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

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 (PT) symmetric Hamiltonians. By exactly solving the non-Hermitian two-body problem of spin-1/2 (spin-1) bosons in a 3D harmonic trap, we find that the system can exhibit third-order (fifth-order) exceptional points (EPs) with ultrasensitive 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 similar to epsilon(1/(2ks+1)) under a k-body interaction anisotropy. Moreover, we propose to detect the ultrasensitive 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.