  Topological states of matter, as quantum Hall systems or topological
insulators, cannot be distinguished from ordinary matter by local measurements
in the bulk of the material. Instead, global measurements are required,
revealing topological invariants as the Chern number. At the heart of
topological materials are topologically protected edge states that occur at the
intersection between regions of different topological order. Ultracold atomic
gases in optical lattices are promising new platforms for topological states of
matter, though the observation of edge states has so far been restricted in
these systems to the state space imposed by the internal atomic structure. Here
we report on the observation of an edge state between two topological distinct
phases of an atomic physics system in real space using optical microscopy. An
interface between two spatial regions of different topological order is
realized in a one-dimensional optical lattice of spatially chirped amplitude.
To reach this, a magnetic field gradient causes a spatial variation of the
Raman detuning in an atomic rubidium three- level system and a corresponding
spatial variation of the coupling between momentum eigenstates. This novel
experimental technique realizes a cold atom system described by a Dirac
equation with an inhomogeneous mass term closely related to the SSH-model. The
observed edge state is characterized by measuring the overlap to various
initial states, revealing that this topological state has singlet nature in
contrast to the other system eigenstates, which occur pairwise. We also
determine the size of the energy gap to the adjacent eigenstate doublet. Our
findings hold prospects for the spectroscopy of surface states in topological
matter and for the quantum simulation of interacting Dirac systems.
