Ask for user authentication per tab

I am trying to create a simple website with authentication. There will be a login page, and when the login is successful it should go to the index page. However, after the successful login, if the user copies the index page URL and opens a new TAB and tries to go index page in that tab, it should redirect to login page and ask for user authentication again.

Is there an easy way to do this. Can it be done with PHP? with PHP I was not able to do it because after the login it keeps the session alive and when you open a new tab and try to go index page it does not ask for user authentication again.