Ref  in the arXiv paper, C. M. Caves and B. L. Schumaker, Phys Rev A 31, 3068 (1985), gives a clean description of a parametric amplifier as the prototype of a two-photon device, at the bottom of its second page:
In a [parametric amplifier], an intense laser beam at frequency
$2\Omega$ —the pump beam— illuminates a suitable nonlinear medium. The
nonlinearity couples the pump beam to other modes of the electromagnetic
field in such a way that a pump photon at frequency $2\Omega$ can be
annihilated to create "signal" and "idler" photons at frequencies
$\Omega\pm\epsilon$ and, conversely, signal and idler photons can be
annihilated to create a pump photon.
One way to think of the present situation would be as a dual of this description. That is, the medium, the Josephson junction, oscillates at a pump frequency $2\Omega$, and interacts nonlinearly with the vacuum state.
From the arXiv paper itself, there is a clear parallel,
Quantum theory allows us to make more detailed predictions than just that
photons will simply be produced. If the boundary is driven sinusoidally at
an angular frequency $\omega_d = 2\pi f_d$, then it is predicted that
photons will be produced in pairs such that their frequencies, $\omega_1$ and
$\omega_2$, sum to the drive frequency, i.e., we expect $\omega_d = \omega_1 + \omega_2$.
One of the comments on the Nature News page, Edward Schaefer at 2011-06-06 12:39:04 PM, makes a point that I think is worth highlighting, that "The mirror transfers some of its own energy to the virtual photons to make them real."