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Triplet q-cat states of the Biedenharn–Macfarlane q-oscillator with q > 1

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Abstract

The normalized triplet q-cat states associated with three orthogonal subspaces of the Fock space representation of the Biedenharn–Macfarlane q-oscillator are constructed as eigenstates of the cubic power of the q-boson annihilation operator. Their corresponding resolution of the identity conditions by three appropriate positive definite measures in the q-integral on the whole complex plane is realized. We show that the antibunching effect and sub-Poissonian statistics as two nonclassical behaviors of the light field are demonstrated by three and two the measurable triplet q-cat states, respectively. The bipartite entanglements via the parity symmetry are another nonclassical behavior of the triplet q-cat states that are examined in this work. One remarkable property is that, contrary to the simple harmonic oscillator, the amount of entanglement in the bipartite entangled triplet q-cat states is an oscillatory function of coherency parameters and oscillation pattern depends on the deformation parameter q. In general, the entanglement becomes weaker as the parameter q increases. Clearly, the triplet q-cat states and their measures as well as the three nonclassical behaviors mentioned above are converted to their corresponding counterparts in the simple harmonic oscillator in the limit \(q\rightarrow 1\).

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Notes

  1. Preparing the figures of this article, we have used the approximations \(C_k(|z|^2)\simeq \sum ^{100}_{n=0}\frac{q^{-\frac{3}{2}n(3n+2k+1)}|z|^{6n+2k}}{\prod _{l=1}^{3n+k} \frac{q^l-q^{-l}}{q-q^{-1}}}\) for \(k=0, 1, 2\).

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Acknowledgements

This research has been supported by the University of Tabriz under Grant S/3899.

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  1. Department of Theoretical Physics and Astrophysics, Faculty of Physics, University of Tabriz, P. O. Box 51666-16471, Tabriz, Iran

    H. Fakhri & M. Sayyah-Fard

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  1. H. Fakhri
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Fakhri, H., Sayyah-Fard, M. Triplet q-cat states of the Biedenharn–Macfarlane q-oscillator with q > 1. Quantum Inf Process 19, 19 (2020). https://doi.org/10.1007/s11128-019-2507-z

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