Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms

S. de Léséleuc, V. Lienhard, P. Scholl, D. Barredo, T. Lahaye and A. Browaeys (LCF)

Topological matter has attracted a lot of interest over the last years, as it challenges conventional classifications of phases of matter and promises interesting applications in a variety of fields. If topological effects at the single particle level are now well understood, the interplay of interactions and topology is a much more open field, for which quantum simulation could bring new insights. A major challenge for quantum simulation platforms is thus the realization of topological phases of matter where interactions play a crucial role.

Many quantum simulation platforms, as diverse as ultracold atoms, superconducting qubits, or exciton-polariton micro-cavities, have been used in recent years to explore synthetic topological matter. However, so far, all these experiments can be described in the single-particle regime, and reaching the strongly interacting regime is a very active field of research. Using arrays of single atoms trapped in optical tweezers and excited to Rydberg levels, we have realized a synthetic version of the Su-Schrieffer-Heeger model, a one-dimensional chain where strong and week couplings between adjacent sites alternate. Depending whether the chain ends with strong or weak links, it is called trivial or topological, and one can show that in the latter case, two degenerate, localized zero-energy states appear on the edges. We have observed these single-particle edge states by microwave spectroscopy (part A of the figure). However, in contrast with other approaches, our platform easily allows injecting many excitations in the system and reaching the many-body ground state at half-filling. In this many-body regime, recent theoretical classifications of topological interacting systems predicted that the phase thus realized would acquire new properties with respect to the single-particle case: in particular, breaking a symmetry (called sub-lattice symmetry) that would lift the degeneracy between edge states at the single-particle level does not lift the degeneracy in the many-body regime (part B of the figure). This first realization of a symmetry-protected topological phase for interacting bosons is published in Science

A Site-resolved microwave spectroscopy reveals the existence of two zero-energy edge modes for a Su-Schrieffer-Heeger chain in the topological configuration (bottom), that do not exist in the trivial configuration (top).  

B Altering the position of a single atom at the end of the chain lifts the degeneracy of the two edge modes in the single-particle regime (left), while, for a chain half-filled with interacting particles, the edge modes remain degenerate as predicted by the general classification of symmetry-protected topological phases for interacting bosons (right).

S. de Léséleuc, V. Lienhard, P. Scholl, D. Barredo, S. Weber, N. Lang, H. P. Büchler, T. Lahaye and A. Browaeys, Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms, Science 365, 775 (2019).

These results were obtained in the framework of the project XY systems with Local Optical control of Spins (XYLOS) funded by theme 1 of LabEx PALM.