  We report what we believe is the weakest interaction between solitons ever
observed. Our experiment involves temporal optical cavity solitons
recirculating in a coherently-driven passive optical fibre ring resonator. We
observe two solitons, separated by up to 8,000 times their width, changing
their temporal separation by a fraction of an attosecond per round-trip of the
100 m-long resonator, or equivalently 1/10,000 of the wavelength of the soliton
carrier wave per characteristic dispersive length. The interactions are so weak
that, at the speed of light, they require an effective propagation distance of
the order of an astronomical unit to fully develop, i.e. tens of millions of
kilometres. The interaction is mediated by transverse acoustic waves generated
in the optical fibre by the propagating solitons through electrostriction.
