# Mass-imbalanced fermionic mixture in a harmonic trap

## TL;DR

This paper investigates the properties of a small number of mass-imbalanced fermions interacting with an impurity in a harmonic trap, revealing differences from static impurity cases and exploring Efimov states.

## Contribution

It provides new insights into the shell structure, energy scaling, and Efimov states in mass-imbalanced fermionic mixtures with up to five particles.

## Key findings

- Dynamic light-impurity physics differs from static heavy-impurity.
- Calculated energies at unitarity and extrapolated to zero-range limit.
- Found Efimov states for systems with 2 to 4 particles, but not for 5+1 systems at explored mass ratios.

## Abstract

The mass-imbalanced fermionic mixture is studied, where $N\le5$ identical fermions interact resonantly with an impurity, a distinguishable atom. The shell structure is explored, and the physics of a dynamic light-impurity is shown to be different from that of the static heavy-impurity case. The energies in a harmonic trap at unitarity are calculated and extrapolated to the zero-range limit. In doing so, the scaling factor of the ground state, as well as of a few excited states, is calculated. In the $2 \le N \le 4$ systems, pure $(N+1)$ Efimov states exist for large enough mass ratio. However, no sign for a six-body Efimov state in the $(5+1)$ system is found in the mass ratio explored, $M/m \le 12$.