Squeeze operator

From Wikipedia, the free encyclopedia

Quantum optics operators
Ladder operators
Creation and annihilation operators
Displacement operator
Rotation operator (quantum optics)
Squeeze operator
Anti-symmetric operator
[edit this template]

The squeeze operator for a single mode is

$\hat{S}(z) = \exp \left ( {1 \over 2} (z^* \hat{a}^2 - z \hat{a}^{\dagger 2}) \right ) , \qquad z = r e^{i\theta}$

where the operators inside the exponential are the ladder operators. 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. It is important to note that the squeezing operator does not commute with the displacement operator:

$\hat{S}(z) \hat{D}(\alpha) \neq \hat{D}(\alpha) \hat{S}(z)$