The twist number of planar linear trees

Abstract

We propose a new atomic beamsplitter which uses Raman transitions via the far detuned excited state of an atom induced by four standing light waves. The splitting is not restricted to the Raman-Nath regime, and spontaneous emission is strongly suppressed. Therefore this scheme can be applied even for very slow atoms with strong transitions.

Planar Manhattan Local Minimal and Critical Networks

“…In investigation of local minimal and critical networks the notion of linear tree and some important properties of such trees obtained in [18] will be useful. This is due to the following simple fact.…”