use code inside ajax success method
var json = jQuery.parseJSON(data);
console.log("success", json);
and in servlet write code 
Gson gson = new Gson();
JsonElement element = gson.toJsonTree(<Object_to_be_passed>);
out.write(element.toString());
and also you have to import two packages com.google.gson.Gson and com.google.gson.JsonElement in servlet
if you pass a model class in json use the variable names to access data in ajax
like if you have a model class Address having fields name and phone
you should write code in ajax is json.name & json.phone
Example
index.jsp
<%@page contentType="text/html" pageEncoding="UTF-8"%>
<!DOCTYPE html>
<html>
    <head>
        <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
        <script src="jquery-3.2.1.js"></script>
        <title>Ajax Sample</title>
    </head>
    <body>
        <div>
            <textarea id="text"></textarea>
            <button onclick="load()">Load Now</button>
        </div>
        <script>
            function load() {
                $.ajax({
                    url: "GetData",
                    type: 'POST',
                    success: function (data, textStatus, jqXHR) {
                        alert(data);
                        var json = jQuery.parseJSON(data);
                        document.getElementById("text").innerHTML = 'Name: ' + json.name + ' & Phone:' + json.phone;
                    }
                });
            }
        </script>
    </body>
</html>
Index.java servlet
import com.google.gson.Gson;
import com.google.gson.JsonElement;
import java.io.IOException;
import javax.servlet.ServletException;
import javax.servlet.http.HttpServlet;
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpServletResponse;
/**
 *
 * @author Chirag
 */
public class Index extends HttpServlet {
    protected void processRequest(HttpServletRequest request, HttpServletResponse response)
            throws ServletException, IOException {
        response.setContentType("text/html;charset=UTF-8");
        try (PrintWriter writer = response.getWriter()) {
            Gson gson = new Gson();
            JsonElement element = gson.toJsonTree(new Address("Chirag", "123456"));
            writer.write(element.toString());
        }
    }
    class Address {
        private final String name;
        private final String phone;
        public Address(String name, String phone) {
            this.name = name;
            this.phone = phone;
        }
        public String getName() {
            return name;
        }
        public String getPhone() {
            return phone;
        }
    }
    @Override
    protected void doGet(HttpServletRequest request, HttpServletResponse response)
            throws ServletException, IOException {
        processRequest(request, response);
    }
    @Override
    protected void doPost(HttpServletRequest request, HttpServletResponse response)
            throws ServletException, IOException {
        processRequest(request, response);
    }
    @Override
    public String getServletInfo() {
        return "Get Ajax Result";
    }
}
I used the deployment descriptor to create the servlet address GetData.
  following the snip part of web.xml
<servlet>
    <servlet-name>Index</servlet-name>
    <servlet-class>Index</servlet-class>
</servlet>
<servlet-mapping>
    <servlet-name>Index</servlet-name>
    <url-pattern>/GetData</url-pattern>
</servlet-mapping>
This code place the value to textarea in html and also make a alert of passed data from servlet to jsp.
Hope it helps..:)