  Systems consisting of cold atoms trapped near photonic crystal waveguides
have recently emerged as an exciting platform for quantum atom-light
interfaces. Such a system enables realization of tunable long-range
interactions between internal states of atoms (spins), mediated by guided
photons. Currently, experimental platforms are still limited by low filling
fractions, where the atom number is much smaller than the number of sites at
which atoms can potentially be trapped. Here, we show that this regime in fact
enables interesting many-body quantum phenomena, which are typically associated
with short-range disordered systems. As an example, we show how the system can
realize the so-called "random singlet phase", in which all atoms pair into
entangled singlets, but the pairing occurs over a distribution of ranges as
opposed to nearest neighbors. We use a renormalization group method to obtain
the distribution of spin entanglement in the random singlet phase, and show how
this state can be approximately reached via adiabatic evolution from the ground
state of a non-interacting Hamiltonian. We also discuss how experimentally this
random singlet phase can be observed. We anticipate that this work will
accelerate the route toward the exploration of strongly correlated matter in
atom-nanophotonics interfaces, by avoiding the requirement of perfectly filled
lattices.
