We propose to use sub-wavelength confinement of light associated with the near field of plasmonic systems to create nanoscale optical lattices for ultracold atoms. Our approach combines the unique coherence properties of isolated atoms with the sub-wavelength manipulation and strong light-matter interaction associated with nano-plasmonic systems. It allows one to considerably increase the energy scales in the realization of Hubbard models and to engineer effective long-range interactions in coherent and dissipative many-body dynamics. Realistic imperfections and potential applications are discussed.PACS numbers: 37.10. Gh, 73.20.Mf, 78.67.Bf Coherent optical fields provide a powerful tool for manipulating ultracold atoms [1,2]. However, diffraction sets a fundamental limit for the length-scale of such manipulations, given by the wavelength of light [3]. In particular, the large period of optical lattices determines the energy scale of the associated many-body atomic states [4][5][6][7]. The resulting scaling can be best understood by noting that in the first Bloch band the maximum atomic momentum ∼ 1/ , where is the lattice spacing. This sets the maximum kinetic energy to h 2 /m 2 [8]. For conventional optical lattices the lattice spacing is set by half the wavelength of the trapping light ∼ 500 nm; this yields corresponding tunneling rates of up to a few tens of kHz. Additionally, for atoms in their electronic ground states interactions are restricted to short range.Recent experimental [9] and theoretical [10,11] work has demonstrated that integrating plasmonic systems with cold atoms represents a promising approach to achieving subwavelength control of atoms. In particular, the experiments of Ref. [9] showed that ultracold atoms can be used to probe the near fields of plasmonic structures, paving the way to eventually trap atoms above such structures. In this Letter we propose and analyze a novel approach to the realization of high-density optical lattices using the optical potential formed from the near field scattering of light by an array of plasmonic nanoparticles. By bringing atom trapping into the subwavelength and nanoscale regime we show that the intrinsic scales of tunneling and onsite interaction for the Hubbard model can be increased by several orders of magnitude compared to conventional optical lattices. In addition, subwavelength confinement of the atoms results in strong radiative interactions with the plasmonic modes of the nanoparticles [12]. The coupled atom-plasmon system can be considered as a scalable cavity array that results in strong, long range spin-spin interactions between the atoms with both dissipative and coherent contributions [13,14]. Such a system can be used for entanglement of remote atoms as well as for novel realizations of coherent and dissipative many-body systems.To illustrate our approach we first consider a single metallic nanosphere in vacuum illuminated by a plane wave. For spheres small compared to a wavelength the dominant contribution to the scattered field is ...