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 is the Sudarshan-Glauber displacement operator.R. J. Glauber "Coherent and Incoherent States of the Radiation Field", Physical Review 131, 2766 (1963). Coherent and Incoherent States of the Radiation Field. http://link.aps.org/doi/10.1103/PhysRev.131.2766

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.V. I. Man'ko, G. Marmo, F. Zaccaria and E. C. G. Sudarshan, Proceedings of the IV Wigner Symposium, eds. N. Atakishiyev, T. Seligman and K. B. Wolf (World Scientific, Singapore, 1996), p. 421

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