Pass a parameter to a controller using jquery ajax

I have created a view and a controller, the controller I am wanting to return some search results. I am calling the controller using jquery

   <input type="text" id="caption" />
        <a href="#" id="search">Search</a>
        <script>
            $("#search").click(function () {
                alert('called');
                var p = { Data: $('#search').val() };
                $.ajax({
                    url: '/Ingredients/Search',
                    type: "POST",
                    data: JSON.stringify(p),
                    dataType: "json",
                    contentType: "application/json; charset=utf-8",
                    success: function (data) {
                        alert(data);
                    },
                    error: function () {
                        alert("error");
                    }
                });
            });

My controller looks like this

 [HttpPost]
    public ActionResult Search(string input)
    {
        var result = _db.Ingredients.Where(i => i.IngredientName == input);

        return new JsonResult() {Data = new {name="Hello There"}};
    }

My problem is I am not sure how to get the varible from my jquery call into the controller, I have put a breakpoint on the controller and its been hit however the input string is always null.

What have I done wrong?