## Quantum Walks With Neutral Atoms: Quantum Interference Effects of One and Two Particles

Date:
2015-11-11
Author(s):

Carsten Robens, Stefan Brakhane, Dieter Meschede, Andrea Alberti

Reference:

Proceedings of the XXII International Conference ICOLS (2015)

We report on the state of the art of quantum walk experiments with neutral atoms in state-dependent optical lattices. We demonstrate a novel state-dependent transport technique enabling the control of two spin-selective sublattices in a fully independent fashion. This transport technique allowed us to carry out a test of single-particle quantum interference based on the violation of the Leggett-Garg inequality and, more recently, to probe two-particle quantum interference effects with neutral atoms cooled into the motional ground state.

## Decoherence Models for Discrete-Time Quantum Walks and their Application to Neutral Atom Experiments

Date:
2014-12-19
Author(s):

Andrea Alberti, Wolfgang Alt, Reinhard Werner, Dieter Meschede

Reference:

New J. Phys. 16, 123052 (2014)

We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum-walk experiments realized with neutral atoms walking in an optical lattice.

## Propagation of Quantum Walks in Electric Fields

Date:
2013-10-14 - 2014-01-28
Author(s):

C. Cedzich, T. Rybár, A. H. Werner, A. Alberti, M. Genske, R. F. Werner

Reference:

Phys. Rev. Lett. 111, 160601 (2013)

We study one-dimensional quantum walks in a homogenous electric field. The field is given by a phase which depends linearly on position and is applied after each step. The long time propagation properties of this system, such as revivals, ballistic expansion, and Anderson localization, depend very sensitively on the value of the electric field, Φ, e.g., on whether Φ/(2π) is rational or irrational. We relate these properties to the continued fraction expansion of the field.

## Electric quantum walks with individual atoms

Date:
2013-05-07 - 2014-01-28
Author(s):

Maximilian Genske, Wolfgang Alt, Andreas Steffen, Albert H. Werner, Reinhard F. Werner, Dieter Meschede, Andrea Alberti

Reference:

Phys. Rev. Lett. 110, 190601

We report on the experimental realization of electric quantum walks, which mimic the effect of an electric field on a charged particle in a lattice. Starting from a textbook implementation of discrete-time quantum walks, we introduce an extra operation in each step to implement the effect of the field. The recorded dynamics of such a quantum particle exhibits features closely related to Bloch oscillations and interband tunneling.

## propagation and spectral properties of quantum walks in electric fields

Date:
2013-02-08
Author(s):

C. Cedzich, T. Rybár, A. H. Werner, A. Alberti, M. Genske, R. F. Werner

Reference:

arXiv:1302.2081v1 [quant-ph]

We study one-dimensional quantum walks in a homogeneous electric field. The field is given by a phase which depends linearly on position and is applied after each step. The long time propagation properties of this system, such as revivals, ballistic expansion and Anderson localization, depend very sensitively on the value of the electric field $\Phi$, e.g., on whether $\Phi/(2\pi)$ is rational or irrational.

## Electric quantum walks with individual atoms

Date:
2013-05-07
Author(s):

M. Genske, W. Alt, A. Steffen, A. H. Werner, R. F. Werner, D. Meschede and A. Alberti

Reference:

DOI: 10.1103/PhysRevLett.110.190601
PACS: 05.60.Gg, 03.75.-b, 73.40.Gk

We report on the experimental realization of electric quantum walks, which mimic the effect of an electric field on a charged particle in a lattice. Starting from a textbook implementation of discrete-time quantum walks, we introduce an extra operation in each step to implement the effect of the field. The recorded dynamics of such a quantum particle exhibits features closely related to Bloch oscillations and interband tunneling.

## Quantum Walks with Non-Abelian Anyons

Date:
2011-06-17
Author(s):

L. Lehman, V. Zatloukal, G.K. Brennen, J.K. Pachos, and Z. Wang

Reference:

Phys. Rev. Lett. 106, 230404 (2011).

We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned anyons on a surface, by modeling it with a discrete time quantum walk. During the evolution, the spatial degree of freedom of the mobile anyon becomes entangled with the fusion degrees of freedom of the collective system. Each quantum trajectory makes a closed braid on the world lines of the particles establishing a direct connection between statistical dynamics and quantum link invariants.

## Realization of a Quantum Walk with One and Two Trapped Ions

Date:
2010-03-09
Author(s):

F. Zähringer, G. Kirchmair, R. Gerritsma, E. Solano, R. Blatt, and C. F. Roos

Reference:

Phys. Rev. Lett. 104, 100503 (2010)

## Anyonic quantum walks

Date:
2010-03-01
Reference:

G. K. Brennen, D. Ellinas, V. Kendon J. K. Pachos, I. Tsohantjis, Z. Wang
Annals of Physics, Volume 325, Issue 3, March 2010, pp. 664-681

The one dimensional quantum walk of anyonic systems is presented. The anyonic walker performs braiding operations with stationary anyons of the same type ordered canonically on the line of the walk. Abelian as well as non-Abelian anyons are studied and it is shown that they have very different properties. Abelian anyonic walks demonstrate the expected quadratic quantum speedup. Non-Abelian anyonic walks are much more subtle. The exponential increase of the system’s Hilbert space and the particular statistical evolution of non-Abelian anyons give a variety of new behaviors.

## Statistical dynamics of a non-Abelian anyonic quantum walk

Date:
2010-09-07
Reference:

Lauri Lehman, Vaclav Zatloukal, Gavin K. Brennen, Jiannis K. Pachos, Zhenghan Wang,
http://arxiv.org/abs/1009.0813

We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned anyons on a surface. The dynamics is modelled by a discrete time quantum walk and the spatial degree of freedom of the mobile anyon becomes entangled with the fusion degrees of freedom of the collective system. Each quantum trajectory makes a closed braid on the world lines of the particles establishing a direct connection between statistical dynamics and quantum link invariants.