You can't do what you ask (and the linked site does not do exactly that either).
You can, however, modify the part of the url after the #
sign, which is called the fragment, like this:
window.location.hash = 'something';
Fragments do not get sent to the server (so, for example, Google itself cannot tell the difference between http://www.google.com/
and http://www.google.com/#something
), but they can be read by Javascript on your page. In turn, this Javascript can decide to perform a different AJAX request based on the value of the fragment, which is how the site you linked to probably does it.