Solving the transport without transit quantum paradox of the spatial adiabatic passage technique

TL;DR

This paper resolves the quantum paradox in adiabatic transport by demonstrating that particle transit through the middle well always occurs, with ultra-high velocities emerging in the adiabatic limit, challenging classical intuition.

Contribution

It provides a Bohmian trajectory analysis showing that transit always occurs through the middle well, clarifying the paradox and revealing relativistic effects at high velocities.

Findings

Transport always involves transit through the middle well.

Ultra-high Bohmian velocities occur in the adiabatic limit.

Relativistic corrections are needed to avoid superluminal propagation.

Abstract

We discuss and solve the transport without transit quantum paradox recently introduced in the context of the adiabatic transport of a single particle or a Bose--Einstein condensate between the two extreme traps of a triple-well potential. To this aim, we address the corresponding quantum dynamics in terms of Bohmian trajectories and show that transport always implies transit through the middle well, in full agreement with the quantum continuity equation. This adiabatic quantum transport presents a very counterintuitive effect: by slowing down the total time duration of the transport process, ultra-high Bohmian velocities are achieved such that, in the limit of perfect adiabaticity, relativistic corrections are needed to properly address the transfer process while avoiding superluminal matter wave propagation.