Effect of the next-nearest-neighbor's interaction on the population transfer in a four-particle Landau-Zener system

Abstract

The study of transition probabilities in few-body systems and their long-range interactions using the Landau-Zener method could be helpful for solving a wide range of problems in fields of quantum simulations, Rydberg blockade, quantum gates, and dipole transition in Rydberg atoms. Here, the transition probabilities for a four-particle system in a square-shaped lattice are studied by solving the many-body Landau-Zener Hamiltonian in the next-nearest-neighbor approximation. It is observed that the complete transition occurs for the anti-ferromagnetic coupling while it is limited to a constant probability for the ferromagnetic coupling. These probabilities suppress when the magnetic field's energy rate is increased. We demonstrate that in the presence of the next-nearest-neighbor's interactions, the final probabilities’ behavior is different. Considering the next-nearest-neighbor's interactions, it is possible to achieve the complete transition in imperfect anti-ferromagnetic regions. At the same time, the complete transition does not occur in perfect anti-ferromagnetic regions for certain values of the sweeping rate. These results emphasize that it is necessary to consider the next-nearest-neighbors’ interactions in a many-body system. Furthermore, the implementation of this Hamiltonian in the dipole-dipole and van der Waals interaction reveals that a steeper decrease for dipole-dipole interaction.