# Experimentally accessible invariants encoded in interparticle correlations of harmonically trapped ultra-cold few-fermion mixtures

## TL;DR

This paper introduces a numerical method to identify a specific invariant in many-body correlations of ultra-cold fermion mixtures, aiding experimental analysis of interparticle interactions without affecting center of mass excitations.

## Contribution

A novel numerical approach to extract an invariant from correlations in ultra-cold fermion mixtures, facilitating experimental identification of eigenstates.

## Key findings

- Identification of a correlation-encoded invariant.
- Invariant enables labeling of center of mass excitations.
- Method applicable for arbitrary mass ratios.

## Abstract

System of a two-flavor mixture of ultra-cold fermions confined in a one-dimensional harmonic trap is studied in the frame of the center of mass. We present a numerical method of obtaining energetic spectra in this frame for an arbitrary mass ratio of fermionic species. We identify a specific invariant encoded in many-body correlations which enable one to determine an eigenstate of the Hamiltonian and to label excitations of the center of mass. The tool presented may be particularly useful in experimental analysis of the interparticle interactions which do not affect the center of mass excitations in a harmonic potential.