I would ask the new company if they would allow you to give a 2 week notice to your old company and allow you to work it if they allow you to. Not good to burn bridges when leaving jobs as you never know down the road would you might be working for or alongside, especially if staying in the same field and geographic area. You could also ask the company to give you any take home materials to look over/ study to help shorten your learning curve time-frame.