Entanglement generation in few-nucleon scattering

Abstract

Inspired by a recent Letter [S. R. Beane et al., Phys. Rev. Lett. 122, 102001 (2019)], the entanglement generated in the elastic $S$-wave scattering of $p+^{3}\mathrm{He}$ and $n+^{3}\mathrm{H}$ is studied, where the proton, neutron, $^{3}\mathrm{He}$, and $^{3}\mathrm{H}$ are all regarded as qubits. To deal with the Coulomb interaction between the proton and $^{3}\mathrm{He}$, 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 $S$-wave $n+p$ 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.