We present a continuous non-local model that faithfully replicates the rich topological and spectral features of the Su-Schrieffer-Heeger (SSH) model. Remarkably, our model shares the SSH models bulk energy spectrum, eigenstates, and Zak phase, hallmarks of its topological character, while introducing a tunable length-scale a quantifying non-locality. This parameter allows for a controlled interpolation between non-local and local regimes. Furthermore, for a specific value of a the exact spectral equivalence to the discrete SSH model is established. Distinct from previous continuous analogues based on Schrödinger or Dirac-type Hamiltonians, our approach maintains chiral symmetry, does not require an external potential and features periodic energy bands. On finite domains, the model supports a flat band with zero energy formed by a countable infinite set of exponentially localized zero-energy edge states of topological origin. Beyond SSH, our method lays the foundation for constructing non-local, continuous analogues of a wide class of bipartite and multipartite lattices, opening new paths for theoretical exploration and new challenges for experimental realization in topological quantum matter.

Using a quantum gas setup consisting of a Bose-Einstein condensate strongly coupled to a high-finesse optical cavity by a transverse pump laser, we experimentally observe an instability of a dissipative continuous time crystal (CTC) towards a time crystalline state exhibiting two prominent oscillation frequencies. Applying a mean-field approximation model and a Floquet analysis, we theoretically confirm that this transition is a manifestation in a many-body system of a torus bifurcation between a limit cycle (LC) and a limit torus (LT). We theoretically illustrate the LC and LT attractors using the minimal model and experimentally reconstruct them using Takens' embedding theorem applied to the non-destructively measured intracavity photon dynamics.