  Strongly interacting solitons confined to an optical resonator would offer
unique capabilities for experiments in communication, computation, and sensing
with light. Here we report on the discovery of soliton crystals in monolithic
Kerr microresonators-spontaneously and collectively ordered ensembles of
co-propagating solitons whose interactions discretize their allowed temporal
separations. We unambiguously identify and characterize soliton crystals
through analysis of their 'fingerprint' optical spectra, which arise from
spectral interference between the solitons. We identify a rich space of soliton
crystals exhibiting crystallographic defects, and time-domain measurements
directly confirm our inference of their crystal structure. The crystallization
we observe is explained by long-range soliton interactions mediated by
resonator mode degeneracies, and we probe the qualitative difference between
soliton crystals and a soliton liquid that forms in the absence of these
interactions. Our work explores the rich physics of monolithic Kerr resonators
in a new regime of dense soliton occupation and offers a way to greatly
increase the efficiency of Kerr combs; further, the extreme degeneracy of the
configuration space of soliton crystals suggests an implementation for a robust
on-chip optical buffer.
