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arxiv: 2604.27214 · v1 · submitted 2026-04-29 · ⚛️ physics.optics

Measurement of complex scattering matrix in a nano-cavity array for boundary scattering tomography

Andrew Tang , Romil Audhkhasi , Virat Tara , Abhi Saxena , Gokul Nath , Arka Majumdar This is my paper

Pith reviewed 2026-05-07 10:13 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords silicon photonicscoupled cavity arrayscattering matrixhomodyne detectionboundary tomographyquantum simulationracetrack resonators
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The pith

Boundary homodyne measurements along one edge reconstruct the full scattering matrix of a silicon photonic cavity array.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that an on-chip homodyne setup confined to a single boundary of a 3 by 3 silicon photonic racetrack resonator array can measure the complex scattering matrix and thereby reconstruct the edge scattering matrix. This replaces approaches that require imaging scattered light from internal resonators or adding dedicated scatterers, both of which reduce scalability in foundry-compatible devices. The boundary-only method supports Hamiltonian tomography in two-dimensional coupled cavity arrays intended for quantum simulation. A sympathetic reader would care because simpler characterization removes a practical barrier to using these arrays as programmable quantum simulators.

Core claim

We experimentally demonstrate an on-chip homodyne measurement setup along a single boundary of a 3×3 silicon photonic racetrack resonator array and reconstruct the system's edge scattering matrix.

What carries the argument

The on-chip homodyne detection setup that collects complex-valued boundary data to reconstruct the edge scattering matrix without internal access.

Load-bearing premise

Homodyne measurements collected only along one boundary are sufficient to accurately reconstruct the full edge scattering matrix without requiring bulk cavity access or additional built-in scatterers.

What would settle it

A direct comparison showing that the boundary-reconstructed matrix fails to predict the array's measured transmission or reflection spectra at multiple ports would falsify the reconstruction claim.

Figures

Figures reproduced from arXiv: 2604.27214 by Abhi Saxena, Andrew Tang, Arka Majumdar, Gokul Nath, Romil Audhkhasi, Virat Tara.

Figure 1
Figure 1. Figure 1: Complex scattering matrix measurement along a single edge of a 2D CCA array. Dark purple view at source ↗
Figure 2
Figure 2. Figure 2: A) The complete architecture consisting of 2D CCA and the phase measurement structures, view at source ↗
Figure 3
Figure 3. Figure 3: A) S11-port measurements on the outer edge of the CCA in blue with fitting in orange as a function of phase difference between MZI arms, θ. B) Normalized fitted complex transmission with real and imaginary components plotted separately view at source ↗
Figure 4
Figure 4. Figure 4: A) Remaining S-port measurements along a single edge of the CCA as a function of phase view at source ↗
read the original abstract

On-chip silicon photonic coupled cavity arrays (CCA) are a promising platform for quantum simulators, with access to high Quality (Q) factor resonators, tunability, and foundry compatibility. Furthermore, scalable two-dimensional (2D) silicon photonic CCAs allow for simulation of rich physical phenomena via Hamiltonian engineering. However, complete reconstruction of the Hamiltonian is limited by access to cavities in the bulk, with current approaches relying on imaging scattered light from bulk resonators. These approaches often require additional scatterers to be built in, limiting scalability, while also being hampered by imaging technology in the near-infrared range. Instead of these approaches, Hamiltonian tomography algorithms that require homodyne boundary measurements have been demonstrated in literature, however measurements of complex scattering measurements along a CCA boundary have not been shown. Here, we experimentally demonstrate an on-chip homodyne measurement setup along a single boundary of a $3\times 3$ silicon photonic racetrack resonator array and reconstruct the system's edge scattering matrix.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript experimentally demonstrates an on-chip homodyne measurement setup along a single boundary of a 3×3 silicon photonic racetrack resonator array and reconstructs the system's edge scattering matrix, positioning this as an alternative to bulk-access methods for Hamiltonian tomography in coupled-cavity arrays.

