Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Nonlinear Optics without Photons   Spontaneous parametric down-conversion is a well-known process in quantum
nonlinear optics in which a photon incident on a nonlinear crystal
spontaneously splits into two photons. Here we propose an analogous physical
process where one excited atom directly transfers its excitation to a pair of
spatially-separated atoms with probability approaching one. The interaction is
mediated by the exchange of virtual rather than real photons. This nonlinear
atomic process is coherent and reversible, so the pair of excited atoms can
transfer the excitation back to the first one: the atomic analogue of
sum-frequency generation of light. The parameters used to investigate this
process correspond to experimentally-demonstrated values in ultrastrong circuit
quantum electrodynamics. This approach can be extended to realize other
nonlinear inter-atomic processes, such as four-atom mixing, and is an
attractive architecture for the realization of quantum devices on a chip. We
show that four-qubit mixing can efficiently implement quantum repetition codes
and, thus, can be used for error-correction codes.

33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
2
The categories of this paper are: math
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci