We show that arbitrarily-high-order exceptional points (EPs) can be achieved in a repulsively interacting two-species Bose gas in one dimension. By exactly solving the non-Hermitian two-boson problem, we demonstrate the existence of third-order EPs when the system is driven across the parity-time symmetry-breaking transition. We further address the fourth-order EPs with three bosons and generalize the results to the $N$-body system, where the EP order can be as high as $N+1$. Physically, such high order originates from the intrinsic ferromagnetic correlation in spinor bosons, which causes the entire system to collectively behave as a single huge spin. Moreover, we show how to create an ultrasensitive spectral response around EPs via an interaction anisotropy in different spin channels. Our work puts forward the possibility of atomic sensors made from highly controllable ultracold gases.

• Received 9 November 2018

DOI:https://doi.org/10.1103/PhysRevA.99.011601