Just wanted to say that the answer provided by Thomas Fritsch is definitely not correct. I have produced laser-induced plasma in the laboratory with a ~5 nanosecond pulsed Nd:YAG laser, frequency-doubled at 532nm. It is possible; there is plenty of literature evidence that it is also possible with 1064nm.
See, for example, "Laser Spark Ignition: Laser Development and Engine Testing" (McMillian et al, 2008) http://dx.doi.org/10.1115/ICEF2004-0917.
They provide a chart with the energy density values required to ignite a plasma in mid-air, typically on the order of 10^12-10^13 W/cm2. When I was producing these in the lab, I found the threshold was also about 3*10^12 W/cm2 at 532nm (though I must admit, I wasn't sure my lenses were diffraction-limited).
If you don't believe me, there is even more compelling evidence as a video by youtuber Styropyro (https://www.youtube.com/watch?v=-BeTq99LqUo), see timestamp 9:11, where he ignites a plasma in mid-air with a tatoo-removal passively Q-switched Nd:YAG laser, also frequency-doubled (532nm). A Youtube search on "laser induced plasma" provides several more videos with people doing it at various frequencies in visible and IR. You most definitely don't need an extreme-UV laser to ionize air.
Now answering the author's question, you probably don't want to use this technique in a light show where the public is present. (1) you need insane beam powers that will easily blind a bystander if the laser is not shot straight up in the sky; (2) Even if you guarantee you shoot into the sky, you'll face problems with the FAA (airplanes!!).
I think there are demonstrations of this technology for volumetric displays (say, https://www.youtube.com/watch?v=GNoOiXkXmYQ), but I'm quite sure they are not ready for public viewing for the reasons I cited above. Maybe I'm mistaken; as if the laser pulse is sufficiently short (say, femtoseconds), then it may be possible to produce laser-induced plasmas at tolerable power levels. I'll be glad to hear comments!