Physics:Non-linear coherent states
From HandWiki
Coherent states are quasi-classical states that may be defined in different ways, for instance as eigenstates of the annihilation operator
- [math]\displaystyle{ a|\alpha\rangle=\alpha|\alpha\rangle }[/math],
or as a displacement from the vacuum
- [math]\displaystyle{ |\alpha\rangle=D(\alpha)|0\rangle }[/math],
where [math]\displaystyle{ D(\alpha)=\exp(\alpha a^{\dagger}-\alpha^* a) }[/math] is the Sudarshan-Glauber displacement operator.[1]
One may think of a non-linear coherent state [2] by generalizing the annihilation operator:
- [math]\displaystyle{ A=af(a^{\dagger}a) }[/math],
and then using any of the above definitions by exchanging [math]\displaystyle{ a }[/math] by [math]\displaystyle{ A }[/math] . The above definition is also known as an [math]\displaystyle{ f }[/math]-deformed annihilation operator.[3][4]
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
- ↑ Man'ko, V I; Marmo, G; Sudarshan, E C G; Zaccaria, F (1997). "f-oscillators and nonlinear coherent states". Physica Scripta 55 (5): 528–541. doi:10.1088/0031-8949/55/5/004. ISSN 0031-8949.
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