There are a number of herbicides that will kill Jerusalem Artichoke, including picloram (often sold under the name Tordon) and triclopyr (often sold under the name Garlon 3A). Whether you'd really want to use them is another question. If you use picloram, in particular, you won't be able to grow broadleaved plants in that area for a few years.
Solarizing the area by covering it with with clear plastic might work. But, Jerusalem Artichoke is a rhizomatous plant, it might respond by trying to spread out of the area covered by the plastic.
You'd have to try it and see what happens.
Using glass for that purpose would be courting disaster. If it gets broken, you can forget about walking around in your yard bare footed.
Jerusalem Artichoke also doesn't tolerate clipping very well. If you are diligent about regularly mowing it off, it will eventually give up. It will likely require at least a couple of year's worth of consistent effort, though.
