Rocket Science · Open Research Platform · Breakwater Layer

Getting Started

Student onboarding · task assignments · deliverable formats

What Is This Project?

Hasse et al. (PRA 109, 053105, 2024) demonstrated a stroboscopic travelling-wave measurement scheme for a single trapped ²⁵Mg⁺ ion. A train of ~22 phase-locked Raman pulses — one per motional cycle — maps the ion's motional phase-space dynamics onto its spin state. The scheme uses an AC Stark lattice with effective wavelength λ_eff ≈ 140 nm (sub-optical resolution) and a Lamb–Dicke parameter η ≈ 0.4 (outside the usual small-η regime).

This dossier is a Breakwater Claim Analysis: it takes the paper's claims, classifies them (compatible / underdetermined / inconsistent), identifies discriminant conditions, and defines work packages to resolve the underdetermined claims. Three claims are settled. Five remain open — those are your tasks.

Your job in one sentence

Use the simulation infrastructure, analytic estimates, and the paper's experimental data to resolve the five underdetermined claims — or to demonstrate that they cannot yet be resolved and to state precisely what additional data or theory is needed.

Site Map

This table shows every page, what it contains, and whether it is infrastructure you use, reference you read, or a task you work on.

Page	Content	Role
Overview	Project summary, navigation, quick status	orientation
Dossier	Claim Analysis Ledger (L1–L8), Risk Register, Council Decisions	reference ✓
Framework	Hamiltonian, coupling operator, measurement channels, Lock-Key	reference ✓
Tutorial	Doppler mechanism, analytic estimates, work packages, starting points	task definitions
Numerics	Interactive viewer for simulation JSON (9 default runs)	tool
Simulate	Simulation page (browser engine not in this snapshot)	stub
Code	Simulation engine documentation (Hilbert space, Hamiltonian, observables)	reference ✓
Reference	Commented paper walk-through + 27-entry bibliography	reference ✓
Start	This page — onboarding, tasks, deliverable formats	orientation
Sail essay	Ideal-limit derivation with deviation analysis (30 pp.)	reference ✓

Reading Assignments

Read in this order. Budget approximately 4 hours for the essential tier.

essential Hasse et al. — the paper itself (arXiv). Read fully before anything else.

essential Framework + Tutorial — the Hamiltonian, Doppler mechanism, analytic estimates, and work packages.

essential Code §1–§5 — Hilbert space, Hamiltonian, stroboscopic protocol, initial state, observables. This tells you exactly what the simulator computes.

recommended Dossier — the Claim Ledger, Risk Register, and Council Decisions. Understand what L1–L8 mean and why some are settled.

recommended Sail essay §1–§3 — the ideal-limit derivation, deviation analysis, and Monroe comparison. This is where the physics arguments live.

recommended Bibliography — Leibfried2003 §II.D, §III (trapped-ion background). Follow the "new reader" path.

deep Full bibliography themes 3–7 — Monroe programme, BAE, tomography, phase-space methods. Consult as needed for specific WPs.

Tools at Your Disposal

You have a working quantum simulator and pre-computed reference data. Use them.

Simulate page (browser engine not in this snapshot)

The interactive browser simulator is part of the dossier architecture but is not included in this packaged snapshot. See REBUILD.md for instructions to restore it from the source repository.

For all systematic work, use the Python sweep engine below. Pre-computed data is available on the Numerics page.

Numerics page

numerics.html displays pre-computed default runs (9 datasets at N_max = 30–40). You can also upload your own JSON from the Simulate page. Use this for quick comparison and for loading reference data without re-running simulations.

Python / QuTiP

The Python sweep engine (scripts/stroboscopic_sweep.py) is the primary tool for systematic work. It uses the same Hamiltonian as the browser engine (exact Fock-basis expm, no LD truncation) with Float64 precision throughout. Three modes: single_run, sweep_1d, state_comparison. See ARCHITECTURE.md for design and usage.

Task Cards

Each task card corresponds to one work package. They are ordered by the Council's recommended sequence, but see the parallelism note below for which can run simultaneously.

Parallelism: WP-A.1, WP-A.2, WP-A.3, and WP-B can all run in parallel — they have no mutual dependencies. WP-C is gated on WP-A (all three sub-packages). WP-D is gated on WP-A + WP-C. Assign WP-B to a student who wants to start immediately with the simulator. Assign WP-A.1 or WP-A.3 to a student comfortable with analytic calculations.

