@Entity
public class TestEntity {
    public enum MyEnum {
        FOO,
        BAR;
    }

    @Id
    @GeneratedValue(strategy = GenerationType.TABLE, generator = "pkGen")
    @TableGenerator(allocationSize = 1000, initialValue = 0, name = "pkGen", table = "PRIMARY_KEYS")
    private int id;

    @ElementCollection(targetClass = MyEnum.class)
    @Enumerated(EnumType.STRING)
    @MapKeyClass(String.class)
    Map<String, MyEnum> col = new HashMap<>();

    public Map<String, MyEnum> getCol() {
        return col;
    }
}

@LocalBean 
public class EclipseLinkBean {

@PersistenceContext
private EntityManager em;

    public void test() {
        CriteriaBuilder builder = em.getCriteriaBuilder();
        CriteriaQuery<TestEntity> q = builder.createQuery(TestEntity.class);
        Root<TestEntity> testEntity = q.from(TestEntity.class);
        MapJoin<TestEntity, String, MyEnum> col = testEntity.joinMap("col");
        q.where(builder.equal(col.key(), "foobar"));
        em.createQuery(q).getResultList();
    }

    public void test2() {
         em.createQuery("SELECT te FROM TestEntity te JOIN te.col c WHERE KEY(c) = 'foobar'").getResultList();
    }
}

	@ElementCollection()
	Map<String, Integer> col = new HashMap<>();