Legal Question in Business Law in North Carolina

Did "John" have a patent? Did John have a non-disclosure agreement before he divulged the details to his professors? What proof does John have? The answers will depend on what John does next.

John can sue for patent infringement if he has a patent or an application pending (provided this is not a provisional patent - this is not my area of a law and John should see a patent attorney if John had filed something with the US Patent & Trademark Office). If John had a non-disclosure agreement, then he can sue for that. Again, John needs to see an intellectual property lawyer about that. If John did not seek to protect himself in any way, then he may not be entitled to any protection under the law.