shunter is right. to fly in the US of A you will need to first apply for your FAA licence.
any flying you do there can be put into your log book as you have flown it. however if you fly as safty pilot in a single pilot aircraft, that time is only valid in your FAA log book, not in you JAA one.
some people tend to have two log books, one for JAA and one for FAA. one person i know only uses his FAA logbook for safty pilot flying in the US. all left hand seat flying he does goes into his JAA logbook as that time is valid back here.