Driven-dissipative topological phases in parametric resonator arrays

Topological Pumping of Photons in Nonlinear Resonator Arrays.

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 the interactions and the adiabatic modulations enables robust transport of Fock states with few photons per site. We analyze the transport mechanism via an effectiv...

Photon solid phases in driven arrays of nonlinearly coupled cavities.

We introduce and study the properties of an array of QED cavities coupled by nonlinear elements, in the presence of photon leakage and driven by a coherent source. The nonlinear couplings lead to photon hopping and to nearest-neighbor Kerr terms. By tuning the system parameters, the steady state of the array can exhibit a photon crystal associated with a periodic modulation of the photon blocka...

Entanglement in Topological Phases

In this report, the research conducted on entanglement in topological phases is detailed and summarized. This includes background developed and an explanation of the structure of the code written it MATLAB to compute various aspects of entanglement for topological systems. Topological phases are generally those that cannot be described by Landau symmetry-breaking, including the fractional quant...

Geometrical phases and symmetries in dissipative systems.

Steady-state phases and tunneling-induced instabilities in the driven dissipative Bose-Hubbard model.

We determine the steady-state phases of a driven-dissipative Bose-Hubbard model, describing, e.g., an array of coherently pumped nonlinear cavities with a finite photon lifetime. Within a mean-field master equation approach using exact quantum solutions for the one-site problem, we show that the system exhibits a tunneling-induced transition between monostable and bistable phases. We characteri...