Coherently-pumped (Kerr) solitons in an ideal optical microcavity are expected to undergo random quantum motion that determines fundamental performance limits in applications of soliton microcombs. Here, this diffusive motion and its impact on Kerr soliton timing jitter is studied experimentally. Typically hidden below technical noise contributions, the quantum limit is discerned by measuring counter-propagating solitons. Their relative motion features only weak interactions and also presents excellent common mode suppression of technical noise. This is in strong contrast to co-propagating solitons which are found to have relative timing jitter well below the quantum limit of a single soliton on account of strong mutual motion correlation. Good agreement is found between theory and experiment. The results establish the fundamental limits to timing jitter in soliton microcombs and provide new insights on multi-soliton physics.Recently, coherently pumped solitons 1,2 have been realized in optical microcavities 3 . Unlike earlier temporal optical solitons, these new solitons are able to regenerate through Kerr-induced parametric amplification 4,5 , and strong resonant build-up in the high-Q microcavity enables access to optical nonlinearity at low power levels 6 .

Counterpropagating (CP) solitons generated in high-Q microcavities not only offer useful dual-comb sources, but also provide a new platform to study soliton interactions. Here, we demonstrate and theoretically explain a manifestation of soliton trapping that occurs between CP solitons in a silica microcavity introducing a Kerr soliton dimer. In conventional soliton trapping, the group velocities of two solitons can be synchronized by a Kerr-effect-mediated interaction. The solitons can then copropagate with a fixed temporal delay. However, as shown here, when counterpumping a microcavity using slightly detuned pump frequencies and in the presence of backscattering, the group velocities of clockwise and counterclockwise solitons undergo periodic modulation instead of being locked to a constant velocity. Upon emission from the microcavity, the solitons feature a relative oscillatory motion around a locked average relative displacement with an amplitude that can be larger than the soliton pulse width. This relative motion introduces a sideband fine structure into the optical spectrum of the CP solitons. Our observation provides insights on coherently pumped soliton dimers in microcavities.

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We present the technical design of the pulsed-optical timing distribution system for LCLS-II and characterize its performance with out-of-loop measurements indicating a long-term timing stability of one femtosecond.