In quantum physics, the squeeze operator for a single mode of the electromagnetic field is
formula_1
where the operators inside the exponential are the ladder operators. It is a unitary operator and therefore obeys formula_2, where formula_3 is the identity operator.
Its action on the annihilation and creation operators produces
formula_4
The squeeze operator is ubiquitous in quantum optics and can operate on any state. For example, when acting upon the vacuum, the squeezing operator produces the squeezed vacuum state.
The squeezing operator can also act on coherent states and produce squeezed coherent states. The squeezing operator does not commute with the displacement operator:
 formula_5
nor does it commute with the ladder operators, so one must pay close attention to how the operators are used. There is, however, a simple braiding relation, 
formula_6
Application of both operators above on the vacuum produces displaced squeezed state:
formula_7.
Or Squeezed coherent state:
formula_8.
Derivation of action on creation operator.
As mentioned above, the action of the squeeze operator formula_9 on the annihilation operator formula_10 can be written as formula_11
References.
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