Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bloch-Messiah decomposition and Magnus expansion for parametric
  down-conversion with monochromatic pump   We discuss the Bloch-Messiah decomposition for the broadband squeezed light
generated by type-I parametric down-conversion with monochromatic pump. Using
an exact solution for this process, we evaluate the squeezing parameters and
the corresponding squeezing eigenmodes. Next, we consider the Magnus expansion
of the quantum-mechanical evolution operator for this process and obtain its
first three approximation orders. Using these approximated solutions, we
evaluate the corresponding approximations for the Bloch-Messiah decomposition.
Our results allow us to conclude that the first-order approximation of the
Magnus expansion is sufficient for description of the broadband squeezed light
for squeezing values below 12.5 dB. For higher degrees of squeezing we show
fast convergence of the Magnus series providing a good approximation for the
exact solution already in the third order. We propose a quantitative criterion
for this ultra-high-gain regime of parametric down-conversion when the
higher-orders terms of the Magnus expansion, known in the literature as the
operator-ordering effects, become necessary.

4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom