Optical lattice for a tripodlike atomic level structure

Standard optical potentials use off-resonant laser standing wave induced AC-Stark shift. In a recent development [Phys. Rev. Lett. {\bf 117}, 233001 (2016)] three-level scheme in $\Lambda$ configuration coupled coherently by resonant fields was introduced leading to an effective lattice with subwavelength potential peaks. Here as extension of that work four level atomic setup the tripod is used create spin $1/2$-like two-dimensional dark-space 1D motion and presence external gauge fields. Most interestingly for possible application, lifetime dark subspace up two orders magnitude larger than similar system. The model quite flexible lattices significant nearest, next-nearest, or next-next-nearest hopping rates, $J_1,J_2,J_3$ opening new intriguing possibilities study, e.g. frustrated systems. characteristic Wannier functions lead also type inter-site interactions not realizable typical lattices.