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Beating the spectroscopic Rayleigh limit via post-processed heterodyne detection

Wiktor Krokosz, Mateusz Mazelanik, Michał Lipka, Marcin Jarzyna, Wojciech Wasilewski, Konrad Banaszek, Michał Parniak

TL;DR

The paper addresses surpassing the spectroscopic Fourier limit by post-processing heterodyne measurements. It introduces a time-resolved heterodyne approach with Hermite-Gauss mode projections to extract sub-Fourier spectral separation for two Gaussian lines, demonstrated for thermal and phase-averaged coherent sources. Precision limits are derived from Fisher information and the Cramér-Rao bound, and validated experimentally with large pulse ensembles, showing saturation of the CRB and improvement over direct sensing. This provides a practical, accessible route to spectral superresolution in systems where a simple measurement setup is advantageous, with potential applications in optomechanics, lasing microstructures, and quantum transducers.

Abstract

Quantum-inspired superresolution methods surpass the Rayleigh limit in imaging, or the analogous Fourier limit in spectroscopy. This is achieved by carefully extracting the information carried in the emitted optical field by engineered measurements. An alternative to complex experimental setups is to use simple homodyne detection and customized data analysis. We experimentally investigate this method in the time-frequency domain and demonstrate the spectroscopic superresolution for two distinct types of light sources: thermal and phase-averaged coherent states. The experimental results are backed by theoretical predictions based on estimation theory.

Beating the spectroscopic Rayleigh limit via post-processed heterodyne detection

TL;DR

The paper addresses surpassing the spectroscopic Fourier limit by post-processing heterodyne measurements. It introduces a time-resolved heterodyne approach with Hermite-Gauss mode projections to extract sub-Fourier spectral separation for two Gaussian lines, demonstrated for thermal and phase-averaged coherent sources. Precision limits are derived from Fisher information and the Cramér-Rao bound, and validated experimentally with large pulse ensembles, showing saturation of the CRB and improvement over direct sensing. This provides a practical, accessible route to spectral superresolution in systems where a simple measurement setup is advantageous, with potential applications in optomechanics, lasing microstructures, and quantum transducers.

Abstract

Quantum-inspired superresolution methods surpass the Rayleigh limit in imaging, or the analogous Fourier limit in spectroscopy. This is achieved by carefully extracting the information carried in the emitted optical field by engineered measurements. An alternative to complex experimental setups is to use simple homodyne detection and customized data analysis. We experimentally investigate this method in the time-frequency domain and demonstrate the spectroscopic superresolution for two distinct types of light sources: thermal and phase-averaged coherent states. The experimental results are backed by theoretical predictions based on estimation theory.
Paper Structure (5 sections, 13 equations, 2 figures)

This paper contains 5 sections, 13 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Heterodyne superresolving estimation
  3. Precision limits
  4. Results
  5. Summary

Figures (2)

  • Figure 1: The experimental setup takes in a laser beam, which is then split in two using a half-wave plate $\left(\lambda/2\right)$ and a polarizing beam splitter (PBS). Both beams are then transmitted into one of the acousto-optic modulators (AOMs), which encode the local oscillator (LO) frequency as well as the programmatically set signal. The quarter-wave plate $\left(\lambda/4\right)$, convex lens, beam stop and mirror constitute a double pass AOM setup. Once the laser light is properly modulated, the two signals are then joined together and directed into a differential photodiode (DPD). Finally, the heterodyne signal is collected and I/Q demodulated.
  • Figure 2: Plots representing the measured separation estimation precision in the case of thermal (a) and phase-averaged coherent (b) states. Each of the plots corresponds to a single $\mathcal{S}$ value, shown in ascending order. The data points are compared with the CRB given by the calculated FI for heterodyne sensing (solid curves) and DS (dashed curves). The error bars correspond to 2 standard deviations of the evaluated measured precision. The insets represent the estimator bias for each data point in the main plot.