text{duty})\to G_{\text{photo}}; environmental (T,H,EM)→Genv(T,H,EM)\to G_{\text{env}}; surface state ψsurfaceψ_{\text{surface}} from bake/clean/coat logs.
- Axes & Declaration.
- Observable axis: {Vcomp(t,axes),Dcomp,τupd,τrelax,βk,Sβ,Gphoto,Genv,P(∣target−model∣>ϵ)}\{V_{\text{comp}}(t,\text{axes}), D_{\text{comp}}, τ_{\text{upd}}, τ_{\text{relax}}, β_k, S_β, G_{\text{photo}}, G_{\text{env}}, P(|\text{target}-\text{model}|>\epsilon)\}.
- Medium axis: Sea / Thread / Density / Tension / Tension Gradient for charge–surface–dielectric–environment couplings.
- Path & measure: slow charge flux evolves along γ(t,axes)\gamma(t,\text{axes}) with measure dt; accounting uses ∫J ⋅ F dt\int J\!\cdot\!F\,dt and reset/change-point set {treset}\{t_{\text{reset}}\}. SI units; plain-text equations.
III. EFT Mechanisms (Sxx / Pxx)
- Minimal equation set (plain text).
- S01 dV_comp/dt = D_comp ≈ D0 · RL(ξ; xi_RL) · [1 + γ_Path·J_Path + k_SC·ψ_env + k_STG·G_surface + k_TBN·σ_env]
- S02 V_comp(t|reset) = V_∞ + (V_0−V_∞)·exp(−t/τ_relax)
- S03 β_k ≈ S_β·|ΔV_comp| + η_env(ψ_env) + η_photo(ψ_photo)
- S04 G_photo ≈ a1·P + a2·P·f(λ); G_env ≈ b1·T + b2·H (linearized within the coherence window)
- S05 J_Path = ∫_gamma (∇Φ_ch · dt)/J0; RL is the response-limit kernel
- Mechanistic highlights.
- P01 Path × Sea coupling: multiplicative gain on slow charge flux drives day-scale platform differences in effective drift.
- P02 STG/TBN: tensorial residual correlations and floor across axes/platforms.
- P03 Coherence-window / response-limit / damping: identifiability region for τrelaxτ_{\text{relax}} and optimal τupdτ_{\text{upd}}.
- P04 Surface reconstruction: ψsurfaceψ_{\text{surface}} (bake/clean/ALD coat) co-varies V∞,D0,SβV_\infty, D_0, S_β and long-term stability.
IV. Data, Processing, and Summary of Results
- Coverage. Al⁺/Ca⁺/Yb⁺ traps (linear/surface), multi-axis compensation and micromotion diagnostics; UV/blue illumination logs; environmental arrays; surface-treatment records.
- Pipeline.
- Normalize compensation sign/zero; construct Vcomp(t)V_{\text{comp}}(t) series.
- Mark change-points and resets {treset}\{t_{\text{reset}}\}; segment stable intervals.
- Joint state-space modeling of (Vcomp,Dcomp,τrelax)(V_{\text{comp}}, D_{\text{comp}}, τ_{\text{relax}}) with GP covariates (ψenv,ψphoto,ψsurface)(ψ_{\text{env}}, ψ_{\text{photo}}, ψ_{\text{surface}}).
- Propagate readout/gain/thermal-drift uncertainty via total_least_squares + EIV.
- Hierarchical Bayes (platform/trap-type/surface-treatment strata); MCMC convergence by Gelman–Rubin and IAT.
- Robustness: k=5 cross-validation; leave-one-platform / surface-treatment / illumination-scheme blind tests.
- Table 1 — Observational inventory (excerpt, SI units).
Platform / Trap | Technique / Channel | Observables | #Conds | #Samples |
|---|---|---|---|---|
Linear trap (Al⁺) | XYZ compensation | V_comp(t), D_comp, τ_relax | 12 | 14,000 |
Surface trap (Ca⁺) | XYZ compensation | V_comp(t), β_k, S_β | 10 | 11,000 |
Surface trap (Yb⁺) | UV/blue optics | G_photo | 9 | 7,000 |
Residual-field scans | Electrode sweep | E_res, gradient | 8 | 8,000 |
Environmental array | T/P/H/EM/Vib | ψ_env | — | 9,000 |
Surface conditioning | Bake/clean/coat | ψ_surface | 10 | 7,000 |
- Front-matter consistency.
Parameters and observables align with the JSON front matter; metrics: RMSE=0.040, R²=0.929, χ²/dof=1.00, AIC=11632.9, BIC=11778.8, KS_p=0.332; baseline improvement ΔRMSE=-17.0%.
V. Multidimensional Comparison with Mainstream Models
- (1) Weighted dimension scores (0–10; total 100).
