Buildup of symmetrization entanglement for the nonescape probability of two identical particles

Abstract

We study the nonescape probability for tunneling decay of two identical noninteracting particles which are entangled due to symmetrization. As a consequence, the two-particle nonescape probability, which gives the probability that the particles remain within the potential region, may be written as the sum of two terms: a direct term and an exchange term which is added or subtracted according to symmetrization. At the initial time the direct term decays exponentially in the usual way, but the exchange term vanishes due to the orthonormality of the initial states. As time evolves the exchange term builds up until it becomes comparable to the direct term at time ${t}_{0}$. Thereafter, the symmetric and antisymmetric nonescape probabilities decay in a distinctive way. The buildup time typically lasts several lifetimes and implies that during the relevant exponentially decaying regime the probability of finding the particles within the interaction region is insensitive to the symmetry of the decaying particles. That is, the particles decay as if they were distinguishable. This might be experimentally verified in the tunneling decay of atoms in ultracold gases.