Interacting non-Hermitian ultracold bosonic systems in three-dimensional harmonic trap: two-body exact solutions and high-order exceptional points.

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 $s$. What is even more interesting is that 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. These results could provide a convenient route towards more powerful sensor devices in spinor cold atomic systems.