We propose the use of photonic crystal structures to design subwavelength optical lattices in two dimensions for ultracold atoms by using both Guided Modes and Casimir-Polder forces. We further show how to use Guided Modes for photon-induced large an
d strongly long-range interactions between trapped atoms. Finally, we analyze the prospects of this scheme to implement spin models for quantum simulation
The integration of nanophotonics and atomic physics has been a long-sought goal that would open new frontiers for optical physics. Here, we report the development of the first integrated optical circuit with a photonic crystal capable of both localiz
ing and interfacing atoms with guided photons in the device. By aligning the optical bands of a photonic crystal waveguide (PCW) with selected atomic transitions, our platform provides new opportunities for novel quantum transport and many-body phenomena by way of photon-mediated atomic interactions along the PCW. From reflection spectra measured with average atom number N = 1.1$pm$0.4, we infer that atoms are localized within the PCW by Casimir-Polder and optical dipole forces. The fraction of single-atom radiative decay into the PCW is $Gamma_{rm 1D}/Gamma$ = 0.32$pm$0.08, where $Gamma_{1D}$ is the rate of emission into the guided mode and $Gamma$ is the decay rate into all other channels. $Gamma_{rm 1D}/Gamma$ is quoted without enhancement due to an external cavity and is unprecedented in all current atom-photon interfaces.
