We describe potentials which act as approximate cloaks for matter waves. These potentials are derived from ideal cloaks for the conductivity and Helmholtz equations. At most energies $E$, if a potential is surrounded by an approximate cloak, then it becomes almost undetectable and unaltered by matter waves originating externally to the cloak. For certain $E$, however, the approximate cloaks are resonant, supporting wave functions almost trapped inside the cloaked region and negligible outside. Applications include dc or magnetically tunable ion traps and beam switches.

• Received 2 June 2008

DOI:https://doi.org/10.1103/PhysRevLett.101.220404