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Non-linear coherent states
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Non-linear coherent states : ウィキペディア英語版
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^-\alpha^
* a) 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 〔R. de J. León-Montiel and H. Moya-Cessa,
International Journal of Quantum Information 9, (S1) 349 (2011). Modeling non-linear coherent states in fiber arrays.
http://dx.doi.org/10.1142/S0219749911007319〕 by generalizing the
annihilation operator:
: A=af(a^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.〔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.〕
==References==


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