Displacement_operator
In the quantum mechanics study of optical phase space, the displacement operator for one mode is the shift operator in quantum optics,
- ,
where is the amount of displacement in optical phase space, is the complex conjugate of that displacement, and and are the lowering and raising operators, respectively.
The name of this operator is derived from its ability to displace a localized state in phase space by a magnitude . It may also act on the vacuum state by displacing it into a coherent state. Specifically, where is a coherent state, which is an eigenstate of the annihilation (lowering) operator.