Production of Atomic Number States: a Bethe Ansatz Analysis

We analyze the conditions for producing atomic number states in a one-dimensional optical box by the method of laser culling. We solve the problem using the Bethe Ansatz, and justify the use of that method for the present problem. Our approach provides a general theoretical framework that spans a wide range of interaction strength. The limit of strong interactions, so-called Tonks-Girardeau regime, is equivalent to non-interacting fermions. We discuss the relative merits of laser culling of fermions as compared with bosons in terms of possible experimental realization as well as projected fidelity.