Abstract.
I will present two topics of research in our group related to synthetic topological quantum matter [1]: (i) topological phases in 3D optical lattices, more specifically a proposal for experimental realization of Weyl semimetals in ultracold atomic gases [2], and (ii) anyons [3,4]. I will present one possible route to engineer anyons in a 2D electron gas in a strong magnetic field sandwiched between materials with high magnetic permeability, which induce electron-electron vector interactions to engineer charged flux-tube composites [3]. I will also discuss intriguing concepts related to extracting observables from anyonic wavefunctions [4]: one can show that the momentum distribution is not a proper observable for a system of anyons [4], even though this observable was crucial for the experimental demonstration of Bose-Einsten condensation or ultracold fermions in time of flight measurements. I will show how time of flight measurements can be used to extract anyonic statistics [4].

[1] N. Goldman, G. Juzeliunas, P. Ohberg, I. B. Spielman, Rep. Prog. Phys. 77, 126401 (2014).
[2] Tena Dubček, Colin J. Kennedy, Ling Lu, Wolfgang Ketterle, Marin Soljačić, Hrvoje Buljan, Weyl points in three-dimensional optical lattices: Synthetic magnetic monopoles in momentum space, Phys. Rev. Lett. 114, 225301 (2015).
[3] M. Todorić, D. Jukić, D. Radić, M. Soljačić, and H. Buljan, The Quantum Hall Effect with Wilczek's charged magnetic flux tubes instead of electrons, arXiv:1710.10108 [cond-mat.str-el]
[4] Tena Dubček, Bruno Klajn, Robert Pezer, Hrvoje Buljan, Dario Jukić, Quasimomentum distribution and expansion of an anyonic gas, Phys. Rev. A 97, 011601(R) (2018)-