There are two ways of adding Basic Authentication to jQuery Ajax calls.

You can use beforeSend in jQuery callback to add a HTTP header with the authentication details e.g.:

beforeSend: function (xhr) {
    xhr.setRequestHeader ("Authorization", "Basic XXXXXX"); 
}

Alternatively you can do it using jQuery ajaxSetup function:

$.ajaxSetup({
    headers: { 'Authorization': "Basic XXXXX" }
});

A few links to the mentioned functions

Basic Authentication HTTP Header

The authentication header is constructed as follows: username and password are joined into a string username:password and the result string is encoded using Base64.

Example Basic Authentication HTTP header:

Authorization: Basic QWxhZGRpbjpvcGVuIHNlc2FtZQ==