A simple phonon multiplexer

Simple multiplexing phonon structures are presented. Such structures can be deposited on a surface with current ultra-high vacuum technologies. In the atomic domain they are supposed to be made out of two parallel mono-atomic chains of atoms and of a simple coupling device made out of two other atoms interacting together and with the two chains. We show analytically that these simple structures can transfer with selectivity and directivity one phonon from one chain to the other, leaving neighbor phonons unaffected. We give closed-form relations enabling to obtain the values of the relevant physical parameters for this multiplexing phenomenon to happen at a chosen wavelength. Finally, we illustrate this general theory by an application.