new seed alfalfa question

So I decieded to have a 30 ac field plowed up last year that was growing brome grass for the last 10 years.
I know it would have been better to rotate to been or corn for a couple years but, I didn't want to pay to have it plowed again.
So I planted bearless barley with alfalfa, it came in better than I thiught and next year I think I will have a ok stand.
So my question, there is some grass that survived not much, how should I kill it?
This is not RR, it was Nimbus variety
And should I add some seed in the spring to thicken the stand to keep weeds and grass out?

I don't want it to choke off the alfalfa eventually.
I'm thinking there is probably some alfalfa seeds that still will germinate in the spring.
Thanks

new seed alfalfa question