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arXiv:2306.03239 · Physical Review C

Entanglement maximization in low-energy neutron-proton scattering

Gerald A. Miller

Published Sep 28, 2023• 30 citations
arXivHTMLPDF

Abstract

The entanglement properties of neutron-proton scattering are investigated using a measure that counts the number of entangled pairs produced by the action of a scattering operator on a given initial neutron-proton state. All phase shifts relevant for scattering at laboratory energies up to 350 MeV are used. Entanglement is found to depend strongly on the initial state. Entanglement is maximized in very low energy scattering if the initial spin state is $|\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\rangle}$, but not if the initial state is $|\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\rangle}$. At such energies the Hamiltonian obeys Wigner SU(4) symmetry, and an entanglement maximum is a sign of that symmetry. At higher energies the angular dependence of entanglement is strong and the entanglement is large for many scattering angles. The tensor force is shown to play a significant role in producing entanglement at laboratory kinetic energies greater than about 50 MeV.

DOI
10.1103/physrevc.108.l031002

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In this Letter, I work out spin entanglement properties of neutron-proton scattering using the exact S-matrix, considering both S-wave and higher partial wave contributions. The dependence of spin entanglement on momentum, scattering angle, and initial spin configuration is investigated for realistic nuclear forces, while low-energy properties of spin entanglement are analyzed within the framework of pionless effective field theory at leading order. New connections are found between spin entanglement and symmetry emergence of strong interactions. These results lead to a more complete understanding of how spin entanglement is generated via neutron-proton interaction. They also lay the theoretical foundation for controllable production of entangled nucleon-nucleon pairs in future experiments.
We investigate polarization states of the outgoing neutron-proton (npnpnp) pair in elastic polarized neutron and proton scattering, aiming to find unambiguous evidence for entanglement of their spin states. To obtain complete information about these states, we calculate, using the high-precision nucleon-nucleon potential AV18, the final polarizations of the neutron and proton as well as their spin correlation coefficients, which unequivocally define the corresponding spin density matrix. We compute all terms contributing to polarizations and spin correlations, e.g., not only induced polarizations and correlations resulting from unpolarized npnpnp scattering but also contributions from single polarization and correlation transfers from individual polarized incoming nucleons and, for the first time, allotment to both quantities stemming from a doubly spin polarized initial state. We find that for the most part the final spin states are statistical mixture of states. The only pure states occur for highly polarized incoming neutrons and protons with maximal polarizations. By quantifying the degree of entanglement through entanglement power and concurrence, we observed that the entanglement of impure final states increases with energy. Among the pure spin states resulting from incoming states with maximal neutron and proton polarizations, we found, at Elab=100{E}_{\mathrm{lab}}=100Elab​=100 MeV, cases of strongly entangled Bell-type states with only a small admixture of entanglement-spoiling contributions.
We investigate polarization states of the outgoing neutron-proton (npnpnp) pair in elastic polarized neutron and proton scattering, aiming to find unambiguous evidence for entanglement of their spin states. To obtain complete information about these states, we calculate, using the high precision nucleon-nucleon potential AV18, the final polarizations of the neutron and proton as well as their spin correlation coefficients, which unequivocally define the corresponding spin density matrix. We compute all terms contributing to polarizations and spin correlations, e.g. not only induced polarizations and correlations resulting from unpolarized npnpnp scattering, but also contributions from single polarization and correlation transfers from individual polarized incoming nucleons, and, for the first time, allotment to both quantities stemming from a doubly spin polarized initial state. We find that for the most part the final spin states are statistical mixture of states.The only pure states occur for highly polarized incoming neutrons and protons with maximal polarizations. By quantifying the degree of entanglement through entanglement power and concurrence, we observed that the entanglement of impure final states increases with energy. Among the pure spin states resulting from incoming states with maximal neutron and proton polarizations, we found, at Elab=100E_{lab}=100Elab​=100~MeV, cases of strongly entangled Bell-type states with only a small admixture of entanglement-spoiling contributions.
Abstract Generation of an entangled spin state as a result of a low-energy elastic collision of two protons is considered. The scattering process is described by a theoretical model that is in good agreement with the available experimental data on the angular differential cross sections of proton–proton collisions at low energies. The entanglement of the spin state of final protons as a function of the scattering angle is analyzed using Bell’s inequality and pair concurrence. The numerical results for different values of the collision energy are compared with the results without considering nuclear forces. It is shown that nuclear interaction significantly enhances the effects of spin entanglement.
Abstract Quantum entanglement in scattering processes has most often been treated in general terms only. A few examples of detailed calculations exist for atomic systems but for nuclear processes it is an almost unexplored area, although it may be important for interpretation of some measured quantities. The present treatment is a study of the time-development of the deuteron-like compound state created in the n – p scattering process. The increase and decay of neutron–proton entanglement in this state is calculated for low transferred momenta over the atto-second range. It is well known that the very high value for the bound proton cross sections ( σ = 81.9 barns) is caused by a specific feature in the deuteron, a virtual 0+ state close to its binding level. In scattering this state causes a negative phase shift δ s in the outgoing neutron wave function, increasing linearly with the transferred momentum. This phase shift is produced during a short-lived virtual energy transfer Δ E in exciting the 0+ state and Δ E is estimated here from the ratio of the phase shift δ observed and the time Δ t it takes to create the entanglement. It is further argued that the nuclear excitation decreases after the n – p encounter in proportion to the degree of n – p entanglement calculated, i.e. as long as the scattering state has deuteron characteristics. This phase shift is neglected in low energy neutron scattering text-books (which are based on the Fermi pseudo potential) and may be negligible for thermal neutron scattering, but will be important already at epithermal energies (0.1–1 eV). The phase shift has measurable consequences in interpretation of INS (inelastic neutron scattering) since its associated energy shift increases quadratically with the transferred momentum. It explains quantitatively certain anomalies found in scattering on water, where water vibration modes are excited far below the expected transferred momentum limit. This paper ends with a short discussion about quantum entanglement in scattering processes in general, with the present example as a starting point.
We study the connection between accidental symmetries in the nuclear interaction and spin entanglement in two-nucleon scattering. Specifically, we incorporate different levels of Wigner SU(4) and Serber symmetries into leading-order potentials derived from chiral effective field theory. We conduct a quantitative analysis by computing the full S matrix, demonstrating that the neutron-proton spin entanglement can be related to the symmetry properties of the interaction and the presence of certain operators and partial waves. Furthermore, we study the order-by-order evolution of the spin entanglement, up to next-to-next-to-leading order in Weinberg power counting, for both neutron-proton and neutron-neutron scattering. Entanglement suppression is not observed in neutron-neutron scattering, which can be attributed to the Pauli principle and the absence of accidental symmetries in this system. We conclude that entanglement is a useful guide for studying the power counting and symmetries in nuclear interactions derived from effective field theories.