Topological pumping of photons in nonlinear cavity arrays

In physics, there are several phenomena in which topology plays an important role. The earliest example of this is perhaps Archimedes pump where this was exploited to pump water up a hill using a rotating screw, followed by quantum Hall effect physics and topological quantum computing in more recent times. Three decades ago, Thouless proposed topological pumping for the robust transport of quantum particles in one dimensional periodic lattices, by means of an adiabatic and cyclic deformation of the underlying Hamiltonian. In addition, he showed that the number of particles transported during one pump cycle is quantized and can be related to a topological invariant, known as the Chern number. As a consequence, the transport is robust against small disorder and perturbation. 

 We show how to implement topological or Thouless pumping of interacting photons in one dimensional nonlinear resonator arrays, by simply modulating the frequency of the resonators periodically in space and time. The interplay between interactions and the adiabatic modulations enables robust transport of Fock states with few photons per site. We analyze the transport mechanism via an effective analytic model and study its topological properties and its protection to noise. We conclude by a detailed study of an implementation with existing circuit QED architectures