How to maintain session in same browser

Hi

In my website, when user logged in, I maintain his/her username in a session but when user opens another tab and use the same website at that time session doesn't work.

For Example: User logged in with his/her details in my website and than when he open another tab of same browser and browse same website at that time it doesn't maintain session for that user.

Kindly let me know how to acheive this?