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Quantum Fisher-information limits of resonant nanophotonic sensors: why high-Q is not optimal even at the quantum limit

J. Sumaya-Martinez

TL;DR

Problem addressed: whether high quality factor remains optimal under quantum-limited readout for resonant nanophotonic sensors. Approach: model the slit as a phase-and-loss channel inside an MZI and compute QFI for coherent and Gaussian probes, showing the key metric is the phase generator derivative. Key contributions: analytic QFI expressions, demonstration that optimal geometry is determined by boundary-induced phase sensitivity rather than Q, and a practical design rule balancing phase sensitivity and losses. Significance: provides physically transparent guidelines for quantum-enhanced nanophotonic sensing applicable to a range of resonant sensors.

Abstract

We develop a quantum metrological framework for resonant nanophotonic sensors based on subwavelength Fabry--Perot slit cavities. Building on classical Fisher-information analyses of resonant transmission sensors, we model parameter encoding as a phase-and-loss quantum channel embedded in one arm of a Mach-Zehnder interferometer. We derive the quantum Fisher information (QFI) for coherent and Gaussian probe states under linear loss and show that, even at the quantum limit, optimal estimation precision is governed by the generator of parameter-dependent phase shifts rather than by the cavity quality factor. Consequently, the operating point that maximizes the QFI does not generally coincide with the maximum-Q resonance. Quantum resources enhance sensitivity but do not redefine the optimal geometry. Our results provide physically transparent design principles for quantum-enhanced nanophotonic sensing.

Quantum Fisher-information limits of resonant nanophotonic sensors: why high-Q is not optimal even at the quantum limit

TL;DR

Problem addressed: whether high quality factor remains optimal under quantum-limited readout for resonant nanophotonic sensors. Approach: model the slit as a phase-and-loss channel inside an MZI and compute QFI for coherent and Gaussian probes, showing the key metric is the phase generator derivative. Key contributions: analytic QFI expressions, demonstration that optimal geometry is determined by boundary-induced phase sensitivity rather than Q, and a practical design rule balancing phase sensitivity and losses. Significance: provides physically transparent guidelines for quantum-enhanced nanophotonic sensing applicable to a range of resonant sensors.

Abstract

We develop a quantum metrological framework for resonant nanophotonic sensors based on subwavelength Fabry--Perot slit cavities. Building on classical Fisher-information analyses of resonant transmission sensors, we model parameter encoding as a phase-and-loss quantum channel embedded in one arm of a Mach-Zehnder interferometer. We derive the quantum Fisher information (QFI) for coherent and Gaussian probe states under linear loss and show that, even at the quantum limit, optimal estimation precision is governed by the generator of parameter-dependent phase shifts rather than by the cavity quality factor. Consequently, the operating point that maximizes the QFI does not generally coincide with the maximum-Q resonance. Quantum resources enhance sensitivity but do not redefine the optimal geometry. Our results provide physically transparent design principles for quantum-enhanced nanophotonic sensing.

Paper Structure

This paper contains 13 sections, 10 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Classical slit Fabry--Perot phase and parameter dependence
  3. Quantum-channel model and interferometric protocol (Option A)
  4. Phase-and-loss encoding
  5. Mach--Zehnder interferometric readout
  6. Quantum Fisher information
  7. Coherent-state benchmark
  8. Gaussian quantum probes (squeezing)
  9. Main result: QFI versus quality factor
  10. Discussion and outlook
  11. Conclusion
  12. Connection between classical Fisher information and the quantum limit
  13. Role of loss and fundamental bounds in quantum metrology

Figures (2)

  • Figure 1: Comparison of normalized $Q(\theta)$ and normalized generator strength $(\partial_\theta\varphi)^2$ versus a representative parameter $\theta$. The maxima need not coincide, illustrating that resonance sharpness alone does not determine optimal estimation performance.
  • Figure 2: Representative (normalized) QFI for coherent and squeezed probes under loss in the MZI protocol. Quantum resources amplify sensitivity without shifting the optimal geometry governed by the phase generator.