Fidelity of fermionic atom-number states subjected to tunneling decay

Atom-number states are a valuable resource for ultracold chemistry, atom interferometry and quantum information processing. Recent experiments have achieved their deterministic preparation in trapped few-fermion systems. We analyze the tunneling decay of these states, both in terms of the survival probability, and the non-escape probability, which can be extracted from measurements of the full counting statistics. At short times, the survival probability exhibits deviations from the exponential law. The decay is governed by the multi-particle Zeno time which exhibits a signature of quantum statistics and contact interactions. The subsequent exponential regime governs most of the dynamics, and we provide accurate analytical expressions for the associated decay rates. Both dynamical regimes are illustrated in a realistic model. Finally, a global picture of multi-particle quantum decay is presented.