Discriminant Sheet
Frequency-Agile Light for Hybrid Optomechanical Control
1 Purpose
This sheet states the single falsifiable prediction that separates the chirped-photonics programme from incremental improvement of existing optomechanical control. If the discriminant is satisfied, the programme warrants coastline status. If it is null, the scaffold collapses to a technology-transfer project and should be reclassified accordingly.
2 The Discriminant
3 Falsifiability Structure
| Outcome | Observation | Consequence |
|---|---|---|
| POSITIVE | |A| > 0 at ≥ 3σ for at least one chirp rate, and A → 0 as r → 0 | Frequency-trajectory control is a distinct regime. Coastline warranted. |
| NULL | A consistent with zero across all accessible chirp rates | No directional advantage. Programme reduces to engineering improvement. |
| ANOMALOUS | |A| > 0 but sign flips with chirp rate | Nontrivial dynamics present. Extend investigation; coastline deferred. |
4 Why This Discriminant
In a static-detuning experiment, there is no preferred direction of frequency approach; the laser sits at a fixed offset and the system responds symmetrically. A nonzero A therefore cannot arise from static control. It requires that the history of the frequency trajectory leaves a measurable imprint on the coupled optomechanical dynamics.
Hysteresis control. WGM resonators generically exhibit thermal bistability, which can produce direction-dependent effects even under slow frequency scans. To exclude generic hysteresis as the origin of a nonzero A, the POSITIVE outcome requires A → 0 in the quasi-static limit (r → 0). The discriminant is sharpened: the programme claims that non-adiabatic traversal constitutes a distinct resource.
Secondary observables (optional). The binary capture outcome is robust but coarse. If A ≠ 0, finer observables can distinguish mechanism: (a) capture-time distribution, (b) post-capture oscillation amplitude, (c) transient centre-of-mass displacement.
5 Minimal Experimental Test
System: SiO₂ microsphere (⌀ ~ 30–80 µm), optically levitated in vacuum, probe near 1550 nm.
Protocol: (i) Prepare identical launch conditions. (ii) Apply linear chirp across an identified WGM resonance at rate r. (iii) Alternate sign of r shot-to-shot. (iv) Record binary outcome: captured / not captured. (v) Repeat at N ≥ 100 per chirp rate, scan r over 2–3 decades. (vi) Control: repeat in quasi-static sweep limit; require A → 0 as r → 0.
Required from Breunig platform: (a) Shot-to-shot chirp-rate reproducibility Δr/r < 1%. (b) Trigger synchronisation to launch event at ≤ 10 ns jitter. (c) Instantaneous linewidth during chirp < WGM linewidth. (d) Minimum achievable chirp rate in the kHz–MHz matching range.
6 Generalisation
The chirp-direction asymmetry is not specific to WGM systems. An analogous discriminant can be defined for any resonant system where a chirped probe traverses a narrow feature coupled to a motional degree of freedom: cavity-coupled atoms in flight, optically levitated nanoparticles near photonic crystal cavities, or ion–cavity systems with Doppler broadening. In each case, the test is: does the direction of traversal matter?
Harbour position: Pre-Coastline discriminant sheet. If POSITIVE → seed Coastline “Frequency-Trajectory Control of Resonant Systems.” If NULL → archive as Sail “Chirped Photonics: An Interpretive Note.”