Sharing session data between rails and wordpress

I have two web apps running. One is a rails app which is the beef of the application, and the other is a wordpress app(for an online store).

My challenge is sharing login data/session data between the two apps. So If I log into the rails app, and then click the shopping tab, how do I transfer the user session over to the wordpress site?

Also Vice versa. If I am shopping on the wordpress site, and want to login to purchase items, how can I login via the rails app?

I believe there are single sign on plugins that can achieve this, but I have not found anything that is to specific on how to achieve this. For some reason wordpress is awfully terrible to develop around :(.