Fig. 6: Periodically tilted triangular optical lattice.

a Potential landscapes of triangular optical lattice without and with an additional 1D periodic potential (whose amplutude and phase are \({V}^{\prime}\) and \({\phi }^{\prime}\), respectively) for \(2{V}_{1}={V}_{2}={V}_{3}={V}^{\prime}\) and \({\phi }^{\prime}=0\). The amplutudes of the three standing waves forming the triangular optical lattice are denoted by V₁, V₂, and V₃. The cuts along r = r(1, 0) and \({\bf{r}}=r(1/2,\sqrt{3}/2)\) are shown in b. The spatial coordinate r = (x, y) and its norm r are measured in units of the lattice constant a. c, d Same as a and b, respectively, for \({V}_{1}={V}_{2}={V}_{3}={V}^{\prime}\) and \({\phi }^{\prime}=\pi /12\).