Rostock 2019 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 36: Photonics II

Q 36.4: Talk

Wednesday, March 13, 2019, 14:45–15:00, S Gr. HS Maschb.

Reducibility of non-Abelian holonomies in waveguide optics — •Julien Pinske, Lucas Teuber, and Stefan Scheel — Institut für Physik, Universität Rostock, Albert-Einstein-Str. 23, 18059 Rostock, Germany

Classical waveguide optics are a well known tool for the simulation of Hamiltonian systems [1]. This is due to the analogy of the paraxial Helmholtz equation to the Schrödinger equation. Implementation of a system with degenerate eigenstates generates a non-Abelian gauge field which yields a non-trivial holonomy group. The holonomy can thus be used to generate unitary gates which are the key building blocks of quantum information processing [2]. Irreducibility of the holonomy group corresponds to computational universality.

For means of illustration we consider a Hamiltonian with a 4-dimensional degenerate subspace. Thus generating a subgroup of U(4) for the set of realizable gates.

We present the non-Abelian gauge field of the system as well as the field strength tensor. The Ambrose-Singer theorem [3] is the state of the art method for examining reducibility of holonomies. We find that our system spans up a true subgroup of the unitary group U(4) and is therefore reducible. We believe that the implementation of non-Abelian holonomies through coupled waveguides could become a key tool for building quantum networks.

[1] F. Dreisow, A. Szameit et al: PRL Vol. 105, 143902 (2010).

[2] P. Zarandi, M. Rasetti: PLA Vol. 264, 94 (1999).

[3] W. Ambrose, I. M. Singer: Trans. AMS Vol. 75, 428 (1953).