It is shown that the interplay of a confining potential with a periodic potential leads for free particles to states spatially confined on a fraction of the total extension of the system. A more complex “slicing” of the system can be achieved by increasing the period of the lattice potential. These results are especially relevant for fermionic systems, where interaction effects are in general strongly reduced for a single species at low temperatures.

• Received 1 October 2003

DOI:https://doi.org/10.1103/PhysRevA.70.043627