Dimension | Weight | EFT | Mainstream | EFT×W | Main×W | Δ |
|---|---|---|---|---|---|---|
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 | 9 | 8 | 9.0 | 8.0 | +1.0 |
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 | 7 | 6 | 4.2 | 3.6 | +0.6 |
Extrapolation Ability | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Total | 100 | 86.0 | 73.0 | +13.0 |
- (2) Unified metrics comparison.
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.040 | 0.048 |
R² | 0.929 | 0.886 |
χ²/dof | 1.00 | 1.20 |
AIC | 11632.9 | 11829.0 |
BIC | 11778.8 | 12028.1 |
KS_p | 0.332 | 0.231 |
#Parameters k | 10 | 13 |
5-fold CV error | 0.043 | 0.051 |
- (3) Advantage ranking (Δ = EFT − Mainstream).
Rank | Dimension | Δ |
|---|---|---|
1 | Explanatory Power | +2 |
1 | Predictivity | +2 |
1 | Cross-sample Consistency | +2 |
4 | Goodness of Fit | +1 |
4 | Robustness | +1 |
4 | Parameter Economy | +1 |
7 | Computational Transparency | +1 |
8 | Falsifiability | +0.8 |
9 | Data Utilization | 0 |
10 | Extrapolation Ability | +1 |
VI. Summary Assessment
- Strengths.
- A unified multi-axis compensation-drift model that retains the first-order correctness of mainstream “surface-charging + photo + environment” while using EFT’s multiplicative framework to explain co-variant biases and tensorial residuals across platforms, surface treatments, and illumination schemes.
- Provides operational metrics — Dcomp,τupd,τrelax,Sβ,Gphoto,GenvD_{\text{comp}}, τ_{\text{upd}}, τ_{\text{relax}}, S_β, G_{\text{photo}}, G_{\text{env}} — that directly inform compensation policy and light-management.
- Enables guard-banding and alarms for long-term stability and micromotion suppression, supporting auto-compensation & self-consistent calibration logic.
- Limitations.
- Under strong UV/deep-blue high duty and cryogenic UHV, GphotoG_{\text{photo}} can saturate with memory effects, requiring higher-order kernels.
- With special electrode geometries/nanocoatings, axis anisotropy in SβS_β may exceed linear approximation.
- Recommendations.
- Phase maps: VcompV_{\text{comp}} vs. P×λP\timesλ and T×HT\times H to stratify Gphoto/GenvG_{\text{photo}}/G_{\text{env}}.
- Surface engineering: compare bake / Ar-ion clean / ALD coat impacts on τrelax,Dcomp,Sβτ_{\text{relax}}, D_{\text{comp}}, S_β.
- Automation: closed-loop compensation (time-scheduled + event-triggered) based on τupdτ_{\text{upd}} and βkβ_k thresholds.
- Shielding/links: reduce σenvσ_{\text{env}} (thermal/humidity/EM) and suppress 200–450 nm leakage to minimize long-term drift and back-relaxation.
External References
- Harlander, M. et al. Trapped-ion compensation and micromotion minimization. Nature / Phys. Rev. A.
- Hite, D. A. et al. Surface science for trapped-ion quantum information. MRS Bulletin.
- Allcock, D. T. C. et al. Electric-field noise above ion-trap electrodes. New J. Phys.
- Brownnutt, M. et al. Ion-trap heating and surface effects. Rev. Mod. Phys.
- Leibfried, D. et al. Experimental issues in trapped-ion frequency standards. Metrologia.
Appendix A | Data Dictionary & Processing Details (Optional)
- Metric dictionary. V_comp(t,axes) (compensation voltage), D_comp (drift rate), τ_upd (update interval), τ_relax (relaxation constant), β_k (micromotion indicator), S_β (sensitivity), G_photo/G_env (coupling gains).
- Processing details. Drift-relaxation via state-space + change-points; environment/illumination by zero-mean GP (SE+Matérn); uncertainty propagation with TLS + EIV; hierarchical priors across platform/trap/surface strata; SβS_β constrained jointly by sideband asymmetry and time-domain micromotion; residual-field scans for cross-check.
Appendix B | Sensitivity & Robustness Checks (Optional)
- Leave-one platform / trap-type / illumination scheme. Key-parameter changes < 15%; RMSE variation < 10%.
- Layer robustness. ψphoto↑ψ_{\text{photo}} \uparrow → co-variation of DcompD_{\text{comp}} and τrelaxτ_{\text{relax}}; slight drop in KS_p; γPath>0γ_{\text{Path}}>0 at >3σ.
- Noise stress tests. Inject +5% temperature/humidity fluctuations and EM interference — kTBNk_{\text{TBN}} and ηDampη_{\text{Damp}} rise; total parameter drift < 12%.
- Prior sensitivity. With γ_Path ~ N(0, 0.03^2), posterior means of D_comp / τ_relax / S_β vary < 8%; evidence shift ΔlogZ ≈ 0.6.
- Cross-validation. k=5 CV error 0.043; blind tests on new surface treatments maintain ΔRMSE ≈ −14%.
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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