How to apply a Field Formatter to a node field programmatically?
The entity view builder provides a method to build a render array for a single field using a field formatter:

Drupal\Core\Entity\EntityViewBuilderInterface::viewField()

  /**
   * Builds a renderable array for the value of a single field in an entity.
   *
   * The resulting output is a fully themed field with label and multiple
   * values.
   *
   * This function can be used by third-party modules that need to output an
   * isolated field.
   * - Do not use inside node (or any other entity) templates; use
   *   render($content[FIELD_NAME]) instead.
   * - The FieldItemInterface::view() method can be used to output a single
   *   formatted field value, without label or wrapping field markup.
   *
   * The function takes care of invoking the prepare_view steps. It also
   * respects field access permissions.
   *
   * @param \Drupal\Core\Field\FieldItemListInterface $items
   *   FieldItemList containing the values to be displayed.
   * @param string|array $display_options
   *   Can be either:
   *   - The name of a view mode. The field will be displayed according to the
   *     display settings specified for this view mode in the $field
   *     definition for the field in the entity's bundle. If no display settings
   *     are found for the view mode, the settings for the 'default' view mode
   *     will be used.
   *   - An array of display options. The following key/value pairs are allowed:
   *     - label: (string) Position of the label. The default 'field' theme
   *       implementation supports the values 'inline', 'above' and 'hidden'.
   *       Defaults to 'above'.
   *     - type: (string) The formatter to use. Defaults to the
   *       'default_formatter' for the field type. The default formatter will
   *       also be used if the requested formatter is not available.
   *     - settings: (array) Settings specific to the formatter. Defaults to the
   *       formatter's default settings.
   *     - weight: (float) The weight to assign to the renderable element.
   *       Defaults to 0.
   *
   * @return array
   *   A renderable array for the field values.
   *
   * @see \Drupal\Core\Entity\EntityViewBuilderInterface::viewFieldItem()
   */
  public function viewField(FieldItemListInterface $items, $display_options = []);


To apply this method on a field object you can use $field-&gt;view() or if you only want a single value from a multivalue field without the wrapper and label you can also use it on a field item (delta).

EDIT: With this code you can find the values that you need.

$nid = 76;
$node = \Drupal::service('entity.manager')-&gt;getStorage('node')-&gt;load($nid);
foreach ($node-&gt;field_aaaa as $i =&gt; $delta) {   
  dpm($delta-&gt;value);
  dpm((string) \Drupal::service('renderer')-&gt;render($delta-&gt;view(array('type' =&gt; 'title_formatter'))));
}