Google Apps SAML Single Sign On authentication and SSO Email Login

Hello, we are building a PHP Laravel application for a company that uses Google Apps to provide their email. Using Google Apps' SAML SSO capabilities, we need some software built that can do the following: 1) Allow a user to enter their Google Apps username/password, authenticate with Google's server, and return true or false. 2) Allow a user who has "logged in" to our system using this method to click a link which will open their email or another app in a new window, without them having to login again. 3)Clear session and logout.