Bloch oscillations of coherently driven dissipative solitons in a synthetic dimension

Synthetic dimensions can introduce band properties without a periodic structure in real space, but they have largely been studied in linear systems. A study using an optical resonator has now shown non-linear soliton states in synthetic frequency space. 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.

Automated summary

Synthetic dimensions can introduce band properties without a periodic structure in real space, and a study in an optical resonator has now shown non-linear soliton states in synthetic frequency space. By coupling the discrete degrees of freedom of a physical system, synthetic dimensions can construct fictitious lattice structures, providing a way to study band properties in the absence of a real periodic lattice structure. Non-linearities and dissipation in synthetic dimensions have potential for rich physics, but have not been extensively explored.