The atomic nucleus is not just a bag of protons and neutrons. It is a quantum system where particles are bound by invisible threads of entanglement. When two protons or neutrons interact, their states become intertwined so that describing one without the other is impossible.
Scientists took measures of entanglement (entropy, mutual information, and relative entropy) and applied them to neon, magnesium, and silicon nuclei. These nuclei lie near the so-called island of inversion, where the usual order of energy levels flips. Calculations showed that in ground states, entanglement between protons and neutrons is weak, but between identical particles it is strong. But when the nucleus gets excited, proton-neutron correlations become just as strong as those between identical particles.
This is like a dance floor: in a calm state, pairs dance with themselves, but when the music speeds up, everyone starts swapping partners. Such a picture helps explain why some neutron-rich nuclei behave differently than the simple shell model predicts. Entanglement turns out to be a sensitive tool that catches subtle changes in nuclear structure.
as written by the authors arXiv:2601.06544
Quantum entanglement provides a unique perspective for probing nuclear structure. In this work, we employ quantum entanglement measures, including proton-neutron entanglement entropy, mutual information, and quantum relative entropy, to investigate the evolution of entanglement patterns as we approach neutron-rich nuclei. The study is carried out in the vicinity of the $$N=20$$ island of inversion region consisting of even-$$A$$ Ne, Mg, and Si isotopes, and also for isotones corresponding to $$N=20$$. The state-of-the-art \textit{ab initio} valence space in-medium similarity renormalization group method has been used for this purpose. We have highlighted the role of proton-neutron entanglement entropy in the formation of the island of inversion region. Mutual information provides insight into the strength of correlations between proton-proton, neutron-neutron, and proton-neutron single-particle states. While these correlations are relatively weak between protons and neutrons in the ground states, they become comparable to like-particle correlations in excited states. The quantum relative entropy is also studied between $$0^+$$ and $$2^+$$ states of the Ne, Mg, and Si isotopes, as well as $$N=20$$ isotones, using the Kullback-Leibler divergence and Jensen-Shannon divergence. We have performed these calculations by expressing the nuclear wavefunctions in a Slater-determinant basis and analyzing them through complementary partitions, including proton-neutron and mode-resolved factorizations.
The island of inversion is a region of nuclei where the magic number 20 ceases to be magic: energy levels rearrange, and the nucleus becomes unexpectedly stable or deformed.
In Greg Egan's novel "Schild's Ladder," quantum entanglement is used for instantaneous communication between distant points in space, echoing the idea of nonlocal correlations in the nucleus.