jQuery UI is a toolkit for rendering common components, such as datepickers, draggables, etc. No adjustments are needed to make it work with Laravel Mix.
mix.js('resources/js/app.js', 'public/js')
.sass('resources/sass/app.scss', 'public/css');
npm install jquery-ui --save-dev
// resources/js/app.js
import $ from 'jquery';
window.$ = window.jQuery = $;
import 'jquery-ui/ui/widgets/datepicker.js';
// resources/sass/app.scss
@import '~jquery-ui/themes/base/all.css';
// resources/js/app.js
$('#datepicker').datepicker();