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 -