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We show that arbitrarily high-order exceptional points (EPs) can be achievedin a repulsively interacting two-species Bose gas in one dimension. By exactlysolving the non-Hermitian two-boson problem, we demonstrate the existence ofthird-order EPs when the system is driven across the parity-time symmetrybreaking transition. We further address the fourth-order EPs with three bosonsand generalize the results to $N$-body system, where the EP order can be ashigh as $N+1$. Physically, such high order originates from the intrinsicferromagnetic correlation in spinor bosons, which renders the entire systemcollectively behave as a single huge spin. Moreover, we show how to createultra-sensitive spectral response around EPs via an interaction anisotropy indifferent spin channels. Our work puts forward the possibility of atomicsensors made from highly controllable ultracold gases.

High order exceptional points in ultracold Bose gases