A. Potentials The potential of an optical tweezer array can be represented by a sum of n identical Gaussian profiles of width σ and spatial period d : We require neighboring wells to overlap, which can be accomplished by setting σ < ∼ d ; Figure 1(a) shows that this condition is satisfied for σ = d/ 4. For this choice of parameters, the potential is well approximated by a cosine, as can be seen from the Fourier coefficients FIG. 1: (a) Two neighboring Gaussian profiles (red and black curves) and their sum (green); (b) effective external potential. Numerical evaluation yields 6 a$_{n}$ = 2 d d ∫ 0 cos ( 2 nπx d ) [ − N ∑ n =0 e − ( x − dn ) $^{2}$/ 2 σ 2 ] dx. (7) 0 1 2 3 4 5 x [d$_{0}$] -10 -8 -6 -4 -2 0 V efe /V 0 E$_{G}$ E$_{P}$ d 4 4 (a) (b) V$_{t}$ ( x ) = − V$_{0}$ N ∑ n =0 e − ( x − dn ) $^{2}$/ 2 σ $^{2}$. (6)