  Here we use a slow light quantum light-matter interface at room temperature
to implement an analog simulator of complex relativistic and topological
physics. We have realized the famous Jackiw-Rebbi model (JR), the celebrated
first example where relativity meets topology. Our system is based upon
interacting dark state polaritons (DSP's) created by storing light in a
rubidium vapor using a dual-tripod atomic system. The DSP's temporal evolution
emulates the physics of Dirac spinors and is engineered to follow the JR regime
by using a linear magnetic field gradient. We also probe the obtained
topologically protected zero-energy mode by analyzing the time correlations
between the spinor components. Our implementation paves the way towards quantum
simulation of more complex phenomena involving many quantum relativistic
particles.
