Emergent topological properties in modulated Kronig-Penney-type models

Ultracold atom gases trapped in optical potentials offer a clean and controllable platform to realize quantum models that are difficult to implement in condensed matter systems [1]. Recent theoretical [2] and experimental [3] developments allow to create periodic sub-wavelength potentials that overcome the diffraction limit imposed by the wavelength of the used laser beams. These potentials support the paradigmatic Kronig-Penney model and its variations which not only describe the behaviour of electrons in a one-dimensional crystal but also have been shown to host topologically protected edge states [4]. Developing control strategies for such systems is of fundamental interest in quantum technologies that rely on robust states for computations [5].

In this work we analyze the topological properties of an advanced Kronig-Penney model. The emergent topological behaviour is observed under translations and height modulation of the periodic potential in a one-dimensional infinite well. The energy bands split into sub-bands displaying Hofstadter's butterfly-like structure under the change of the spatial modulation frequency. This leads to the redistribution of the topological invariants classifying the bands to a set of sub-bands indicating the same charge transport at lower filling. The spectral function is calculated which shows the existence of a topologically protected flat edge modes. Finally, many-body quenches are studied between the topologically trivial and non-trivial regimes revealing deviations from the orthogonality catastrophe [6].

[1] P. Windpassinger et al., Rep. Prog. Phys. 76, 086401 (2013).

[2] M. Lacki et al., Phys. Rev. Lett. 117, 233001 (2016).

[3] Y. Wang et al., Phys. Rev. Lett. 120, 083601 (2018).

[4] I. Reshodko et al., New J. Phys. 21, 013010 (2019).

[5] C. P. Koch et al., EPJ Quantum Technol. 9, 1 (2022).

[6] P. W. Anderson: Phys. Rev. Lett. 18, 1049 (1967).