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

• Received 8 June 2021
• Revised 25 September 2021
• Accepted 21 October 2021

DOI:https://doi.org/10.1103/PhysRevA.104.053312