High intensity laser and neutrino pair production Given the very small rest mass of the neutrino, visible photons have plenty energy for neutrino pair creation. What would be the probability of $\gamma \to \nu + \bar\nu$?
Would the neutrinos be produced in their mass eigenstates or as $\nu_e$ etc?
 A: Interesting question!
First off, it's actually not clear that visible photons have enough energy for this process: the upper limit on the neutrino mass is at the scale of an electron volt, which is about the same as the energy of visible or infrared photons. There is some tantalizing cosmic ray evidence for eV-scale neutrino masses.  But your question is still interesting for higher-energy photons.
The Feynman diagram for electron-positron production (or equivalent diagrams for annihilation or $\rm e\gamma$ scattering) has two $\rm ee\gamma$ vertices.
The simplest neutrino-production diagram $\gamma\gamma\to\nu\bar\nu$ would likewise have two $\nu\nu\gamma$ vertices.  However, the neutrino does not interact with the photon at tree level, because the neutrino is not charged. So that first-order diagram contributes nothing to the process that you're interested in.
The simplest loop diagram would probably be something like $\gamma\gamma \to WW \to \nu\nu$, but the requirement to have two virtual heavy bosons means that the cross-section for such a process would be vanishingly small at low energies.
A: In addition to the previous answer, the reaction $ \gamma\gamma \to ep \to \nu\nu$ should also be possible. 
https://en.m.wikipedia.org/wiki/Electron%E2%80%93positron_annihilation
A: Occasionally I came over the same question as well. This process is studied by stellar physics and is named "plasmon decay" or bremsstrahlung neutrino emission (similar to photon emission within dense matter). It is considered as significant part of energy dissipation by stars from deep inside. Lobanov disregards weak currents and calculates cross section in ultra-relativistic limit.
I started to look into this by asking myself whether low energy neutrino beams can be generated from photons and also came to Lobanov paper. However, this emission is induced by dense star matter where plasma experiences certain high density shocks. Seems yes -  high density laser and strong magnetic field would be able to produce significant fluxes of neutrino. 
In particular I am looking for this paper. If anyone can share (I am not academician) :) The paper is about generation of 20 MeV neutrino beams, which appear to be highly collimated.
Pakhomov A.V. Neutrino generation by high-intensity lasers. Journal of
Physics G: Nuclear and Particle Physics, 2002, vol. 28, no. 6, pp. 1469–1476.
*)
this paper is mentioned in this one
http://engjournal.ru/articles/1041/1041.pdf
PS. follow-up idea: 
Take Laser Driven Accelerator (laser plasma accelerates electrons within femtosecond-scale multiple buckets with some frequency) and apply strong magnetic field on top of it to emulate stellar dense matter.
Will this construction generate neutrinos? 
*) PSS. found at 
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.199.5513&rep=rep1&type=pdf
PSSS. Three articles relate to the question:
"Photon decay γ → νν¯ in an external magnetic
field"
http://cds.cern.ch/record/340351/files/9712289.pdf
"Photon-pair conversion into neutrinos in a strong magnetic field"
https://arxiv.org/abs/hep-ph/0108046
"Photon decay into neutrinos in a strong magnetic field"
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.14.3326
Indeed, as said in other replies:
g + g -> nu + nu-bar is the only possibility. g -> nu + nu-bar is only in the presence of other dense matter or strong EM-field
