Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Steady-state phase diagram of a driven QED-cavity array with cross-Kerr
  nonlinearities   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 bistability. 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.

10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
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The categories of this paper are: nlin
2
The categories of this paper are: math
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg