Unless you wish to multiply your problem with couch grass ten x ten fold then do not rotavate the area.
What was one stem/root will be cut up into a lots of bits all of which will grow.
I had couch grass on my allotment plot, time is a great healer.
I covered the growing areas with manure and the paths in between with 7 or so layers of newspaper and then covered in bark mulch.
As the grass grows in both cases you pull it up, it comes up easily as it is not so heavily anchored.
Over time it disappears and covering decreases it to start with but you have to stay on top of pulling it up lest it should get a foothold again.
After that all you have to do is to top dress with compost/rotted manure and bark chip for paths to keep it all under control.
I now have growing strips devoid of couch grass and paths that are the same all in about 1-2 years. The former if you spend lots of time on keeping on top of it, however I did not so it will be this coming year that will be year 2 for me and it will be gone.