Momentum disequilibrium and quantum entanglement of Rydberg multidimensional states
Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071, Granada, Spain
2 Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071, Granada, Spain
Accepted: 16 April 2021
Published online: 26 April 2021
The quantum entanglement of the two components of a hydrogenic system with dimensionality is investigated for the ground and excited states from first principles, that is, in terms of the Coulomb potential parameters (the dimensionality and the nuclear charge) and the state’s hyperquantum numbers. To quantify this multidimensional entanglement, we use an heuristic quantifier and a practical genuine entanglement measure which are closely related to the variance and disequilibrium of the system in momentum space, respectively. Then, our interest is focused on the multidimensional entanglement of highly excited (Rydberg) states, obtaining at the leading order a simple dependence on the dimensionality and the principal hyperquantum number n which characterizes the state. Applications to various specific low-lying and high-lying hydrogenic states are shown. In particular, it is rigorously shown that the momentum disequilibrium and the entanglement for the Rydberg multidimensional states follow a scaling law of and type for two-dimensional and D-dimensional () systems, respectively.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021