Skip to main content

Interactions, Spins and Edges in Optical Lattices with Topological Band Structures

Periodic Reporting for period 1 - ISOTOP (Interactions, Spins and Edges in Optical Lattices with Topological Band Structures)

Reporting period: 2016-05-01 to 2018-04-30

The main objective of this action is to study many-body phases in topological band structures. Specifically, this proposal will address the many-body effects due to interactions and moreover high spins in a fermionic quantum gas. Quantum technology becomes more and more important in every day life. However, our understanding of Quantum Mechanics is still far from complete. There are many phases of matter (high Tc superconductivity, fractional Quantum-Hall effect, etc.) where the underlying mechanisms are still not fully understood. Quantum simulation with ultra cold quantum gases might help to shed light on these problems. In this action, we try to simulate the effect of magnetic fields on graphene, via shaking of the optical lattice in which we trap our ultra cold atoms. Together with the ultimate control of both the interactions and the number of spins, this system will be a viable tool for better understanding the interplay between topology, interactions and spin. The goal of this action is to be able to detect topology and study the interplay between interaction, spins and topology.
We have been able to detect topology via several different methods. First, we have directly observed the Berry curvature of ultra cold atoms in an optical lattice, which the indication of the geometry and topology in the system (published in Science, Fläschner et al., 2016). We have extended the study to dynamical evolution of the geometry and topology, by rapidly changing the geometry of the system. This allowed us to observe dynamical topological defects in the evolution of the wave function (Fläschner et. al., Nature Physics (2018)). Moreover, in the static system, we were able to observe the Dirac points characterising the topology of the honeycomb structure (as in graphene). Smoothly deforming the geometry of the system (which would correspond to putting strain on graphene) allowed us to observe and quantify the merging of the topological defects (Tarnowski et al., PRL (2017)). Furthermore, studying the topology of the evolutional path of the dynamical topological defects allowed us to obtain the topology of the underlying Hamiltonian, hence seeing topology with topology (arXiv:1709.01046 (2017)). In order to do the engineering of these shaken systems, one has to know the underlying band structure with great precision and we were able to determine the exact band structure down to the 0.12% level and fully measure the two-dimensional band structure (Fläschner et al., PRA 2018). Recently, we have also been able to observe a completely new phenomena in topological materials, the so-called quantised circular dichroism. In stead of doing drift or transport measurements on topological materials, we have looked at dissipative dynamics of the topological system and extracted the topology of the system from that (Asteria et al., arXiv:1805.11077 (2018)). Currently, we are working on using Machine Learning techniques to determine the topology, which allows us to fully map out the two-dimensional topological phase diagram of the Haldane model. The deep-learning techniques also allow us to map out the superfluid-to-Mott-Insulator transition and might be a feasible method to detect the effect of interactions and spins on topological systems (Rem et al., arXiv:1809.05519).

In January 2017, I was invited to present our results on Berry curvature and dynamical topological defects in Amsterdam. In February 2017, I've presented the results at a workshop in Munich. During the conference Quantum Optics X, I presented a poster in Gdansk in September 2017. In November 2017, I presented the results including linking number at the FOR2414 workshop in Hamburg. I gave a presentation about our results in December 2017 in Stuttgart. In May 2018, I've presented our results on measuring the band structure at the DAMOP meeting in Fort Lauderdale. Klaus Sengstock gave an invited talk at the same conference about circular dichroism.
"For the first time, we have been able to directly measure the Berry curvature of a system (publication in Science). Afterwards, several other research groups have used these ideas to also see Berry curvature in other systems, even solid state systems. The linking number and circular dichroism phenomena are completely new manifestations of topology allowing researchers to ""see"" topology from a different perspective. Furthermore, we have applied Machine Learning techniques for the first time to identify quantum phase transitions in experimental data."