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Even and odd \(\lambda\)-deformed binomial states: minimum uncertainty states

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Abstract.

Following the lines of the recent papers (Ann. Phys. 362, 659670 (2015) and Mod. Phys. Lett. A 37, 1550198 (2015)), we introduce even and odd \(\lambda\)-deformed binomial states (\(\lambda\)-deformed BSs) \( \vert M,\eta,\lambda\rangle_{\pm}\), in which for \(\lambda =0\), they lead to ordinary even and odd binomial states (BSs). We show that these states reduce to the \(\lambda\)-deformed cat-states in the special limits. We establish the resolution of identity property for them through a positive definite measure on the unit disc. The effect of the deformation parameter \(\lambda\) on the nonclassical properties of introduced states is investigated numerically. In particular, through the study of squeezing, we show that in contrast with the odd BSs, the odd \(\lambda\)-deformed BSs have squeezing. Also, we show that the even and odd \(\lambda\)-deformed BSs minimize the uncertainty relation for large values of \(\lambda\).

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Authors and Affiliations

  1. Department of Physics, Azarbaijan Shahid Madani University, PO Box 51745-406, Tabriz, Iran

    B. Mojaveri & S. Amiri Faseghandis

  2. Department of Physics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

    A. Dehghani

Authors
  1. B. Mojaveri
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  2. A. Dehghani
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  3. S. Amiri Faseghandis
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Correspondence to B. Mojaveri.

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Mojaveri, B., Dehghani, A. & Faseghandis, S.A. Even and odd \(\lambda\)-deformed binomial states: minimum uncertainty states. Eur. Phys. J. Plus 132, 128 (2017). https://doi.org/10.1140/epjp/i2017-11397-8

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