2026-04-21 — Rabi-rate reconciliation (v0.2 — resolved)

Status: resolved. The v0.3 sweep adopts a per-train π/2 calibration (each train given its own Ω); the earlier single-Ω candidates are archived here for reference. Upstream: 2026-04-21-kickoff.md §9 Q1, now pointing to this memo.

1. History — three candidate values

Over the strobo 2.0 conversation three Rabi values were in play:

(A) t_π = 1.122 µs (original phrasing), equivalent to Ω/(2π) = π/(2π · 1.122 µs) = 0.4456 MHz.
(B) Ω/(2π) = 0.178 MHz (updated value from the user), t_π = 2.809 µs.
(C) Ω/(2π) = 0.300 MHz (Hasse 2024 Table II AC-beam, repo canonical).

None of these is a π/2-calibration for strobo 2.0's short trains: with B the trains deliver only N·θ_pulse ≈ π/9 (weak probe), with C about π/5, with A about π/4. Hasse 2024 uses its C value with N = 30 × 100 ns to deliver a full π/2 analysis rotation; a short strobo-2.0 train needs a stronger Ω to compensate for the shorter N·δt.

2. Current (v0.3) resolution — per-train π/2 calibration

Each strobo 2.0 train is now assigned the Ω that makes N · Ω · e⁻η²⁄² · δt = π/2:

Train	N	δt (ns)	Ω/(2π) (MHz)	source
T1	3	100	0.9008	π/2 calibration (v0.3)
T2	7	50	0.7722	π/2 calibration (v0.3)

This matches the Hasse App. D convention (π/2 per train) and makes the v0.3 amplitudes directly comparable to Hasse Fig. 2(b)'s 0.76(3) and Fig. 6's ±0.9 range.

3. |C|_vacuum predictions at all five values

At the clean anchor (δ₀ = 0, ϑ₀ = 0, |α| = 0) the coherence contrast reduces to the closed form

|C|_vacuum = |sin(N · Ω_eff · δt)|,   Ω_eff = Ω · e⁻η²⁄²,   e⁻η²⁄² = 0.9250.

| Ω/(2π) [MHz] | |C|_vac T1 | |C|_vac T2 | source | |-------------:|-------------:|------------:|--------------------------------------| | 0.178 | 0.305 | 0.354 | v0.1 pre-calibration sweep | | 0.300 | 0.500 | 0.573 | Hasse 2024 Table II AC (their N=30) | | 0.446 | 0.702 | 0.788 | from t_π = 1.122 µs | | 0.9008 | 1.000 | 0.966 | T1 π/2 calibration (v0.3) | | 0.7722 | 0.975 | 1.000 | T2 π/2 calibration (v0.3) |

The tool numerics/rabi_calibration.py generates this table and plots the full curve on plots/00_rabi_calibration.png. Engine cross-check (full Fock-basis) at the π/2 points:

T1 cal on T2 (Ω=0.901 MHz): closed form 0.966, engine 0.850 — 12 % below. The gap is the intra-pulse Magnus correction.
T2 cal on T2 (Ω=0.772 MHz): closed form 1.000, engine 0.919 — 8 % below. Same mechanism.

So at the π/2 calibration the engine returns |C| ≈ 0.92 on carrier at α = 0 — the main v0.3 sweep peak values (2026-04-21-sweep-complete.md §2) agree with this to within 3 % across all α.

4. Lab-feasibility note

The required Ω/(2π) ≈ 0.77–0.90 MHz is 2.6–3× higher than Hasse's Table II AC-beam value (0.300 MHz). Achieving it requires either (i) more AC-beam power on the ion or (ii) a different beam geometry. If the existing lab apparatus cannot reach these Rabi rates, strobo 2.0's native regime remains the weak-probe v0.1 setting and any experimental comparison against the v0.3 dataset would require a matched re-calibration.

5. Alternative read-off protocol (retained from v0.1)

If the lab prefers to re-measure rather than derive Ω from first principles, the original one-shot read-off still works: prepare a ground motional state, run T2 on carrier, fit the σ_z fringe to |C|_obs · sin(φ − φ*), and compare |C|_obs to column 3 of §3. The mapping is monotone and unambiguous on [0, 1] MHz.

v0.1 2026-04-21 — three-candidate memo, open pending lab input. v0.2 2026-04-21 — resolved via per-train π/2 calibration adopted for the v0.3 sweep. Candidates retained as reference; lab-feasibility note added.