The realization of synthetic magnetism (static or dynamical) in neutral quantum gases constitutes one of the most active research fields in the physics of cold atoms as it opens fascinating possibilities of the study of correlation effects in interacting gauge field systems.
For current experiments (e.g. [1,2]) typically a Hall-like response of a particle current constitutes a fingerprint of the presence of emulated magnetic fields. But also, vice-versa, these scenarios might be exploited to study the Hall-response in strongly interacting coherent quantum systems. In the first part of my talk I will focus on the possible measurements and properties of the Hall coefficient in quantum gas experiments [3,4].
In the second part I will broaden the perspective and discuss some possible scenarios for the simulation and study of dynamical or density dependent gauge fields in optical lattices [5,6].
 M. Mancini, L. Fallani, et al. Science 349, 1510 (2015)
 D. Genkina, I. Spielman, et al. arXiv:1804.06345
 S. Greschner, M. Filippone, and T. Giamarchi. PRL 122, 083402 (2019)
 M. Filippone, C.-E. Bardyn, S. Greschner, and T. Giamarchi. arXiv:1903.02000
 S. Greschner, L. Cardarelli, and L. Santos. PRA 97, 053605 (2018)
 L. Cardarelli, S. Greschner, and L. Santos. PRL 119, 180402 (2017)