Quantum walks with neutral atoms: Disproving classical trajectory theories
Dr. Andrea Alberti (Institut für Angewandte Physik, Universität Bonn)

The discrete-time quantum walk is a prime example of quantum transport: a spin-1/2 particle is delocalised over a very large Hilbert space through discrete steps in space and time. The motion of the quantum particle is strongly influenced by an effective spin-orbit coupling, which strongly correlates position and spin degrees of freedom. We experimentally investigate this type of quantum motion using ultracold atoms in spin-dependent optical lattices: Two fully independent optical lattices, whose relative position is actively stabilized to λ/5000 precision, are employed to selectively displace atoms in spin-up and spin-down states.
Quantum walks allows the observation of different textbook transport phenomena like Bloch oscillations, Landau-Zener tunnelling, and Zitterbewegung motion. Besides these classic examples, quantum transport dynamics is made far richer by time discreteness—an inherent property of the walks: quantum resonance phenomena can be observed depending on the rational or irrational character of an artificial field applied to the atoms [1].
Physical insight into the “quantumness” of the walk is given by interaction-free measurements of the atom’s position, which allow us to strictly rule out any physical interpretation of the experiments based on classical, well-defined trajectories [2]. Our ex¬periment demonstrates a 6σ violation of the Leggett-Garg inequality, proving the nonclassicality of the motion of a single atom—the most massive object that has been so far tested by a Leggett-Garg falsification experiment.
The realisation of two-dimensional quantum walks gives us the possibility to explore in the near future a host of topological phenomena through the direct observation, e.g., of exotic “metallic” states delocalized along spatial boundaries.

[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); 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)
[2] 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)