Implement simple arrow key navigation into my AJAX live search

This should be a pretty simple project for someone who knows their way around AJAX/JS. Basically, I have a search engine that searches a database of movie titles. Using AJAX, the web app currently displays a live list of results. Whilst these results can be clicked on, I'd like users to be able to use the up and down arrow keys on their keyboard to select a result. You can see what I mean in the attached image. Basically, the user should be able to arrow key down from the search box when they've started typing and select an option. Pressing the enter key should auto-fill the box, just as clicking on an option does now. Also attached is the index page which includes the functionality and the PHP used for the back-end search of the database. I hope that makes sense.