How do I convert this php array into a JavaScript array of objects?

// responseData is fetched via Ajax-Get
var obj = jQuery.parseJSON(responseData);
alert(obj.property);

// full ajax example
jQuery.ajax({
    url: "/index.php?action=whereMyDataIs", // here php gives the json response
    type: "GET",
    dataType: "json",
    async: false,
    success: function (data) {
        console.log(data);
        alert(JSON.stringify(data));
    }
});

You already have the PHP part (array is build, json_encoded and send as response), the next step is that you fetch this json_response on client-side, by doing a ajax get request to the PHP script providing the response. By specifying dataType:"json" you tell jQuery to automatically parse the incoming data as Object Notation. If you want to output it again, e.g. with alert, you need to stringify it again.

To answer the question regarding amcharts:

// add the loadJson function to AmCharts
// but you could also use jQuery as demonstrated above
AmCharts.loadJSON = function(url) {
  // create the request
  if (window.XMLHttpRequest) {
    // IE7+, Firefox, Chrome, Opera, Safari
    var request = new XMLHttpRequest();
  } else {
    // code for IE6, IE5
    var request = new ActiveXObject('Microsoft.XMLHTTP');
  }

  // load it
  // the last "false" parameter ensures that our code will wait before the
  // data is loaded
  request.open('GET', url, false);
  request.send();

  // parse adn return the output
  return eval(request.responseText);
};

// init chart library
var chart;

// lets build that chart
AmCharts.ready(function() {

   // load the data from your php script (the json response)
   var chartData = AmCharts.loadJSON('script.php');

   // verify in browser console, if the data is loaded and parsed correctly
   console.log(chartData);

   // build the chart
   // ...

   // output the chart
   chart.write("chartdiv");
   });