Ambika,
If you basically want to leverage a pre-logged in session in your downstream tests, then you are left with no other choice but to just sequence them as sequential tests and all of them would run in the same browser.
A Browser session CANNOT be shared across multiple browser sessions, unless and until you manage to recreate "an already logged in user" state via your code.
Your web application may be tracking "logged in" users via either cookies or via some server side mechanism, which ONLY you would be knowing.
If its based on cookies, then you could write code which basically does the following:
1. After a user logs in, your code sniffs up the cookies that are created and via code adds those cookies into the other browser sessions which need a user to be logged in.
Since my web programming skills are close to "zilch" I have no idea if all of this is even possible.
So I will strongly recommend that you tweak your tests such that each of them can run on their own. Not sure what exactly would you be saving here by just having one login and then have rest of your tests try to bank on that session to proceed ahead. To me personally that sounds like a recipe for chaos.