Random singlet phase of cold atoms coupled to a photonic crystal waveguide

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 tunable long-range interactions between internal states (spins), mediated by guided photons. Currently, experimental platforms are still limited low filling fractions, where the atom number is much smaller than sites at which can potentially be trapped. Here, we show that this regime in fact interesting many-body phenomena, typically associated with short-range disordered systems. As example, how realize so-called ``random singlet phase'' (RSP), all pair into entangled singlets, but pairing occurs over distribution ranges opposed to nearest neighbors. We use renormalization group method obtain spin entanglement RSP, and state approximately reached via adiabatic evolution from ground noninteracting Hamiltonian. also discuss experimentally RSP observed. anticipate work will accelerate route toward exploration strongly correlated matter atom-nanophotonics interfaces, avoiding requirement perfectly filled lattices.