Quantum walks and quantum simulations with Bloch oscillating spinor atoms

TL;DR

This paper presents a method to realize quantum walks and simulate the Dirac equation using ultracold spinor atoms in driven optical lattices, enabling exploration of relativistic quantum effects.

Contribution

It introduces a novel scheme for quantum simulation of relativistic particles with spinor atoms, combining state-dependent transport and internal state control.

Findings

Simulates Dirac particle dynamics in 1+1 dimensions

Enables observation of relativistic effects like Zitterbewegung and Klein tunneling

Provides a platform for quantum information processing with entangled spin and motion

Abstract

We propose a scheme for the realization of a quantum walker and a quantum simulator for the Dirac equation with ultracold spinor atoms in driven optical lattices. A precise control of the dynamics of the atomic matter wave can be realized using time-dependent external forces. If the force depends on the spin state of the atoms, the dynamics will entangle the inner and outer degrees of freedom which offers unique opportunities for quantum information and quantum simulation. Here, we introduce a method to realize a quantum walker based on the state-dependent transport of spinor atoms and a coherent driving of the internal state. In the limit of weak driving the dynamics is equivalent to that of a Dirac particle in 1+1 dimensions. Thus it becomes possible to simulate relativistic effects such as Zitterbewegung and Klein tunneling.