I believe Jane is sponsored by S.H.I.E.L.D. to continue her research into opening the wormhole (Bifrost). I don't believe the full line makes it into the film but from the script on IMSDb:
Thor: Know this, son of Coul. You and I, we fight for the same cause -- the protection of this world. From this day forward, count me as your ally. If you return the items you have stolen from Jane Foster.
Coulson: Not stolen. Borrowed. You'll get your equipment back. You're going to need it to continue your research... which, after today's events, SHIELD would like to fully sponsor. If that's all right with you.
It would seem in industry terms that she is more of an independent contractor for S.H.I.E.L.D. at this time rather than being directly employed by them. In The Avengers we get a hint that they move her out of the way from the action:
Coulson: As soon as Loki took the doctor we moved Jane Foster. We've got an excellent observatory in Tromso. She was asked to consult there very suddenly yesterday. Handsome fee, private plane, very remote. She'll be safe.
This is expanded upon in the tie in comic Thor: The Dark World Prelude. In it we see what happens to Jane here after getting moved around. Essentially she is left in the dark and finds out Thor is on Earth after moving to Tromso. She then finds out Thor just leaves without making contact with her. This is enough to push her over the edge and not want to continue on her research anymore. After all she was doing it for him and his actions make it seem like he doesn't want to see her.
Click image to enlarge.
Darcy: Jane... he'll come back.
Jane: No. He won't. Thor was here, and then he just left again. No message, nothing. Not a word. For the last year. every waking thought I had was of him. Of finding him. All the work I did, it was for nothing. So, that's it. I'm done.
Thor: The Dark World Prelude