In quantum physics, the squeeze operator for a single mode of the electromagnetic field is

where the operators inside the exponential are the ladder operators is the identity operator.

Its action on the annihilation and creation operators produces

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:

Application of both operators above on the vacuum produces a displaced squeezed state:

1. .

Or a squeezed coherent state:

1. .

Derivation of action on creation operator

.

. We can now make use of the general equalityUsing these equalities, we obtain

so that finally we get

The same result is also obtained by differentiating the transformed operator

. The technique can be generalised to other operators or state transformations.

See also

• Squeezed coherent state

References