Single Sign On with Tomcat and NodeJS

I have two different applications running on the same server, one is Java-based running in Tomcat with spring-social and spring-security, and the other is a NodeJS application using PassportJS as security framework.

Both apps are configured to access using Google OAuth2 with the same clientId/secret, so I can login with my google account in each of them. But if I change from one of them to another, I need to login again, because the session doesn't exist on the other app.

I'm looking at the session cookies, the Java app creates the JSESSIONID cookie whereas the Node app creates a "connect.sid" cookie. Maybe I could create a session in each app everytime a user do a login? Or I have to deal with OAuth tokens?

Please, could you point me in the right direction? Should I use another library/framework? Thank you in advance.

This might be of help; it looks like it's relatively easy to change the name of the cookie for Express/Connect. The question then just becomes whether the contents of JSESSIONID and connect.sid are in fact the same.