Steady-state phase diagram of a driven QED-cavity array with cross-Kerr nonlinearities

  1. Jiasen Jin,
  2. Davide Rossini,
  3. Martin Leib,
  4. Michael J. Hartmann,
  5. and Rosario Fazio
We 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 main effect of the nonlinear
couplings is to provide an effective cross-Kerr interaction between nearest-neighbor cavities. Additionally correlated photon hopping between neighboring cavities arises. We provide a detailed mean-field analysis of the steady-state phase diagram as a function of the system parameters, the leakage and the external driving, and show the emergence of a number of different quantum phases. A photon crystal associated to a spatial modulation of the photon blockade appears. The steady state can also display oscillating behavior and bi-stability. In some regions the crystalline ordering may coexist with the oscillating behavior. Furthermore we study the effect of short-range quantum fluctuations by employing a cluster mean-field analysis. Focusing on the corrections to the photon crystal boundaries, we show that, apart for some quantitative differences, the cluster mean field supports the findings of the simple single-site analysis. In the last part of the paper we concentrate on the possibility to build up the class of arrays introduced here, by means of superconducting circuits of existing technology. We consider a realistic choice of the parameters for this specific implementation and discuss some properties of the steady-state phase diagram.

Photon solid phases in driven arrays of non-linearly coupled cavities

  1. Jiasen Jin,
  2. Davide Rossini,
  3. Rosario Fazio,
  4. Martin Leib,
  5. and Michael J. Hartmann
We introduce and study the properties of an array of QED cavities coupled by non-linear elements, in the presence of photon leakage and driven by a coherent source. The non-linear
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 to a periodic modulation of the photon blockade. In some cases the crystalline ordering may coexist with phase synchronisation. The class of cavity arrays we consider can be built with superconducting circuits of existing technology.