Article révisé par les pairs
Résumé : The engineering of synthetic dimensions allows for the construction of fictitious lattice structures by coupling the discrete degrees of freedom of a physical system. This method enables the study of static and dynamical Bloch band properties in the absence of a real periodic lattice structure. In that context, the potentially rich physics and opportunities offered by non-linearities and dissipation have remained largely unexplored. Here we investigate the complex interplay between Bloch band transport, non-linearity and dissipation, exploring how a synthetic dimension realized in the frequency space of a coherently driven optical resonator influences the dynamics of the system. We observe and study non-linear dissipative Bloch oscillations along the synthetic frequency dimension, sustained by localized dissipative structures (solitons) that persist in the resonator. The unique properties of the coherently driven dissipative soliton states can extend the effective size of the synthetic dimension far beyond that achieved in the linear regime, as well as enable long-lived Bloch oscillations and high-resolution probing of the underlying band structure.

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