# One-sided SiN atom-hole temporal-to-pole campaign Date: 2026-08-30 Campaign: `sin300_one_port_atom_hole_temporal_q_v1` ## Purpose This campaign transfers the successful Fryett temporal-discovery followed by moving-pole lifetime optimization to a geometry intended for an optically trapped atom. The atom occupies a protected air region, so no topology update can move dielectric into the tweezer aperture. The first stage asks the one-sided input mode to produce a prescribed cavity-like temporal field at the atom. The second stage optimizes the lifetime of the pole that the first stage actually forms. ## Immutable physical contract - Vacuum wavelength at discovery: 780 nm. - Material: nondispersive SiN with index 2 in air. - Slab: 300 nm thick. - Design region: 8 um by 8 um in the slab plane. - Atom: at the origin, polarized along z. - Opening: a through-slab air disk of diameter at least 1 um. Every 50 nm square intersecting the exact radius-0.5 um disk is fixed to air, so the staircase aperture conservatively contains the requested circle. - Port: one x-directed, 500 nm-wide SiN waveguide attached only at the positive x edge. A TM-like fundamental mode is launched toward negative x. - Symmetry: y magnetic and z electric mirror planes; x is explicit. The reduced energy integral is multiplied by four. - Parameterization: 12,800 stored direct 50 nm pixels, of which 11,605 are trainable after the hole, outer-air guard, and exact port pin. There is no spatial filter, projection, binarization, periodic template, or density penalty. - Initialization: density 0.5 on every trainable pixel, zero in fixed air, and one in the pinned waveguide attachment. Fifty nanometres is chosen deliberately. The comparable one-sided 8 um square at 25 nm was already found to exceed the 12 GB reverse-tape envelope. With y/z symmetry, this campaign has a 202 by 95 by 25 reduced grid and 20,980 time steps on the fixed 2 ps tape, comparable to the proven 16 um Fryett solve. ## Stage A: absolute temporal discovery Let the complex local form of the propagated Gaussian port pulse be `s(t)`. The exact discrete normalized target pole obeys \[ a_{k+1}=e^{-(\gamma+i\omega_0)\Delta t}a_k +(1-e^{-\gamma\Delta t})s_k, \qquad \gamma=\frac{\omega_0}{2Q_t}. \] The target values are `Q_t=10,000`, beta one, physical mode volume `V_t=0.1 um^3`, and z-polarized unit overlap at the atom. The corresponding Purcell factor is \[ F_t=\frac{3}{4\pi^2}\lambda_0^3\frac{Q_t}{V_t}, \] because the emitter is fixed in air. The target trace is the analytically delayed prompt mode plus `sqrt(beta F_t)` times the causal pole coordinate. Its amplitude and phase are fixed; there is no fitted target scale. For the measured vector field `E(r_atom,t)`, the sole discovery scalar is \[ J_t=-\frac{\sum_k\|\mathbf E_k-\hat z E_{t,k}\|^2} {\sum_k |E_{t,k}|^2}. \] Raw Adam uses learning rate 0.01 and persistent first/second moments. One 2 ps forward/adjoint pair is exactly one update. There is no line search or rejected Adam step. Stage A runs for at least 150 applied updates and continues longer if necessary. Handoff requires a valid single-pole fit, field/energy Q agreement within 25%, and conservative Q at least 100; iteration count alone cannot activate Stage B. ## Pole, Q, and mode-volume telemetry After the pulse is clear, the centered Ez trace is fitted twice, with the second pass recentered on the first fitted frequency. Total electromagnetic energy is independently fitted at that same pole frequency. The reported Q is \[ Q_{\rm trusted}=\min(Q_E,Q_U). \] The atom-oriented effective volume uses the same three source-off windows: \[ V_{\rm eff}=\frac{4\langle U_{\rm reduced}\rangle} {\epsilon_{\rm air}\langle|E_z(\mathbf r_a)|^2\rangle}. \] Here the local permittivity is exactly one by immutable construction, avoiding the moving-center-permittivity error found in the Fryett telemetry. The plotted normalization uses the same fitted wavelength, \[ \widetilde V=V_{\rm eff}/\lambda_{\rm pole}^3. \] The relative spread of V across all three windows is stored as an explicit single-mode consistency diagnostic. The outgoing-mode overlap is telemetry, not a beta claim: physical beta requires a dipole-driven port/total-loss audit. ## Rejected unconstrained-Q branch The first Stage-B experiment optimized Q alone. It raised trusted Q from 551.341 to 3619.222 in eighteen accepted updates, but atom-oriented normalized mode volume increased from about 4.4 to 17.853 and the field visibly moved away from the aperture. That branch is immutable negative-ablation evidence. The live successor deterministically replays the preserved update-13 Adam state to the exact pre-Q handoff and does not seed from the displaced-field geometry. ## Stage B: moving-pole Q with a hard atom-volume ceiling The handoff preserves the exact evaluated density, resets coordinate-specific optimizer memory because the objective changes, recenters the source on the measured pole, and starts at raw-density trust radius 0.003. The differentiated scalar becomes the log harmonic consensus \[ J_Q=\log\left(\frac{2Q_EQ_U}{Q_E+Q_U}\right). \] The pre-Q geometry is evaluated once in the recentered pole scene and its physical atom-oriented mode volume is frozen as `V_h`. Every accepted geometry must satisfy \[ V_{\rm eff}\le (1+0.002)V_h. \] The 0.2% numerical allowance is more than ten times the handoff's three-window V spread; it accommodates estimator noise without providing a cumulative volume budget. The ceiling never ratchets upward. Ten-pair L-BFGS-B supplies a Q-ascent direction. A second reverse sweep at the same density differentiates `log(V_eff)`. If the Q proposal points toward increasing V, it is orthogonally projected into the local feasible halfspace \[ \nabla\log V_{\rm eff}\mathbin{\cdot}d\le0. \] Alternating box and halfspace projections retain this condition after material clipping. The trial is then replayed. Acceptance requires a trustworthy dual pole fit, strict Q-objective gain, standard actual/predicted agreement, and the global frozen volume ceiling. Both gradients are cached, so a rejected radius costs only a forward replay. Agreement below 0.10 rejects and halves the step; a boundary-using agreement above 0.75 expands it by 1.5. A clipped lower-bound rejection clears stale curvature rather than submitting an identical candidate forever. Frequency is telemetry, not a constraint. When accepted drift reaches one 1 THz source bandwidth, the Gaussian carrier and fit center move to the pole, the cross-scene secant is suppressed, and optimization resumes. This avoids the fixed-frequency wall that stopped the earlier Fryett Q campaign. Stage B runs indefinitely, including after Q=100,000, until explicitly paused. ## Deliberate omissions and future work There is no Q-dependent density cap, temporal minibatching, amplitude-agnostic target fit, source optimization, beta objective, binarization, or smooth boundary stage. Mode volume is a feasibility constraint rather than a weighted objective, so no penalty coefficient can silently trade the atom field away. The temporal stage establishes the one-port, atom-overlapping architecture; the constrained lifetime stage tests how much Q that architecture supports. Physical beta, gradual completion of binarization, and a subpixel smooth-boundary continuation remain separate audited successors.