Ultraweak long-range interactions of solitons observed over astronomical distances

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 pairs of solitons interacting over a range as large as 8,000 times their width. In the most extreme case, their temporal separation changes as slowly as a fraction of an attosecond per roundtrip 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, an effective propagation distance of the order of an astronomical unit can be required to reveal the full dynamical evolution. The interaction is mediated by transverse acoustic waves generated in the optical fibre by the propagating solitons through electrostriction.