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Nonclassicality Generated by Applying Hermite–Polynomials Photon-Added Operator on the Even/Odd Coherent States

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Abstract

We examine nonclassical properties of the quantum state generated by applying Hermite polynomials photon-added operator on the even/odd coherent state (HPECS/HPOCS). Explicit expressions for its nonclassical properties, such as quantum statistical properties and squeezing phenomenon, are obtained. It is interesting to find that the HPECS/HPOCS exhibits sub-Poissonian distribution, anti-bunching effects and negative values of the Wigner function. Thus, we confirm the HPPECS/HPPOCS is a new nonclassical state. Finally, we reveal that the HPPECS/HPPOCS is a novel intelligent state by its squeezing effects in position distribution and quadrature squeezing.

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References

  1. Glauber, R.J.: Photon correlations. Phys.Rev. Lett. 10, 84–86 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  2. Bialynicka-Birula, Z.: Properties of the generalized coherent State. Phys. Rev. 173, 1207–1209 (1968)

    Article  ADS  Google Scholar 

  3. Stoler, D.: Generalized coherent states. Phys. Rev. D 4, 2309–2312 (1971)

    Article  ADS  Google Scholar 

  4. Dodonov, V.V., Malkin, I.A., Man’ko, V.I.: Even and odd coherent states and excitations of a singular oscillator. Physica 72, 597–618 (1974)

    Article  ADS  MathSciNet  Google Scholar 

  5. Dodonov, V.V.: Nonclassical states in quantum optics: a squeezed review of the first 75 years. J. Opt. B: Quantum Semiclass. Opt. 4, R1–R33 (2002)

  6. Deleglise, S., Dotsenko, I., Sayrin, C., Bernu, J., Brune, M., Raimond, J.-M., Haroche, S.: Reconstruction of non-classical cavity field states with snapshots of their decoherence. Nature 455, 510–514 (2008)

    Article  ADS  Google Scholar 

  7. Sanders, B.C.: Review of entangled coherent states. J. Phys. A: Math. Theor. 45, 244002–1-12 (2012)

    MathSciNet  MATH  Google Scholar 

  8. Hu, L.-Y., Xu, X.-X., Wang, Z.-S., Xu, X.-F.: Photon-subtracted squeezed thermal state: nonclassicality and decoherence. Phys. Rev. A 82, 043842–1-12 (2010)

    ADS  Google Scholar 

  9. Lee, S.-Y., Nha, H.: Quantum state engineering by a coherent superposition of photon subtraction and addition. Phys. Rev. A 82, 053812 (2010)

    Article  ADS  Google Scholar 

  10. Yuan, H.-C., Xu, X.-X., Fan, H.-Y.: Generalized photon-added coherent state and its quantum statistical properties. Chin. Phys. B 19, 104205–1-9 (2010)

    Google Scholar 

  11. Agarwal, G.S., Tara, K.: Nonclassical properties of states generated by the excitations on a coherent state. Phys. Rev. A 43, 492–497 (1991)

    Article  ADS  Google Scholar 

  12. Parigi, V., Zavatta, A., Kim, M.S., Bellini, M.: Probing quantum commutation rules by addition and subtraction of single photons to/from a light field. Science 317, 1890–1893 (2007)

    Article  ADS  Google Scholar 

  13. Ourjoumtsev, A., Dantan, A., Tualle-Brouri, R., Grangier, P.h.: Increasing entanglement between Gaussian states by coherent photon subtraction. Phys. Rev. Lett. 98, 030502–1-4 (2007)

    Article  ADS  Google Scholar 

  14. Ren, G., Du, J.-M., Yu, H.-J., Xu, Y.-J.: Nonclassical properties of Hermite polynomial’s coherent state. J. Opt. Soc. Am. B 29, 3412–3418 (2012)

    Article  ADS  Google Scholar 

  15. Wang, Z., Li, H.-M., Yuan, H.-C.: Quasi-probability distributions and decoherence of Hermite-excited squeezed thermal states. J. Opt. Soc. Am. B 31, 2163–2174 (2014)

    Article  ADS  Google Scholar 

  16. Zhang, H.L., Yuan, H.C., Hu, L.Y., Xu, X.X.: Opt. Commun. 356, 223–229 (2015)

    Article  ADS  Google Scholar 

  17. Ren, G., Ma, J.-G., Du, J.-M., Yu, H.-J.: Hermite polynomial’s photon added coherent state and its non-classical properties. Int. J. Theor. Phys. 55, 2071–2088 (2016)

    Article  MATH  Google Scholar 

  18. Solomon Ivan, J., Sabapathy, K.K., Simon, R.: Operator-sum representation for bosonic Gaussian channels. Phys. Rev. A 84, 042311–1-26 (2011)

    ADS  Google Scholar 

  19. Mandel, L., Wolf, E.: Optical Coherence and Quantum Optics. University Press, Cambridge (1995)

    Book  Google Scholar 

  20. Tavassoly, M.K.: On the non-classicality features of new classes of nonlinear coherent states. Opt. Commun. 283, 5081–5091 (2010)

    Article  ADS  Google Scholar 

  21. Veitch, V., Wiebe, N., Ferrie, C., Emerson, J.: Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation. New J. Phys. 15, 013037–1-20 (2013)

    Google Scholar 

  22. Arnoldus, H.F., George, T.F.: Squeezing in resonance fluorescence and Schrodinger’s uncertainty relation. Phys. A 222, 330–346 (1995)

    Article  Google Scholar 

  23. Yurke, B., Stoler, D.: Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion. Phys. Rev. Lett. 57, 13–16 (1986)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work is supported by the Natural Science Foundation of the Anhui Higher Education Institutions of China (Grant No. KJ2015A268 and KJ2016A672).

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Authors and Affiliations

  1. Department of Physics, Huainan Normal University, Huainan, 232001, People’s Republic of China

    Gang Ren, Jian-ming Du, Wen-hai Zhang & Hai-jun Yu

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  1. Gang Ren
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  2. Jian-ming Du
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  3. Wen-hai Zhang
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  4. Hai-jun Yu
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Correspondence to Gang Ren.

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Ren, G., Du, Jm., Zhang, Wh. et al. Nonclassicality Generated by Applying Hermite–Polynomials Photon-Added Operator on the Even/Odd Coherent States. Int J Theor Phys 56, 1537–1549 (2017). https://doi.org/10.1007/s10773-017-3293-y

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