# Optically probing Schwinger angular momenta in a micromechanical resonator

## TL;DR

This paper demonstrates the optical detection of phononic Schwinger angular momenta in a micromechanical resonator, enabling the study of two-mode quantum states and correlations in macroscopic mechanical systems.

## Contribution

It introduces a method to observe and manipulate phononic Schwinger angular momenta using optical detection and post-selection in a micromechanical resonator.

## Key findings

- Successful optical detection of phononic Schwinger angular momenta.
- Conditional preparation of two-mode squeezed states.
- Potential extension to high-dimensional symmetry groups.

## Abstract

We report an observation of phononic Schwinger angular momenta, which fully represent twomode states in a micromechanical resonator. This observation is based on simultaneous optical detection of the mechanical response at the sum and difference frequency of the two mechanical modes. A post-selection process for the measured signals allows us to extract a component of phononic Schwinger angular momenta. It also enables us to conditionally prepare two-mode squeezed (correlated) states from a randomly excited (uncorrelated) state. The phononic Schwinger angular momenta could be extended to high-dimensional symmetry (e.g. SU(N) group) for studying multipartite correlations in non-equilibrium dynamics with macroscopic objects.