WP-B Numerical Anchoring good first task

Goal: Confirm the analytic Doppler estimates against simulation, and explain the σ_z contrast difference between the two simulation methods.

resolves

Risk R5 (Doppler dominance needs explicit confirmation).

prerequisite reading

Tutorial — Doppler estimates table, Rabi instrument function, finite-pulse effects. Code §1–§5.

tools

scripts/stroboscopic_sweep.py --mode single_run — run detuning scans at α = 0, 1, 3, 5. Numerics page — view and compare default runs.

concrete steps

Step 1: Run the default parameters (η = 0.397, Ω/(2π) = 0.300 MHz, ω_m/(2π) = 1.30 MHz, 22 pulses, N_max = 50) for α = 0, 1, 3, 5. Verify your results match the default JSON runs on the Numerics page. Record the σ_z contrast (max−min)/2 for each α.
Step 2: From the simulation coherence plots, measure the coherence envelope FWHM (or half-width at half-maximum) at each α. Compare against the analytic prediction: Doppler width ∝ ηω_m√(2⟨n⟩ + 1).
Step 3: Compute the analytic Rabi instrument function P_↑(δ) = (Ω_R²/Ω_eff²)sin²(Ω_effτ/2) at the key detunings in the Tutorial table. Verify P_↑ drops to ~0.007 at δ_D^peak for α = 1.
Step 4: Investigate the contrast question: the default 22-pulse stroboscopic runs yield uniform contrast_z ≈ 0.56. The HDF5 adaptive-learner data shows 0.61 → 0.71 → 0.84 → 0.75. Propose and test an explanation for the difference (hint: consider detuning-point density near δ = 0 and the adaptive vs. uniform sampling grid).
Step 5: Run a δt sweep — vary the pulse count (e.g. 10, 22, 50, 100) at fixed α = 3 and observe how the spectrum changes. Does the coherence envelope width depend on N_p? It should not (total rotation is fixed at π/2), but the per-pulse Magnus correction changes.

deliverable format

Verification memo (1–3 pages, PDF or Markdown):
— Table: α, contrast_z (sim), coherence FWHM (sim), Doppler width (analytic), ratio
— Figure: overlay of simulation coherence envelope with analytic Doppler convolution
— Paragraph: explanation of contrast difference between methods
— Table: N_p sweep results (contrast, coherence width, max Fock leakage)
— All simulation JSON files attached with provenance hashes

worked micro-example

For α = 0: the analytic RMS Doppler width is σ_D/(2π) = ηω_m/(2π) = 0.52 MHz. The ratio σ_D/Ω = 1.73. From the simulation at α = 0, the coherence envelope (Bloch vector length vs. detuning) should show a central peak near δ = 0 with a width of order ~2 ω_m (the carrier plus first sidebands). Measure the detuning at which coherence drops to 0.95 (from ~1.00 on resonance) and compare with δ ≈ Ω. If they match to ~20%, the Doppler model is confirmed at α = 0. Proceed to α = 1, 3, 5.

WP-A.3 Backaction Scaling prerequisite for WP-C, D

Goal: Quantify the measurement backaction (unitary + projective) as a function of η, α, and N_p.

resolves

Claim L5 ("Backaction is small").

prerequisite reading

Sail essay §1.6 (two types of backaction). Code §5 (observable computation — purity, fidelity). Bibliography theme 4 (Braginsky, Caves, Clerk).

tools

scripts/stroboscopic_sweep.py — single runs report ⟨n⟩, Tr(ρ_m²), and F(ρ_m, ψ₀) vs. detuning. Use --mode sweep_1d for systematic parameter sweeps.

concrete steps

Step 1: Run the default scan at α = 0, 1, 3, 5 and read off the motional purity and fidelity at δ = 0 (on resonance, where backaction is maximal). Record Tr(ρ_m²) and F for each α.
Step 2: Sweep η at fixed α = 3: run η = 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6. Plot purity and fidelity at δ = 0 vs. η. Identify the η threshold where purity drops below 0.99, 0.95, 0.90.
Step 3: Sweep N_p at fixed η = 0.397, α = 3: run N_p = 5, 10, 22, 50, 100. The total rotation is always π/2 (per-pulse rotation adjusts). How does backaction scale with pulse count?
Step 4: For α = 3 at the default parameters, compute the quadrature moments: ⟨X⟩, ⟨P⟩, Var(X), Var(P) before and after the pulse train. This requires extending the simulation output (or post-processing the final state). The quadrature disturbance ΔVar(X), ΔVar(P) is the key backaction metric.
Step 5: Separate unitary and projective contributions: run the simulation without measurement (pure unitary evolution), compute motional purity. Then compute the conditional motional state after spin projection onto |↓⟩ and onto |↑⟩. The difference is the projective backaction.

