EPR pairing dynamics in Hubbard model with resonant $U$

TL;DR

This paper analyzes the collision dynamics of two fermions in the Hubbard model with resonant interaction, revealing a separable scattering matrix that enables EPR pair creation without temporal control.

Contribution

It provides an exact solution showing how the spin part of the scattering matrix mimics a Heisenberg interaction, facilitating EPR pair generation through fermion collisions.

Findings

The scattering matrix is separable into spatial and spin parts.

Spin scattering mimics Heisenberg-type interaction.

EPR pairs can be generated without temporal control.

Abstract

We study the dynamics of the collision between two fermions in Hubbard model with on-site interaction strength $U$. The exact solution shows that the scattering matrix for two-wavepacket collision is separable into two independent parts, operating on spatial and spin degrees of freedom, respectively. The S-matrix for spin configuration is equivalent to that of Heisenberg-type pulsed interaction with the strength depending on $U$ and relative group velocity $\upsilon _{r}$. This can be applied to create distant EPR pair, through a collision process for two fermions with opposite spins in the case of $\left\vert \upsilon _{r}/U\right\vert =1$,\ without the need for temporal control and measurement process. Multiple collision process for many particles is also discussed.