Quantum walks with neutral atoms: A look into the motion of a quantum particle

We learned from physics textbooks that quantum particles behave very differently than their classical counterpart. Exploring the motion of quantum particles has led us to a series of breakthroughs in history, from the double-slit experiment to quantum transport in semiconductor devices.

Ultracold atom experiments offer us a privileged observatory to study the behaviour of massive particles delocalizing through tailored optical potential landscapes. In these experiments, single particles can be directly imaged and addressed with single lattice-site resolution. Furthermore, the great versatility of neutral atoms can be exploited to reproduce the physical behaviour of other quantum particles, like charged particles in external fields [1,2].

After an introduction to neutral-atom experiments in optical lattice potentials, I will present so-called discrete time quantum walks: A Caesium atom with two long-lived internal states behaves like a pseudo spin-1/2 particle. Depending on its spin state, the atom moves at regular time steps either one site to the left or to the right, delocalizing over multiple quantum paths.  In the limit of vanishing lattice constant, its quantum behaviour is described by the one-dimensional Dirac equation. We have recently made use of this system to prove the nonclassicality of the motion of a single atom, which is so far the most massive object that has been tested by a Leggett-Garg falsification experiment [3].

I will conclude with an outlook towards experiments exploring topological transport phenomena. The toy model nature of quantum walks allows us to gain insight into the close link between quantum transport experiments and the mathematical field of topology, which is at the origin of powerful predictions such as the existence of matter-wave currents spinning unidirectionally around a topological island without any friction.

[1] M. Genske, W. Alt, A. Steffen, A. H. Werner, R. F. Werner, D. Meschede, A. Alberti, Electric quantum walks with individual atoms, Phys. Rev. Lett. 110, 190601 (2013)

[2] C. Cedzich, T. Rybár, A. H. Werner, A. Alberti, M. Genske and R. F. Werner, Propagation of quantum walks in electric fields, Phys. Rev. Lett. 111, 160601 (2013)

[3] C. Robens, W. Alt, D. Meschede, C. Emary, and A. Alberti, Ideal Negative Measurements in Quantum Walks Disprove Theories Based on Classical Trajectories, Phys. Rev. X 5, 011003 (2015)