Perfect wave-packet splitting and reconstruction in a one-dimensional lattice

TL;DR

This paper presents a method to perfectly split and reconstruct a quantum wave-packet in a one-dimensional lattice, enabling controlled quantum interference and entanglement distribution for quantum technologies.

Contribution

The authors develop a mathematical framework and identify conditions for Hamiltonians that achieve perfect wave-packet splitting and reconstruction in a 1D lattice.

Findings

Achieved exact wave-packet splitting and reconstruction at time t*

Identified specific Hamiltonians with site-dependent interactions for perfect splitting

Enabled potential applications in quantum interference and entanglement distribution

Abstract

Particle delocalization is a common feature of quantum random walks in arbitrary lattices. However, in the typical scenario a particle spreads over multiple sites and its evolution is not directly useful for controlled quantum interferometry, as may be required for technological applications. In this paper we devise a strategy to perfectly split the wave-packet of an incoming particle into two components, each propagating in opposite directions, which reconstruct the shape of the initial wavefunction after a particular time $t^*$. Therefore, a particle in a delta-like initial state becomes exactly delocalized between two distant sites after $t^*$. We find the mathematical conditions to achieve the perfect splitting which are satisfied by viable example Hamiltonians with static site-dependent interaction strengths. Our results pave the way for the generation of peculiar many-body interference patterns in a many-site atomic chain (like the Hanbury Brown and Twiss and quantum Talbot effects) as well as for the distribution of entanglement between remote sites. Thus, as for the case of perfect state transfer, the perfect wave-packet splitting can be a new tool for varied applications.