Superresolution in separation estimation between two dynamic incoherent sources using spatial demultiplexing

TL;DR

This paper investigates the robustness of spatial mode demultiplexing (SPADE) for superresolution separation estimation between two dynamic incoherent sources, focusing on non-stationary scenarios like rotations and oscillations, and proposes a measurement algorithm to maintain precision.

Contribution

It extends SPADE-based superresolution analysis to non-stationary sources, demonstrating robustness and proposing a method to reduce parameter estimation complexity.

Findings

SPADE remains effective for dynamic sources with rotations and oscillations.

Fisher information analysis confirms robustness of measurement precision.

A new measurement algorithm reduces estimation parameters without losing accuracy.

Abstract

Achieving resolution in the sub-Rayleigh regime (superresolution) is one of the rapidly developing topics in quantum optics and metrology. Recently, it was shown that perfect measurement based on spatial mode demultiplexing (SPADE) in Hermite-Gauss modes allows one to reach the quantum limit of precision for estimation of separation between two weak incoherent stationary sources. Since then, different imperfections such as misalignment or crosstalk between modes have been studied to check how this result translates into more realistic experimental setups. In this paper, we consider another deviation from the perfect setup by discarding the assumption about the stationarity of the sources. This is relevant for example for astrophysical applications where planets necessarily orbit around the star. We analyze two examples of dynamics: rotations and oscillations, showing the robustness of the SPADE-based measurement against them. The analysis is based on Fisher information, which allows one to obtain the precision limit through Cram\'er-Rao bound. Furthermore, we formulate a measurement algorithm that allows for the reduction of one parameter for estimation (system orientation angle) in the stationary sources scenario, maintaining the measurement precision despite the lack of knowledge about this parameter.