# Multi-spatial-mode effects in squeezed-light-enhanced interferometric gravitational wave detectors

## TL;DR

This paper investigates how spatial mode mismatches affect the performance of squeezed-light-enhanced interferometric gravitational wave detectors and explores potential methods to mitigate these effects by squeezing higher-order modes.

## Contribution

It quantifies the impact of spatial mode mismatches on squeezed light in gravitational wave detectors and proposes squeezing higher-order modes to improve robustness, highlighting practical challenges.

## Key findings

- Mode mismatches cause degradation of squeezed states in interferometers.
- Squeezing higher-order modes can enhance robustness to mode mismatches.
- Independent optimization of squeeze angles is necessary for multiple modes.

## Abstract

Proposed near-future upgrades of the current advanced interferometric gravitational wave detectors include the usage of frequency dependent squeezed light to reduce the current sensitivity-limiting quantum noise. We quantify and describe the degradation effects that spatial mode-mismatches between optical resonators have on the squeezed field. These mode-mismatches can to first order be described by scattering of light into second-order Gaussian modes. As a demonstration of principle, we also show that squeezing the second-order Hermite-Gaussian modes $\mathrm{HG}_{02}$ and $\mathrm{HG}_{20}$, in addition to the fundamental mode, has the potential to increase the robustness to spatial mode-mismatches. This scheme, however, requires independently optimized squeeze angles for each squeezed spatial mode, which would be challenging to realise in practise.