复制包含对象的PHP数组项

I would like to copy an array item that contains an object.

$arr = [
    'first_item' => [
        'label' => 'a',
        'date' => new DateTime('1999-12-30')
    ],
    'second_item' => [
        'label' => 'b',
        'date' => new DateTime('1999-12-31')
    ]
];

$copy = $arr['second_item'];
$copy['label'] = 'c'; // OK, does not affect $arr['second_item']
$copy['date']->setDate(2000, 1, 1); // changes $arr['second_item'] as well

Just out of ideas, I tried to replace $copy = $arr['second_item'] by $copy = clone $arr['second_item'] but it (understandably) fails with a *"Fatal error: __clone method called on non-object"* message.