Non linear coherent states

Coherent states are quasi-classical states that may be defined in different ways, for instance as eigenstates of the annihilation operator

or as a displacement from the vacuum

where D ( α ) = exp ⁡ ( α a † − α ∗ a ) is the Sudarshan-Glauber displacement operator.

One may think of a non-linear coherent state by generalizing the annihilation operator:

and then using any of the above definitions by exchanging a by A . The above definition is also known as an f -deformed annihilation operator.