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Claim Analysis Ledger · Hasse et al. (PRA 2024)

One-Sentence Claim

Hasse et al. phase-lock four oscillators (MW reference, optical running-wave phase, spin, motion) and use a stroboscopic Raman pulse train on a short-period travelling polarisation gradient (λ_eff ≈ 140 nm, η_LF ≈ 0.40) to map an ion's motional phase-space dynamics with super-resolution, where position appears as a spin-fringe phase shift and the p-quadrature proxy appears through the characteristic Doppler-detuning spectrum of the analysis pulse, encoding the ion's velocity distribution.

Glossary

Momentum observable

A velocity / p-quadrature proxy inferred from the Doppler-detuning response of the stroboscopic analysis pulse.

Super-resolution

Position sensitivity at λ_eff ≈ 140 nm ≪ optical wavelength. Does not imply sub-x₀ or QND.

Sideband scaling ~η^s

Heuristic. Actual weights depend on n via Laguerre polynomials.

Detuning spectrum

P_↑(δ) as function of analysis-pulse detuning. Encodes velocity distribution via Doppler shift k_eff·v.

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Claim Analysis Ledger

Underdetermined → hold/. Intake: REQUEST unless SWEEP. The Ledger measures; it does not govern.

#	Claim	Status	Discriminant Condition
L1	Four-oscillator phase lock enables stroboscopic interrogation.	COMPATIBLE	Demonstrated experimentally.
L2	Position → phase; p-proxy → Doppler spectrum.	UNDETERMINED	Clean separation for η|α| ≪ 1 or instantaneous pulses. Quantify crosstalk vs. η, α, δt.
L3	"Super-resolution" position sensitivity.	COMPATIBLE	Geometric: λeff ≈ 140 nm.
L4	Decoder faithfully inverts phase + detuning response.	UNDETERMINED	Injectivity + noise stability for target states.
L5	Backaction is small ("near-coherent").	UNDETERMINED	Certification: Tr(ρ²), quadrature disturbance, coherent-state overlap.
L6	"Structurally compatible with BAE."	UNDETERMINED	Exhibit regime where interaction ≈ linear single-quadrature. Bound residual backaction.
L7	Nonclassical tomography feasible.	UNDETERMINED	Injectivity for Fock/squeezed/cat + noise stability.
L8	Phase lock stable over experimental timescales.	COMPATIBLE	Demonstrated. Long-term diffusion uncharacterised. SWEEP

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Evidence Summary

Experimentally established

Four-oscillator phase lock. AC Raman: λ_eff ≈ 140 nm, Ω/(2π) ≈ 0.3 MHz. η_LF ≈ 0.40, η_MF ≈ 0.23, η_HF ≈ 0.18. Timing: t_π/2,S ≈ 23.1 μs.

Analytically grounded

Coherent-state baseline: exp(−η²/2)·exp(i2η Re α). Sideband amplitudes from |0⟩: carrier 0.923, 1st 0.369, 2nd 0.074, 3rd 0.010.

Numerical calibration only

Full decoder for arbitrary states. Backaction beyond ⟨n⟩. Non-Gaussian behaviour. See Numerics for interactive data.

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Risk Register

#	Risk	Source	Severity
R1	Decoder without analytic error bounds.	Scout	High
R2	Phase–Doppler crosstalk at high α (L2).	Guardian, Cart.	Medium
R3	BAE regime narrow or inaccessible (L6).	All	Medium
R4	Injectivity failure for non-Gaussian states (L7).	Guardian, Scout	High
R5	Doppler dominance needs explicit confirmation.	Scout	Medium
R6	δ⟨n⟩ hides coherence redistribution (L5).	Guardian	Medium
R7	Inversion scales poorly with state complexity.	Cartographer	Low→High

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Strategic Resolution

Primary framing: Tomography. η ≈ 0.4 nonlinearity is an asset for characteristic function sampling, a liability for strict BAE. Guardian proviso: backaction first. L6: Undetermined (supervisor). WP-D: no rescue.

Council Decisions

Item	Decision	Justification
Primary framing	Tomography	η ≈ 0.4 is asset for χ(ξ), liability for BAE.
L6	Undetermined	Not established, not excluded.
BAE	Forward view (WP-D)	No rescue.
Sequence	A.3→A.1→A.2→B→C→D	Backaction prerequisite.
Momentum	Doppler detuning primary	δD/Ω ≫ 1 for α ≥ 1.