New Jersey Statutes Title 2A. Administration of Civil and Criminal Justice 2A § 42-5

If a tenant of real estate shall give notice of his intention to quit the premises by him held at a time specified in such notice, and shall not deliver up the possession of such real estate at the time specified in the notice, such tenant, his executors or administrators, shall, from such time, pay to his landlord or lessor, his heirs or assigns, double the rent which he should otherwise have paid, to be levied, sued for and recovered at the same times and in the same manner as the single rent before the giving of such notice could be levied, sued for and recovered. Such double rent shall continue to be paid during all the time such tenant shall continue in possession after the giving of such notice.