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

a|\alpha \rangle =\alpha |\alpha \rangle

or as a displacement from the vacuum

|\alpha \rangle =D(\alpha )|0\rangle

where $D(\alpha )=\exp(\alpha a^{\dagger }-\alpha ^{*}a)$ is the Sudarshan-Glauber displacement operator.^[1]

One may think of a non-linear coherent state ^[2] by generalizing the annihilation operator:

A=af(a^{\dagger }a)

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.^[3]

References

↑ 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
↑ León-Montiel, R. de J.; Moya-Cessa, H. (2011). "Modeling non-linear coherent states in fiber arrays". International Journal of Quantum Information. 9 (S1): 349–355. doi:10.1142/S0219749911007319.
↑ 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; Physica Scripta 55 (1997) 528.

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