Selective population of a large-angular-momentum state in an optical lattice

We propose a method to selectively populate a large angular momentum state of ultracold atoms (each with an orbital angular momentum $l \approx 2 \hbar$) in the Mott regime of a two-dimensional optical lattice. This is done by periodically modulating the lattice amplitude and implementing an additional rectangular lattice of shorter wavelength at an angle of $\pi/4$. The specific pulse sequences are designed using a four-level model for each well and are implemented sequentially. The results are confirmed with numerical simulations of the full Schroedinger equation. The methods of this paper are another step in constructing a modular toolbox of operations for creating higher orbital states in optical lattices.