Quantum walks with nonorthogonal position states

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Quantum walks with nonorthogonal position states. / Matjeschk, R.; Ahlbrecht, A.; Enderlein, M.; Cedzich, Ch; Werner, A. H.; Keyl, M.; Schaetz, T.; Werner, R. F.

In: Physical Review Letters, Vol. 109, No. 24, 240503, 10.12.2012.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Matjeschk, R, Ahlbrecht, A, Enderlein, M, Cedzich, C, Werner, AH, Keyl, M, Schaetz, T & Werner, RF 2012, 'Quantum walks with nonorthogonal position states', Physical Review Letters, vol. 109, no. 24, 240503. https://doi.org/10.1103/PhysRevLett.109.240503

APA

Matjeschk, R., Ahlbrecht, A., Enderlein, M., Cedzich, C., Werner, A. H., Keyl, M., Schaetz, T., & Werner, R. F. (2012). Quantum walks with nonorthogonal position states. Physical Review Letters, 109(24), [240503]. https://doi.org/10.1103/PhysRevLett.109.240503

Vancouver

Matjeschk R, Ahlbrecht A, Enderlein M, Cedzich C, Werner AH, Keyl M et al. Quantum walks with nonorthogonal position states. Physical Review Letters. 2012 Dec 10;109(24). 240503. https://doi.org/10.1103/PhysRevLett.109.240503

Author

Matjeschk, R. ; Ahlbrecht, A. ; Enderlein, M. ; Cedzich, Ch ; Werner, A. H. ; Keyl, M. ; Schaetz, T. ; Werner, R. F. / Quantum walks with nonorthogonal position states. In: Physical Review Letters. 2012 ; Vol. 109, No. 24.

Bibtex

@article{a97c94e52e624105959d6e956bb2a38f,
title = "Quantum walks with nonorthogonal position states",
abstract = "Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal. We develop a general description of such a quantum walk and show how to map it into a standard one with orthogonal states, thereby making available all the tools developed for the latter. This enables a variety of experiments, which can be implemented with smaller step sizes and more steps. Tuning the nonorthogonality allows for an easy preparation of extended states such as momentum eigenstates, which travel at a well-defined speed with low dispersion. We introduce a method to adjust their velocity by momentum shifts, which allows us to experimentally probe the dispersion relation, providing a benchmarking tool for the quantum walk, and to investigate intriguing effects such as the analog of Bloch oscillations.",
author = "R. Matjeschk and A. Ahlbrecht and M. Enderlein and Ch Cedzich and Werner, {A. H.} and M. Keyl and T. Schaetz and Werner, {R. F.}",
year = "2012",
month = dec,
day = "10",
doi = "10.1103/PhysRevLett.109.240503",
language = "English",
volume = "109",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "24",

}

RIS

TY - JOUR

T1 - Quantum walks with nonorthogonal position states

AU - Matjeschk, R.

AU - Ahlbrecht, A.

AU - Enderlein, M.

AU - Cedzich, Ch

AU - Werner, A. H.

AU - Keyl, M.

AU - Schaetz, T.

AU - Werner, R. F.

PY - 2012/12/10

Y1 - 2012/12/10

N2 - Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal. We develop a general description of such a quantum walk and show how to map it into a standard one with orthogonal states, thereby making available all the tools developed for the latter. This enables a variety of experiments, which can be implemented with smaller step sizes and more steps. Tuning the nonorthogonality allows for an easy preparation of extended states such as momentum eigenstates, which travel at a well-defined speed with low dispersion. We introduce a method to adjust their velocity by momentum shifts, which allows us to experimentally probe the dispersion relation, providing a benchmarking tool for the quantum walk, and to investigate intriguing effects such as the analog of Bloch oscillations.

AB - Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal. We develop a general description of such a quantum walk and show how to map it into a standard one with orthogonal states, thereby making available all the tools developed for the latter. This enables a variety of experiments, which can be implemented with smaller step sizes and more steps. Tuning the nonorthogonality allows for an easy preparation of extended states such as momentum eigenstates, which travel at a well-defined speed with low dispersion. We introduce a method to adjust their velocity by momentum shifts, which allows us to experimentally probe the dispersion relation, providing a benchmarking tool for the quantum walk, and to investigate intriguing effects such as the analog of Bloch oscillations.

UR - http://www.scopus.com/inward/record.url?scp=84870904009&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.109.240503

DO - 10.1103/PhysRevLett.109.240503

M3 - Journal article

AN - SCOPUS:84870904009

VL - 109

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 24

M1 - 240503

ER -

ID: 256316906