How to get a JSF application scoped bean from webservice?

Question

I have a jsf 2.0 application without Spring and I have implemented a cache as application scope which should be accessed from a Rest service. Now I would like to call the rest webservice which should check the cache, but when I want access it, it is always null.

I tried already Accessing FacesContext from Web Service and this one https://www.mkyong.com/jsf2/how-to-get-servletcontext-in-jsf-2/ , but it doesn't work for me.

@ManagedBean(eager=true)
@ApplicationScoped
public class CacheController implements Serializable{

    private static final long serialVersionUID = 123L;

    private Map<String, Cache> map = new HashMap<String, Cache>();

    public Map<String, Cache> getMap() {
        return map;
    }

    public void setMap(Map<String, Cache> map) {
        this.map = map;
    }

}


@Path("/service")
public class RestService {

    @POST
    @Path("anlieferung/kennzahlen")
    @Produces(MediaType.APPLICATION_JSON)
    @Consumes(MediaType.APPLICATION_JSON)
    public String getValueFromCache(String item) throws JSONException, ParseException {

                //is always null
        CacheController cacheController= (CacheController) getServletContext().getAttribute("cacheController");

                //is always null
        FacesContext context = FacesContext.getCurrentInstance();
            Application application = context.getApplication();
            CacheController cacheBean = application.evaluateExpressionGet(context, "#{cacheController}", CacheController.class);

        //doSomeStuff and check if the item is in the Cache (CacheController.getMap())
        }
}

I have initialised the cache before over the jsf application and it works. Now I would expected that I get the Cache Object through the FacesContent or ServletContext, but it is always null. Do I need to create something like a ServletListener? Can somebody give me an example? Thank you