How to handle json returned to autocomplete from servlet

How to handle json returned to autocomplete from servlet

I'm trying to use the autocomplete widget to and to populate it I am using a servlet which is returning a JSON array.  Bear with me, I'm not sure how much you need to see so I'm going to include a lot.

Here is how I am constructing the autocomplete right now.  It's not complete yet because I don't really know how to finish:

                $('#usernamesearch').autocomplete({
                    minLength: 2,
                    source: function(request, response) {
                        $.ajax({
                            url: "./UserServlet?action=search",
                            dataType: "json",
                            data: request,
                            success: ""
                        });
                    }
                });

Clearly I need to work on success, that's where my hold up is right now.  Here is the servlet code that builds the JSON array.  The data is coming out of a database using jdbc:

            ResultSet result = stmt.executeQuery();
            JSONArray array = new JSONArray();
            while (result.next()) {
                JSONObject obj = new JSONObject();
                obj.put("fullname", result.getString("fullname"));
                array.add(obj);
            }
            result.close();
            stmt.close();
            log.info(array.toJSONString());
            out.print(array.toJSONString());
            out.flush();

My output from this block of code shows this:
[{"fullname":"andrea danziger"},{"fullname":"Stacey Moda"},{"fullname":"Debbie Jordan"},{"fullname":"Greg Jordan"},{"fullname":"Janet Randall"},{"fullname":"Arjun Ghosh-Dastidar"},{"fullname":"Brian Adamson"}]

This looks like a good JSON array to me, although I'll be the first to admit that I'm not an expert. 
So, what's the next step?  The data is returning, I can see that clearly enough, but how do I parse it and return it to the autocomplete?

I am happy to return the JSON array however it needs to be constructed.  I can also modify the options for the autocomplete.

Thanks in advance.