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We report what we believe is the weakest interaction between solitons everobserved. Our experiment involves temporal optical cavity solitonsrecirculating in a coherently-driven passive optical fibre ring resonator. Weobserve two solitons, separated by up to 8,000 times their width, changingtheir temporal separation by a fraction of an attosecond per round-trip of the100 m-long resonator, or equivalently 1/10,000 of the wavelength of the solitoncarrier wave per characteristic dispersive length. The interactions are so weakthat, at the speed of light, they require an effective propagation distance ofthe order of an astronomical unit to fully develop, i.e. tens of millions ofkilometres. The interaction is mediated by transverse acoustic waves generatedin the optical fibre by the propagating solitons through electrostriction.

Ultra-weak long-range interactions of solitons observed over astronomical distances