Quantum Contact Processes on a Topological Lattice, realized by coherent Rydberg facilitation

Contact processes play an important role in classical non-equilibrium dynamics, describing the spreading of diseases, the dynamics of earthquakes and forest fires and the distribution of information through the internet. Here, we show that their quantum counterpart, where the spreading occurs through coherent couplings, displays even richer dynamics and offers new means of control. A quantum contact process on a topologically non-trivial lattice can be confined to a protected subspace corresponding to edge modes. Furthermore, excitation spreading can be controlled to occur in quantized steps and on demand when employing topological pumps [1]. We here consider a specific type of contact process, the QXP process, which corresponds to coherent Rydberg facilitation in a tweezer array of trapped atoms in a one-dimensional lattice with topologically non-trivial band-structure.

[1] D. J. Thouless, Phys. Rev. B 27, 6083 (1983)