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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 : 

<img src='content_image/369813.jpg'>

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 

Numerical evaluation yields 

<img src='content_image/369810.jpg'>

<img src='content_image/369808.jpg'>

(a) 

<img src='content_image/369809.jpg'>

(b) 