deliverable format

Backaction budget table (2–4 pages):
— Table: η, α, N_p, Tr(ρ_m²) at δ=0, F at δ=0, ΔVar(X), ΔVar(P)
— Figure: purity vs. η at fixed α, with threshold lines
— Figure: purity vs. N_p at fixed η, α
— Statement: "At the experimental parameters (η=0.397, α=3, N_p=22), the unitary backaction reduces motional purity to [X] and fidelity to [Y]. Projective measurement on |↓⟩ further reduces purity to [Z]."
— Assessment: is L5 compatible, underdetermined, or inconsistent?

worked micro-example

Run α = 0, default parameters. On the Simulate page, observe the third plot panel (motional observables). At δ = 0, the motional purity should be very close to 1.0 (the ground state is barely disturbed because the α = 0 state has ⟨n⟩ = 0 and the coupling is weak at low occupation). At δ ≈ ±1 (near sidebands), purity dips — this is where spin–motion entanglement is maximal. The fidelity F(ρ_m, ψ₀) gives the overlap with the initial motional state. If F > 0.99 everywhere, backaction is small for this α.

WP-A.1 Coherent-State Signal Model prerequisite for WP-C, D

Goal: Build an analytic model for the detuning spectrum of a coherent state |α⟩, decomposing the signal into position (phase) and momentum (Doppler) channels, and bound the crosstalk between them.

resolves

Claim L2 ("Position → phase; momentum → Doppler spectrum").

prerequisite reading

Tutorial — Doppler mechanism, Rabi instrument function, finite-pulse effects. Sail essay §1.1–§1.4 (deviation analysis). Bibliography: Leibfried2003 §II.D.

concrete steps

Step 1: For a coherent state |α⟩ oscillating at ω_m, write the time-dependent position x(t) = x₀√2 |α| cos(ω_mt) and velocity v(t). At the stroboscopic sampling time (t = 0 by convention), compute the phase shift k_eff·x(0) and the Doppler shift k_eff·v(0) = 0 (velocity is zero at the position extremum). This is the "phase channel."
Step 2: Now compute the stroboscopic average: the analysis pulse acts at t = 0, but the accumulated signal from N_p pulses at different motional phases (if there is any phase slip) averages over the oscillation. At exact stroboscopic synchronisation, all pulses see the same phase — so v(0) = 0 and the Doppler channel carries only zero-point and quantum fluctuations.
Step 3: Compute the full Rabi lineshape convolved with the quantum velocity distribution of |α⟩. The velocity distribution is a Gaussian centred at v = 0 (at the stroboscopic sampling point) with width set by zero-point fluctuations + coherent amplitude. Compare this convolved lineshape with the simulation coherence envelope.
Step 4: Estimate the crosstalk: the position channel (phase shift) is k_eff·x₀√2|α| = 2η|α|. The momentum channel (Doppler width) is ηω_m√(2⟨n⟩+1). At what α does the phase shift exceed π (wrapping) and the channels become entangled?

deliverable format

Two-channel analytic model (3–5 pages):
— Equations: P_↑(δ₀; α) as convolution of Rabi lineshape with velocity distribution
— Figure: analytic coherence envelope overlaid on simulation for α = 0, 1, 3, 5
— Table: crosstalk bound vs. α (phase-channel leakage into Doppler, and vice versa)
— Assessment: is L2 compatible or underdetermined at the experimental parameters?

WP-A.2 Sideband Truncation Bounds

Goal: Compute sideband weights to order s = 3 using the Laguerre polynomial structure of the coupling matrix elements, and identify where truncation fails.

prerequisite reading

Framework — coupling structure. Tutorial — small-η expansion. Leibfried2003 §II.D (matrix elements of exp(iη(a+a†)) in Fock basis).

concrete steps

Step 1: Write out the matrix elements ⟨n'|exp(iη(a+a†))|n⟩ using the exact formula involving associated Laguerre polynomials. Compute numerically for n, n' = 0…10 at η = 0.397.
Step 2: Truncate to s = 0 (carrier only), s = 1 (±1 sidebands), s = 2, s = 3. For each truncation, compute the approximate detuning spectrum and compare with the exact (full-matrix) simulation at α = 0 and α = 3.
Step 3: Construct a "truncation validity map": for each (η, ⟨n⟩) pair, what is the maximum sideband order s needed to achieve <1% error in the detuning spectrum?
Step 4: Cross-reference the sideband and Doppler descriptions: show that the sideband sum and the velocity convolution give the same result for α = 1 (where both descriptions are tractable).

deliverable format

Truncation validity map (2–3 pages):
— Table: sideband weights |⟨n'|C|n⟩|² for s = 0…4 at η = 0.397, n = 0…5
— Figure: spectrum error vs. truncation order for α = 0, 1, 3, 5
— Contour plot: minimum s for 1% accuracy in (η, ⟨n⟩) plane
— Paragraph: sideband ↔ Doppler consistency check at α = 1

