Notice period in USA

I'm working in USA with H1 VISA for an Indian Software Company A. When I joined A in India, me and my company had a 3 month notice period agreement between both the parties. I came to USA on deputation and the deputation letter has no mention of any notice period. I've been offered a job by company B. The applied for new petition and I got the H1B petition receipt. Now if it is approved, then do I need to serve any notice period for company A? Can I give only 1 week of notice to company A or I need to give 2 weeks of notice? Company B wants me to join ASAP. Can company A has any power or right to play with my relieving letter or experience letter? If there is any violation from their end, what correct legal steps can I take? Also the notice period agreement in India while joining has any validity when I came to USA on deputation on H1 VISA? Can I go ahead and put 1 week of notice period?