The simple answer is that you can't reliably log out of http-authentication.
The long answer:
Http-auth (like the rest of the HTTP spec) is meant to be stateless. So being "logged in" or "logged out" isn't really a concept that makes sense. The better way to see it is to ask, for each HTTP request (and remember a page load is usually multiple requests), "are you allowed to do what you're requesting?". The server sees each request as new and unrelated to any previous requests.
Browsers have chosen to remember the credentials you tell them on the first 401, and re-send them without the user's explicit permission on subsequent requests. This is an attempt at giving the user the "logged in/logged out" model they expect, but it's purely a kludge. It's the browser that's simulating this persistence of state. The web server is completely unaware of it.
So "logging out", in the context of http-auth is purely a simulation provided by the browser, and so outside the authority of the server.
Yes, there are kludges. But they break RESTful-ness (if that's of value to you) and they are unreliable.
If you absolutely require a logged-in/logged-out model for your site authentication, the best bet is a tracking cookie, with the persistence of state stored on the server in some manner (mysql, sqlite, flatfile, etc). This will require all requests to be evaluated, for instance, with PHP.