# Interacting non-Hermitian ultracold atoms in a harmonic trap: Two-body exact solution and high-order exceptional point

## TL;DR

This paper provides an exact solution for interacting ultracold atoms in a 3D harmonic trap with non-Hermitian effects, revealing high-order exceptional points with ultra-sensitive spectral responses useful for advanced sensing.

## Contribution

It introduces an exact two-body solution for non-Hermitian ultracold atoms and establishes a general principle for creating high-order exceptional points with enhanced spectral sensitivity.

## Key findings

- Existence of third- and fifth-order exceptional points in the system
- Spectral response sensitivity scales as rac{1}{3} and rac{1}{5} around EPs
- Proposed detection method via probability dynamics

## Abstract

We study interacting ultracold atoms in a three-dimensional (3D) harmonic trap with spin-selective dissipations, which can be effectively described by non-Hermitian parity-time ($\mathcal{PT}$) symmetric Hamiltonians. By solving the non-Hermitian two-body problem of spin-1/2 (spin-1) bosons in a 3D harmonic trap exactly, we find that the system can exhibit third-order (fifth-order) exceptional point (EP) with ultra-sensitive cube-root (fifth-root) spectral response due to interaction anisotropies in spin channels. We also present the general principle for the creation of high-order EPs and their spectral sensitivities with arbitrary particle number $N$ and arbitrary spin $s$. Generally, with spin-independent interactions, the EP order of bosons can be as high as $2Ns+1$, and the spectral response around EP can be as sensitive as $\sim \epsilon^{1/(2ks+1)}$ under a $k$-body interaction anisotropy. Moreover, we propose to detect the ultra-sensitive spectral response through the probability dynamics of certain state. These results suggest a convenient route towards more powerful sensor devices in spinor cold atomic systems.