jQuery
will not handle authentication, it would only serve as an intermediary, passing, say, username and password to your authentication code inside your application. There's no harm in having jQuery manipulate a login screen or whatever, but in the end, server side code will be what logs a user in.
EDIT: Any JavaScript you include on your site, jQuery or not, will need to be vetted for security. Have a look at this slide deck: Douglas Crockford: Ajax Security to get an overview of the issues. Security is a process though, and you need also to look at your server side code to assure it also is meeting your expectations with regard to security.