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Topological states of matter, as quantum Hall systems or topologicalinsulators, cannot be distinguished from ordinary matter by local measurementsin the bulk of the material. Instead, global measurements are required,revealing topological invariants as the Chern number. At the heart oftopological materials are topologically protected edge states that occur at theintersection between regions of different topological order. Ultracold atomicgases in optical lattices are promising new platforms for topological states ofmatter, though the observation of edge states has so far been restricted inthese systems to the state space imposed by the internal atomic structure. Herewe report on the observation of an edge state between two topological distinctphases of an atomic physics system in real space using optical microscopy. Aninterface between two spatial regions of different topological order isrealized in a one-dimensional optical lattice of spatially chirped amplitude.To reach this, a magnetic field gradient causes a spatial variation of theRaman detuning in an atomic rubidium three- level system and a correspondingspatial variation of the coupling between momentum eigenstates. This novelexperimental technique realizes a cold atom system described by a Diracequation with an inhomogeneous mass term closely related to the SSH-model. Theobserved edge state is characterized by measuring the overlap to variousinitial states, revealing that this topological state has singlet nature incontrast to the other system eigenstates, which occur pairwise. We alsodetermine the size of the energy gap to the adjacent eigenstate doublet. Ourfindings hold prospects for the spectroscopy of surface states in topologicalmatter and for the quantum simulation of interacting Dirac systems.

Real-space imaging of a topological protected edge state with ultracold atoms in an amplitude-chirped optical lattice