42-EFT.WP.Heat.Decoherence v1.0 | Chapter 7: Platform-Specific Decoherence Channels — SC / Semiconductor / Spin / Optomechanics / Acoustics

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Chapter 7: Platform-Specific Decoherence Channels — SC / Semiconductor / Spin / Optomechanics / Acoustics

I. Objectives & Applicability

• Under a unified noise → spectrum → response → rate mapping, specify platform-specific decoherence channels and executable modeling workflows for five mainstream platforms (SC superconducting circuits, semiconductor devices, spin systems, optomechanics, acoustic resonators): identify dominant noise sources and coupling operators, and form platform mappings J(ω) → {Γ_1, Γ_φ} with a traceable metrology chain.
• All formulas/symbols/definitions are in English with backticks; SI units; ω/f and PSD conventions per Chapter 2; spectral estimation & FDT per Chapter 5; open-system mappings per Chapter 4.

II. Minimal Statements & Principles (S70-*)

• S70-1 (Channel superposition & figures)
  Total platform rates: Γ_1 = Σ_c Γ_1^{(c)}, Γ_φ = Σ_c Γ_φ^{(c)}, (1/T_2) = Γ_φ + (1/2) Γ_1, Q = ω_0 / Γ_1 (resonant form).
• S70-2 (Frequency-drift coupling)
  For eigenfrequency ω_0 perturbed by control λ, Δω = (∂ω_0/∂λ) δλ,
  Γ_φ^{(λ)} = (1/2) S_{ΔωΔω}(0) = (1/2) (∂ω_0/∂λ)^2 S_{λλ}(0). Under control sequences,
  χ(t) = ( (∂ω_0/∂λ)^2 / π ) ∫_0^∞ dω S_{λλ}(ω) |F(ω)|^2 / ω^2.
• S70-3 (Relaxation coupling)
  For transition operator A, golden rule
  Γ_1^{(A)}(ω_0,T) = (π/2) |A_{eg}|^2 J_A(ω_0) coth(ħω_0/2k_B T); for dielectric loss channels, participation-ratio mapping:
  1/Q_{die}(ω_0) = Σ_i p_i(ω_0) tanδ_i(ω_0), Γ_1^{(die)} = ω_0 /(2 Q_{die}).
• S70-4 (Phonon/radiative scaling)
  Phonons J_ph(ω) ∝ ω^{s_ph} (bulk often s_ph≈3, piezoelectric ≈1); radiation J_γ(ω) ∝ ω^3; map to Γ_1 ∝ J(ω_0).
• S70-5 (Surface/interface & TLS)
  Surface TLS give S_{λλ}(ω) ≈ A^2/|ω|^γ (γ≈1) and Lorentzian sums; low-ω dominates Γ_φ, high-ω tail impacts Γ_1.
• S70-6 (Quasiparticles / impurity spins)
  SC quasiparticle density x_qp yields Γ_1^{(qp)} ∝ x_qp; spin-bath noise S_{B_zB_z}(ω) via magnetic coupling gives Γ_φ^{(hf)} = (γ·)^2 S_{B_zB_z}(0)/2.
• S70-7 (Optomech & acoustic thermalization)
  Mechanical mode Γ_m(T) = Γ_{m,0} + Γ_{th}(T), with coherent dephasing Γ_{th} ≈ Γ_m n̄(ω_m,T); radiation-pressure backaction and clamping losses add to Γ_1.

III. Platform Models & Channels (SC / Semiconductor / Spin / Optomech / Acoustic)

1. A. SC (Superconducting circuits)
   • Dominant channels: 1/f flux (λ=Φ), critical-current/charge noise (λ=I_c,Q_g), dielectric TLS loss, quasiparticles, radiative leakage.
   • Mapping:
     1. Dephasing: Γ_φ^{(λ)} = (1/2) (∂ω_0/∂λ)^2 S_{λλ}(0); apply |F(ω)|^2 for DD filtering within bandwidth.
     2. Relaxation: participation p_i, tanδ_i → Q_{die}; radiation J_γ(ω_0) → Γ_1^{(rad)}; quasiparticles x_qp → Γ_1^{(qp)}.
2. B. Semiconductors (QDs/2D/trapped charge)
   • Dominant channels: charge noise (gate dielectrics/traps), e–ph coupling (deformation/piezo), interface roughness.
   • Mapping: Γ_1^{(ph)}(ω_0) ∝ J_ph(ω_0); Γ_φ^{(Q)} = (1/2) (∂ω_0/∂Q)^2 S_{QQ}(0); temperature/stress reshape J_ph.
3. C. Spins (NV/donor/QD spin/spin traps)
   • Dominant channels: hyperfine B_n (Overhauser), dipolar spin bath, surface spins/noise, phonon-induced T_1.
   • Mapping: Γ_φ^{(hf)} = (γ_e)^2 S_{B_zB_z}(0)/2; Γ_1^{(ph)}(ω_0) ∝ J_ph(ω_0) coth(ħω_0/2k_B T); DD boosts low-ω magnetic-noise suppression.
4. D. Optomechanics
   • Dominant channels: mechanical internal loss (Akhiezer/thermoelastic/clamping), radiation-pressure backaction, optical loss/absorption heating.
   • Mapping: Γ_{th} ≈ Γ_m n̄(ω_m,T); filter against S_{FF}(ω); optical cavity κ and coupling g_0 shape effective J(ω).
5. E. Acoustic resonators (MEMS/SAW/BAW)
   • Dominant channels: Akhiezer (high T, high f), Landau–Rumer (low T, high f), thermoelastic, interface/surface roughness and anchor losses.
   • Mapping: Q^{-1} = Q_{AKE}^{-1} + Q_{LR}^{-1} + Q_{TED}^{-1} + Q_{surf}^{-1}, Γ_1 = ω_0 / Q; TED couples to Chapter 6 temperature fields.

