Środowiskowe Seminarium z Informacji i Technologii Kwantowych

Ultracold atoms provide a versatile platform for simulating topological and many-bodyphenomena in condensed matter and high-energy physics. The use of atomic darkstates (long-lived superpositions of atomic internal ground states immune to atom-lightcoupling) offers new possibilities for such simulations. Making the dark states positiondependent allows for the generation of a synthetic magnetic field for ultracold atomsadiabatically following the dark states [1]. Recently, two-dimensional (2D) dark-statelattices have been considered [2-3].Here, we present a general description of 2D topological dark state lattices elucidatingan interplay with the sub-wavelength lattices [4]. In particular, we demonstrate that onecan create a 2D Kronig-Penney lattice representing a periodic set of 2D subwavelengthpotential peaks affected by a non-staggered magnetic flux. Away from these patches ofthe strong magnetic field, there is a smooth magnetic flux of the opposite sign,compensating for the former peaks. While the total magnetic flux over an elementarycell is zero, the system supports topological phases due to the smooth backgroundmagnetic flux, where the particle moves in a nearly constant magnetic field, resemblingthe Landau problem. This work paves the way for experimental exploration oftopological phases in dark-state optical lattices, offering new possibilities forsimulating quantum Hall systems, fractional Chern insulators and related stronglycorrelated phases.

[1] N. Goldman, G. Juzeliūnas, P. Öhberg, and I. B. Spielman, Rep. Prog. Phys., 77,126401 (2014).
[2] E. Gvozdiovas, I. B. Spielman, and G. Juzeliūnas, Phys. Rev.. A, 107, 033328 (2023).
[3] S. Nascimbene and J. Dalibard, 135, 153402 (2025).
[4] D. Burba and G. Juzeliūnas, Phys. Rev. Research 7, 043090 (2025).