Logbook — 2026-04-14 — 2D scan at |α|=3 without synced-phase (engine native)

Context. User request: "do the same without synced-phase". Same grid as 2026-04-14-2d-scan-alpha3.md (±15 MHz × [0, 2π), |α| = 3, 1001 × 64 pts) under the engine's native v0.9.1 convention instead of synced-phase.

Subtlety encountered. A first cut of the driver naively dropped ALL inter-pulse evolution (no motional, no spin U_gap). That gives garbage — |C|(δ=0) = 0.04 — because the motional phase doesn't close per cycle and coherence is destroyed. Checking the engine code (stroboscopic_sweep.py:486-498) confirmed the engine's native convention is actually motional Ufree applied, spin δ-phase Ufree NOT applied — a "mixed-frame" convention in which motion evolves in the lab frame but detuning is pulse-only. Driver corrected to match.

Verdict. Engine-native and synced-phase produce dramatically different 2D maps:

Engine-native: single sharp carrier tooth at k = 0 with |C| ≈ 0.9; sidebands (k = ±1, …) at |C| ~ 0.02–0.05. Bright stripes at k = ±10 where motional-phase closure hits a secondary resonance.
Synced-phase: broad Bessel-like comb envelope centred on k = 0; all |k| ≤ 4 teeth at |C| ~ 0.5–0.9; clear φ_α-dependent sideband asymmetry (the velocity signature).

At the carrier (δ = 0, φ_α = 0), both agree: |C| = 0.924. Off-carrier they diverge by an order of magnitude. The difference is the laser-frame detuning phase accumulated between pulses — present in synced-phase, absent in engine-native.

1. Three conventions, now explicit

The v0.9.1 engine allows the user to dial between two kinds of inter-pulse evolution:

convention	motion U_gap	spin-δ U_gap	physical interpretation
"null" (broken)	no	no	unphysical; motion doesn't close cycle → coherence lost
engine-native	yes	no	lab-frame motion, pulse-only detuning (engine default)
synced-phase	yes	yes	laser rotating frame maintained through train (Flag 1)

The "null" convention gave the 0.04 carrier number in my earlier cut and was rejected. The interesting comparison is engine-native vs synced-phase — two internally-consistent physical pictures that differ in where the laser phase reference lives.

2. Numerical comparison at selected (k, φ_α)

φ_α	conv	k=0	k=+1	k=+2	k=+5	k=−1	k=−5
0°	engine	0.924	0.048	0.032	0.025	0.048	0.025
0°	synced	0.924	0.932	0.919	0.580	0.914	0.563
90°	engine	0.894	0.048	0.036	0.048	0.036	0.003
90°	synced	0.894	0.907	0.924	0.891	0.805	0.064
180°	engine	0.924	0.048	0.032	0.025	0.048	0.025
180°	synced	0.924	0.933	0.919	0.580	0.914	0.564
270°	engine	0.943	0.036	0.020	0.003	0.048	0.048
270°	synced	0.943	0.840	0.701	0.064	0.931	0.856

At the carrier, the two conventions agree to within 0.001. At the sidebands, the engine-native amplitudes are ~20× smaller than synced-phase. Both show φ_α-dependent asymmetry between k = ±1 sidebands; the synced version shows it strongly (30% amplitude swing) while the engine version shows it weakly (10% amplitude swing on tiny baselines).

3. Where does the signal go?

Under synced-phase at |α| = 3: - Sum of |C|² over k ∈ {−11, …, +11} at φ_α = 0: ≈ 8.5 (dominant contribution from k ∈ [−4, +4]). Coherence spreads across many sidebands.

Under engine-native: - Sum of |C|² over k ∈ {−11, …, +11} at φ_α = 0: ≈ 0.87 (dominated by the single k = 0 spike with |C| = 0.924; all other sidebands summed contribute ~0.02). Coherence concentrated at carrier.

The engine-native case's "lost" signal (between teeth) presumably goes into σ_z (|Bloch| unchanged) — under engine-native the detuning rotates the spin only during pulses, producing a smooth Rabi-response centred at δ = 0 with width ~Ω_eff that looks nothing like a comb when oversampled at 30 kHz step (the "broad single peak" we recognised in earlier scans). The comb's "teeth" at k·ω_m are still there but narrow and weak.

4. Which convention is the lab seeing?

Under the user's statement "phase is kept synced for all pulses of a train" (2026-04-14), the synced-phase picture is the physically correct one. The engine-native convention is a modeling simplification that would be accurate only if the laser phase reference were reset per pulse.

If Hasse2024 reports a Rabi scan with a broad single peak at δ = 0 and no visible comb, there are two reconciliations:

The scan range is narrow (|δ| < 100 kHz), in which case both conventions look similar — the central tooth dominates in both.
The lab has in practice a mixed convention: phase is synced over pulses (by design), but some mechanism (phase noise, pulse-envelope modulation, probe-linewidth averaging) suppresses the comb structure below detection. The engine-native treatment might incidentally match the observed lineshape while being microscopically wrong.

This is the experimental question for the Schätz/Hasse correspondence: at what detuning range are scans reported, and is the comb observed? Until settled, v0.4 should present both conventions with explicit caveats.

5. Files

../numerics/run_2d_alpha3_unsynced.py — corrected to match engine convention (motional U_gap only).
../numerics/scan_2d_alpha3_unsynced.h5 — engine-native 2D data, 1001 × 64.
../numerics/plot_2d_alpha3_compare.py
../plots/scan_2d_alpha3_compare_overview.png — three-row × two-column side-by-side (|C|, arg C, σ_z).
../plots/scan_2d_alpha3_compare_tooth_envelope.png — per-tooth |C|(k, φ_α) heatmaps and traces.
This entry.

6. Outstanding

Which convention v0.4 presents as "canonical" depends on the experimental correspondence. Default stance: report synced-phase as the physics, document engine-native as the simulation simplification.
Possibly add a inter_pulse_spin_evolution toggle to the engine (opt-in, backward-compatible) so the synced-phase path becomes a first-class engine option rather than a driver-level patch. Worth discussing before v0.4 drafting.

Engine-native behaviour at α = 3 is fully characterised; the comb and its asymmetry are now unambiguously products of inter-pulse spin-δ phase accumulation.