Optical lattices with periodicity well below $\lambda $/2

Optical potentials based on the ac-Stark shift are used extensively in the investigation of lattice models of quantum many body systems. But these potentials are limited by diffraction to have a lattice constant no less than $\lambda $/2, where $\lambda $ is the wavelength of light used. This sets a temperature scale in these lattices given by T\textasciitilde E$_{\mathrm{R}}$/k$_{\mathrm{B}}$ , where E$_{\mathrm{R}}=$h$^{\mathrm{2}}$/8md$^{\mathrm{2\thinspace \thinspace }}$and d is the lattice constant. Study of phenomena like superexchange and magnetic dipole interactions require much lower temperatures than that set by E$_{\mathrm{R}}$. By engineering lattices with subwavelength lattice constants, the temperature requirements to study these phenomena can be relaxed. Recently, we have demonstrated an optical lattice based on dark states with sub-wavelength barriers of width $\lambda $/50 [1]. By stroboscopically dithering the phase of this lattice while remaining in a dark state, a time-averaged potential with sub-wavelength lattice spacing of $\lambda $/(2N) can be realized [2]. Here we report our progress on the realization of such a lattice. [1] arXiv:1712.00655 [2] Phys. Rev. Lett. 115, 140401