As mentioned above, the action of the squeeze operator S ( z ) on the annihilation operator a can be written as S † † ( z ) a S ( z ) = cosh ⁡ ⁡ ( | z | ) a − − z | z | sinh ⁡ ⁡ ( | z | ) a † † . To derive this equality, let us define the (skew-Hermitian) operator A ≡ ≡ ( z a † † 2 − − z ∗ ∗ a 2 ) / 2 , so that S † † = e A .