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Abstract

We theoretically study the few- and many-body dynamics of photons in chiral
waveguides. In particular, we examine pulse propagation through a system of $N$
two-level systems chirally coupled to a waveguide. We show that the system
supports correlated multi-photon bound states, which have a well-defined photon
number $n$ and propagate through the system with a group delay scaling as
$1/n^2$. This has the interesting consequence that, during propagation, an
incident coherent state pulse breaks up into different bound state components
that can become spatially separated at the output in a sufficiently long
system. For sufficiently many photons and sufficiently short systems, we show
that linear combinations of $n$-body bound states recover the well-known
phenomenon of mean-field solitons in self-induced transparency. For longer
systems, however, the solitons break apart through quantum correlated dynamics.
Our work thus covers the entire spectrum from few-photon quantum propagation,
to genuine quantum many-body (atom and photon) phenomena, and ultimately the
quantum-to-classical transition. Finally, we demonstrate that the bound states
can undergo elastic scattering with additional photons. Together, our results
demonstrate that photon bound states are truly distinct physical objects
emerging from the most elementary light-matter interaction between photons and
two-level emitters. Our work opens the door to studying quantum many-body
physics and soliton physics with photons in chiral waveguide QED.