@OneToOne is not generating a unique constraint on the owning table

<?php

/** @Entity */
class Customer
{
    /**
     * @Id @Column(name="id", type="integer")
     */
    private $customerId;

    /**
     * @OneToOne(targetEntity="Cart", mappedBy="customer")
     */
    private $cart;
}

/** @Entity */
class Cart
{
    /**
     * @Id @Column(name="id", type="integer", nullable=false)
     */
    private $cartId;

    /**
     * Shouldn't unique=true be setting a UNIQUE index on customer_id ??
     *
     * @OneToOne(targetEntity="Customer", inversedBy="cart")
     * @JoinColumn(name="customer_id", referencedColumnName="id", nullable=false, unique=true)
     */
    private $customer;
}

CREATE TABLE `customer` (
  `id` int(11) NOT NULL,
  PRIMARY KEY (`id`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8;

CREATE TABLE `cart` (
  `id` int(11) NOT NULL,
  `customer_id` int(11) NOT NULL,
  PRIMARY KEY (`id`),
  KEY `customer_id` (`customer_id`),  /* this should be UNIQUE KEY  */
  CONSTRAINT `cart_ibfk_1` FOREIGN KEY (`customer_id`) REFERENCES `customer` (`id`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8