Slow sound in matter-wave dark soliton gases

We demonstrate the possibility of drastically reducing the velocity of phonons in quasi one-dimensional Bose-Einstein condensates. Our scheme consists of a dilute dark-soliton "gas" that provide the trapping for the impurities that surround the condensate. We tune the interaction between the impurities and the condensate particles in such a way that the dark solitons result in an array of {\it qutrits} (three-level structures). We compute the phonon-soliton coupling and investigate the decay rates of these three-level qutrits inside the condensate. As such, we are able to reproduce the phenomenon of acoustic transparency based purely on matter wave phononics, in analogy with the electric induced transparency (EIT) effect in quantum optics. Thanks to the unique properties of transmission and dispersion of dark solitons, we show that the speed of an acoustic pulse can be brought down to $\sim 5$ $\mu$m/s, $\sim 10^3$ times lower than the condensate sound speed. This is a record value that greatly underdoes most of the reported studies for phononic platforms. We believe the present work could pave the stage for a new generation of "stopped-sound" based quantum information protocols.