WP-C Tomographic Stress-Test gated on WP-A

Goal: Test whether the combined phase + Doppler readout can reconstruct non-trivial motional states (Fock, squeezed, cat), and bound the reconstruction fidelity under realistic noise.

resolves

Claims L4 (decoder fidelity) and L7 (nonclassical tomography).

prerequisite

WP-A.1 (signal model), WP-A.2 (truncation bounds), WP-A.3 (backaction budget). All must be complete.

concrete steps

C.1: Compute the map M: ρ → (phase shift, Doppler spectrum) for Fock states |n⟩ (n = 0–5), squeezed states (r = 0.5, 1.0), and cat states (α = 2, π-phase). Use the Simulate page with the appropriate initial states.
C.2: Test injectivity: are the output spectra distinguishable? Compute the trace distance or fidelity between the output spectra for pairs of input states. If two distinct input states produce the same output spectrum within noise, injectivity fails.
C.3: Add noise (projection noise N_rep = 100, 500, 1000; decoherence T₁ = 1000 μs, T₂ = 500 μs, heating = 10 q/ms) and repeat. At what noise level does discrimination fail?

deliverable format

Injectivity certificate + fidelity table (3–5 pages):
— Matrix: pairwise distinguishability between target states (ideal + noisy)
— Figure: output spectra for Fock |0⟩, |3⟩, squeezed, cat — overlaid
— Statement: injectivity holds/fails for [which states] at [which noise level]
— Assessment: L4 and L7 compatible / underdetermined / inconsistent

WP-D BAE Forward View gated on WP-A + WP-C

Goal: Determine whether there exists an accessible parameter regime where the stroboscopic coupling approximates a single-quadrature (BAE-compatible) measurement. If not, archive L6 as structurally inaccessible.

resolves

Claim L6 ("Structurally compatible with BAE"). Council decision: no rescue.

prerequisite

WP-A (backaction budget, signal model), WP-C (tomographic capability established). Bibliography theme 4 (Braginsky, Caves, Clerk).

concrete steps

Step 1: From the WP-A.3 η-sweep, identify the η range where backaction is predominantly single-quadrature (ΔVar(X) ≪ ΔVar(P) or vice versa). If no such range exists below η = 0.1, BAE is structurally inaccessible at this trap frequency.
Step 2: If a candidate regime exists, check whether it is experimentally accessible (requires λ_eff adjustment, different Raman geometry, or different trap frequency).
Step 3: Write the verdict: compatible (with parameter regime specified), or archive as "structurally inaccessible at η ≈ 0.4; would require η ≲ [threshold]."

deliverable format

BAE feasibility or archival (1–2 pages):
— Statement: L6 is [compatible at η ≤ X / archived as inaccessible]
— Evidence: η-sweep quadrature disturbance data from WP-A.3
— If compatible: specify the parameter regime and experimental requirements
— If archived: state the structural reason (exponential coupling at η ≈ 0.4 couples both quadratures)

Parallelism and Sequencing

Phase 1 (parallel — assign to separate students or pairs):
WP-B (numerical anchoring) — simulator-first, good for building intuition
WP-A.1 (signal model) — analytic + simulation comparison
WP-A.2 (truncation bounds) — mostly algebra + targeted simulation
WP-A.3 (backaction) — simulation-heavy, parameter sweeps

Phase 2 (gated — requires all Phase 1 complete):
WP-C (tomographic stress-test)

Phase 3 (gated — requires Phase 1 + Phase 2):
WP-D (BAE forward view)

Conventions

File naming

Name simulation outputs as WP-[id]_[description]_alpha[N].json, e.g. WP-B_contrast_alpha3.json. Include the provenance hash from the Simulate page in your write-up.

Units

Detuning in units of ω_m. Frequencies in MHz (cyclic, i.e. /(2π)). Time in μs. Lamb–Dicke parameter η is dimensionless. Motional occupation ⟨n⟩ is dimensionless. All spin observables are expectation values in [−1, +1].

Provenance

Every simulation result carries a SHA-256 hash. Include the hash when citing results. If you modify the simulation engine, bump the version string and document the change.

Deliverables

Submit as PDF or Markdown with attached JSON data files. Use the deliverable format specified in each task card. Include figures as inline images or linked SVGs. State your conclusion on each claim (compatible / underdetermined / inconsistent) with explicit justification.

When in doubt

UNDERDETERMINED is an acceptable and honest conclusion. The dossier does not require you to force a positive result. If the evidence is insufficient to resolve a claim, state precisely what additional data or theory is needed. That is a deliverable.