Significance. If the single-boundary reconstruction is shown to be unique and accurate, the result would provide a scalable, foundry-compatible route to characterize edge scattering without additional bulk scatterers or near-IR imaging, directly addressing a key limitation in 2D photonic quantum simulators.

major comments (2)
  1. [Results / Reconstruction section] The central claim that homodyne data collected exclusively along one boundary suffices to reconstruct the full edge scattering matrix for a 3×3 coupled array is load-bearing; the manuscript must demonstrate that the linear map from measured complex amplitudes to matrix elements is invertible (or provide the explicit regularization/priors used), as the skeptic note correctly flags potential rank deficiency without verified constraints such as reciprocity or known loss rates.
  2. [Abstract and Results] No quantitative reconstruction fidelity metrics, error bars on the extracted matrix elements, or comparison against independent calibration (e.g., known device parameters or full-boundary reference data) are referenced in the abstract or described in the provided text; these are required to substantiate that the inverse problem has been solved rather than merely fitted.
minor comments (2)
  1. Clarify the precise definition of the 'edge scattering matrix' (e.g., which couplings are included versus internal Hamiltonian terms) and how it is distinguished from the full system scattering matrix.
  2. Add details on phase calibration, stability of the homodyne setup, and any post-processing steps used to extract complex amplitudes from the raw measurements.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which help clarify the presentation of our experimental results on boundary scattering matrix reconstruction. We provide point-by-point responses below and have revised the manuscript to address the concerns raised.

read point-by-point responses

  1. Referee: [Results / Reconstruction section] The central claim that homodyne data collected exclusively along one boundary suffices to reconstruct the full edge scattering matrix for a 3×3 coupled array is load-bearing; the manuscript must demonstrate that the linear map from measured complex amplitudes to matrix elements is invertible (or provide the explicit regularization/priors used), as the skeptic note correctly flags potential rank deficiency without verified constraints such as reciprocity or known loss rates.

    Authors: We agree that an explicit demonstration of invertibility is essential for the central claim. Our reconstruction employs the known reciprocity of the passive silicon photonic circuit together with independently measured resonator loss rates as constraints. In the revised manuscript we have added a dedicated subsection in Results that constructs the explicit linear map from the four complex homodyne amplitudes (measured along the single boundary) to the nine edge scattering matrix elements. We show that this map is full rank once reciprocity and the measured loss rates are imposed, and we report the condition number of the resulting operator. The derivation and the explicit matrix are now included in the main text with supporting details moved to the supplementary information. revision: yes

  2. Referee: [Abstract and Results] No quantitative reconstruction fidelity metrics, error bars on the extracted matrix elements, or comparison against independent calibration (e.g., known device parameters or full-boundary reference data) are referenced in the abstract or described in the provided text; these are required to substantiate that the inverse problem has been solved rather than merely fitted.

    Authors: We acknowledge that the original submission lacked these quantitative indicators. In the revised manuscript we have added error bars on each extracted matrix element derived from the measured homodyne noise floor, a scalar reconstruction fidelity metric that quantifies agreement with the design parameters, and a direct comparison against an independent calibration dataset obtained from a separate full-boundary measurement on the same device. These additions are now summarized in the abstract and presented with the corresponding figures and tables in the Results section. revision: yes

Circularity Check

0 steps flagged

No significant circularity; experimental measurement with external reconstruction method

full rationale

The paper is framed as an experimental demonstration of homodyne boundary measurements on a 3x3 silicon photonic array followed by reconstruction of the edge scattering matrix. No derivation chain, fitted model, or predictive step is presented that reduces by construction to the inputs. The reconstruction is attributed to established Hamiltonian tomography algorithms cited from the literature rather than derived or fitted within the paper itself. No self-citation load-bearing steps, self-definitional relations, or ansatz smuggling are identifiable from the provided text. The central claim rests on the sufficiency of single-boundary data, which is an empirical question addressed by the experiment rather than a tautological reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work is an experimental demonstration relying on standard linear optics and homodyne detection principles rather than new theoretical constructs or fitted parameters.

axioms (1)
  • standard math Linear response and phase-sensitive detection assumptions standard to homodyne measurements in photonic systems
    Implicit in the description of the on-chip homodyne setup for complex scattering matrix extraction.

pith-pipeline@v0.9.0 · 5483 in / 1159 out tokens · 70662 ms · 2026-05-07T10:13:54.579779+00:00 · methodology

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Reference graph

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