IV. Metrology Chain & Data Contract (Required Fields)

unit_system: "SI"

platform: "SC|Semiconductor|Spin|Optomech|Acoustic"

device:

omega0: "<rad/s>", bias: {lambda: "<Φ|Q|I_c|B|...>", d_omega_d_lambda: "<rad/s/unit>"}

channels:

dephasing:

params: {domega_dlambda: "<rad/s/unit>"}

psd: {S_ll: "<model|table>", one_over_f: {A:"<...>", gamma:"~1", omega_L:"<rad/s>"}}

relaxation:

dielectric: {p: [{region:"...", value:"<...>"}], tan_delta: [{mat:"...", value:"<...>"}]}

radiation: {J_gamma: "<model|NEC|fit>"}

quasiparticle: {x_qp: "<...>"}

spin:

Bz_psd: "<S_BzBz(ω)>", gamma_e: "<rad/s/T>"

phonon:

J_ph: {family:"ohmic|piezo|custom", params:{eta:"<...>", s:"<...>", omega_c:"<rad/s>"}}

control:

sequence: "Ramsey|Echo|CPMG|Uhrig|custom", timing: "<{t_k}>"

outputs:

rates: ["Gamma1","Gamma_phi","T1","T2","Q"], spectra: ["S_eff(ω)","S_ll(ω)"]

uncertainty:

Σ_y: "<blocks>", priors: {eta:"...", s:"...", omega_c:"...", tan_delta:"..."}

references: ["Heat.Decoherence v1.0:Ch.2 S20-*","Ch.4 S40-*","Ch.5 S50-*","Ch.6 S60-*"]

V. Algorithmic Workflows (M7-*)

• M7-1 (Channel identification & spectral assembly)
  Based on platform/process lists, enumerate candidate channels → assemble S_{λλ}(ω), J(ω) via Ch.5 spectral estimation / literature fits.
• M7-2 (Rate mapping & sequence response)
  Use S70-2/3 with filter |F(ω)|^2 to compute {Γ_1, Γ_φ}, yielding T_1/T_2/Q.
• M7-3 (Temperature/frequency/bias sweeps)
  Generate Γ(T, ω_0, λ) response surfaces; identify critical bands and “sweet spots” (∂Γ/∂λ ≈ 0).
• M7-4 (Channel decomposition & priority)
  Allocate {Γ_1, Γ_φ} to channels via Shapley/sensitivity; output mitigation-priority radar.
• M7-5 (Validation & regression)
  Cross-validate with time-domain sequences (Ramsey/echo) and frequency spectra (PSD/CPSD); update dataset and uncertainties.

VI. Implementation Bindings & Interfaces (I70-*)

• I70-1 assemble_platform_psd(platform, data, priors) -> {S_ll(ω), J(ω), meta}
• I70-2 map_rates(omega0, d_omega_d_lambda, S_ll, J, T, control) -> {Gamma1, Gamma_phi, T1, T2, Q}
• I70-3 scan_response(axes, model) -> {Gamma_maps, sweet_spots}
• I70-4 decompose_channels(rates, models) -> {contribs, ranking}
• I70-5 validate_vs_sequences(seq_data, psd) -> {pass@coverage, residuals, update}

Error codes: E/INPUT (missing), E/UNIT (unit mismatch), E/NUMERIC (non-convergence/non-positive spectrum), E/IDENTIFIABILITY (ill-conditioned).

VII. Quality Gates (This Chapter)

• Q1 Conventions & units: ω/f, PSD one-/two-sided, and unit columns consistent with Chs. 2/5; pass check_dim.
• Q2 Positivity & conservation: J(ω) ≥ 0, S_{λλ}(ω) ≥ 0; consistency with Ch. 6 temperature/heat-flow outputs.
• Q3 Identifiability: control cond(F) = J_θ^T Σ^{-1} J_θ; if insufficient, recommend wider bandwidth/temperature or stronger priors.
• Q4 Cross-validation: time/frequency and T/ω sweeps consistent; parameter coverage near nominal.
• Q5 Traceability: materials/process/cavity/TLS/quasiparticle parameter sources & versions traceable in dataset references.

VIII. Cross-References & Anchors (This Chapter)

• Cross-refs (fixed style): Ch. 2 (metrology), Ch. 4 (open-system mapping), Ch. 5 (FDT & spectral estimation), Ch. 6 (heat & temperature fields), Ch. 8 (coherence engineering), Ch. 9 (metrology & inference).
• Anchors: Minimal S70-1—S70-7; Workflows M7-1—M7-5; Interfaces I70-1—I70-5.

IX. Summary
This chapter grounds the cross-platform noise → spectrum → rate mapping in concrete devices, delivering executable channel identification, rate computation, and validation flows, plus prioritized mitigation guidance. Coupled with mechanisms & thermal fields (Chs. 4/5/6) and engineering & metrology (Chs. 8/9), it supports consistent decoherence assessment and optimization across temperatures and fabrication processes.