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arXiv:2312.14484

Entanglement in few-nucleon scattering events

Tanja Kirchner, Wael Elkamhawy, H.‐W. Hammer

Published Dec 22, 2023• 0 citations
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Abstract

We investigate the spin entanglement in few-nucleon scattering processes involving nucleons and deuterons. For this purpose, we consider the entanglement power introduced by Beane et al. We analyze different entanglement entropies as a basis to define the entanglement power of the strong interaction and calculate the corresponding entanglement powers for proton-neutron, neutron-deuteron, proton-deuteron, and deuteron-deuteron scattering. For the latter two processes, we also take into account the modification from the Coulomb interaction. In contrast to proton-neutron scattering, no universal low-energy features are evident in the spin entanglement in neutron-deuteron, proton-deuteron, and deuteron-deuteron scattering.

DOI
10.48550/arxiv.2312.14484

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We investigate the spin entanglement in few-nucleon scattering processes involving nucleons and deuterons. For this purpose, we consider the entanglement power introduced by Beane et al. We analyze different entanglement entropies as a basis to define the entanglement power of the strong interaction and calculate the corresponding entanglement powers for proton-neutron, neutron-deuteron, proton-deuteron, and deuteron-deuteron scattering. For the latter two processes, we also take into account the modification from the Coulomb interaction. In contrast to proton-neutron scattering, no universal low-energy features are evident in the spin entanglement in neutron-deuteron, proton-deuteron, and deuteron-deuteron scattering.
Abstract We investigate the spin entanglement in few-nucleon scattering processes involving nucleons and deuterons. For this purpose, we consider the entanglement power introduced by Beane et al. We analyze different entanglement entropies as a basis to define the entanglement power of the strong interaction and calculate the corresponding entanglement powers for proton–neutron, neutron–deuteron, proton–deuteron, and deuteron–deuteron scattering. For the latter two processes, we also take into account the modification from the Coulomb interaction. In contrast to proton–neutron scattering, no universal low-energy features are evident in the spin entanglement in neutron–deuteron, proton–deuteron, and deuteron–deuteron scattering.
Inspired by a recent Letter [S. R. Beane et al., Phys. Rev. Lett. 122, 102001 (2019)], the entanglement generated in the elastic SSS-wave scattering of p+3Hep+^{3}\mathrm{He}p+3He and n+3Hn+^{3}\mathrm{H}n+3H is studied, where the proton, neutron, 3He^{3}\mathrm{He}3He, and 3H^{3}\mathrm{H}3H are all regarded as qubits. To deal with the Coulomb interaction between the proton and 3He^{3}\mathrm{He}3He, we derive the entanglement power, a physical quantity that measures the average entanglement generated by a scattering process, for charged qubits within the screening method. The entanglement power in the aforementioned two few-nucleon scatterings is found to be generally much smaller than that in the SSS-wave n+pn+pn+p scattering at low energies, with the corresponding cluster effective field theories possessing an enhanced approximate $\text{SU}{(2)}_{1}\ensuremath{\bigotimes}\text{SU}{(2)}_{2}$ symmetry at leading order. Our study suggests that the entanglement generation capacities of effective interactions between nucleons and light nuclei could be more suppressed than realistic nucleon-nucleon interactions at low energies.
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.
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 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.
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.