ticles at the initial (final) well. Criteria i)-iii) are realizable with a suitably tailored optical tweezer array. The array consists of a series of spherically symmetric op- tical tweezers; the particles flow along this line, which we take as the x axis. To avoid particles escaping the array, there should be a substantial overlap between neighboring wells, so that a potential maximum at a point midway between two wells is in fact a saddle point in the full three-dimensional space (see Fig. 1(a)). For a TASEP-like system, it is crucial that the probability of a particle escape from the array be negligible on the time-scale of the experiment. Effective confinement requires a potential barrier to escape the array much larger than k$_{B}$T ; the barrier between adjacent minima should be smaller, to allow transitions between neighbor- ing wells. In what follows we shall assume this condition is satisfied, and consider, for simplicity, a one-dimensional system. Fluctuations of the particle positions in the directions perpendicular to the array will therefore be ignored, but should be included in a more complete analysis. The diameter of the optical tweezer well should be slightly greater than the par- ticle diameter, so that at most one particle can occupy the well at a given time. Due to thermal fluctuations, particles can occasionally overcome the potential bar- rier separating neighboring wells. Since hopping must be asymmetric, we impose a steady fluid motion along the + x axis, which effectively prohibits particle jumps in the opposite direction. In the lattice TASEP particles are inserted in the first site and removed from the last. Experimental realization of this feature is subtler, but can in principle be achieved with the help of optical tweezers at the beginning and end of the array, which drag particles into the first well and out of the last one at prescribed rates. We discuss an alternative method of insertion and removal in Sec. V. The above sketch of an experimental setup motivates our study of Brownian motion of interacting colloidal particles in an optical tweezer array. The Langevin 4