Squeeze operator
In quantum physics, the squeeze operator for a single mode of the electromagnetic field is S ^ ( z ) = exp ( 1 2 ( z ∗ a ^ 2 − z a ^ † 2 ) ) , z = r e i θ {\displaystyle {\hat {S}}(z)=\exp \left({1 \over 2}(z^{*}{\hat {a}}^{2}-z{\hat {a}}^{\dagger 2})\right),\qquad z=r\,e^{i\theta }} where the operators inside the exponential are the ladder operators. It is a unitary operator and therefore obeys S ( z ) S † ( z ) = S † ( z ) S ( z ) = 1 ^ {\displaystyle S(z)\,S^{\dagger }(z)=S^{\dagger }(z)\,S(z)={\hat {1}}} , where 1 ^ {\displaystyle {\hat {1}}} is the identity operator.