Non-linear 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 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 by . The above definition is also known as an -deformed annihilation operator.
