Skip to main content
SpringerLink
Log in

Photon Modulated Coherent States of a Generalized Isotonic Oscillator by Weyl Ordering and their Non-Classical Properties

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

We construct photon modulated coherent states of a generalized isotonic oscillator by expanding the newly introduced superposed operator through Weyl ordering method. We evaluate the parameter A 3 and the s-parameterized quasi probability distribution function to confirm the non - classical nature of the states. We also calculate the identities related with the quadrature squeezing to explore the squeezing property of the states. Finally, we investigate the fidelity between the photon modulated coherent states and coherent states to quantify the non-Gaussianity of the states. The constructed states and their associated non - classical properties will add further knowledge on the potential.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Agarwal, G.S., Wolf, E.: Calculus for functions of non-commuting operators and general phase-space methods in quantum mechanics. II. Quantum Mechanics in phase space. Phys. Rev. D 2, 2161–2186 (1970)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  2. Balantekin, A.B.: Algebraic approach to shape invariance. Phys. Rev. A 57, 4188–4191 (1998)

    Article  ADS  Google Scholar 

  3. Chithiika Ruby, V., Senthilvelan, M.: An observation of quadratic algebra, dual family of nonlinear coherent states and their non-classical properties, in the generalized isotonic oscillator. J. Math. Phys. 53, 082102 (2012)

    Article  MathSciNet  ADS  Google Scholar 

  4. Chithiika Ruby, V., Senthilvelan, M.: A report on the nonlinear squeezed states and their non-classical properties of a generalized isotonic oscillator. J. Phys. A: Math. Theor. 45, 125302 (2012)

    Article  MathSciNet  ADS  Google Scholar 

  5. Chithiika Ruby, V., Karthiga, S., Senthilvelan, M.: Ladder operators and squeezed coherent states of a three-dimensional generalized isotonic nonlinear oscillator. J. Phys. A: Math. Theor. 46, 025305 (2013)

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. Wenger, J., Tualle-Brouri, R., Grangier, P.: Increasing entanglement between Gaussian states by coherent photon subtraction. Phys. Rev. Lett. 92, 153601 (2004)

    Article  ADS  Google Scholar 

  8. Zavatta, A., Viciani, S., Bellini, M.: Quantum to classical transition with single-photon-added coherent states of light. Sci. 306, 660–662 (2004)

    Article  ADS  Google Scholar 

  9. Zavatta, A., Viciani, S., Bellini, M.: Single-photon excitation of a coherent state: Catching the elementary step of stimulated light emission. Phys. Rev. A 72, 023820 (2005)

    Article  ADS  Google Scholar 

  10. Zavatta, A., Parigi, V., Kim, M. S., Jeong, H., Bellin, M.: Experimental demonstration of the bosonic commutation relation via superpositions of quantum operations on thermal light fields. Phys. Rev. Lett. 103, 140406 (2009)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. Kim, M.S.: Recent developments in photon-level operations on travelling light fields. J. Phys. B 41, 133001 (2008)

    Article  ADS  Google Scholar 

  14. 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 

  15. Chatterjee, A., Shekhar Dhar, H., Ghosh, R.: Nonclassical properties of states engineered by superpositions of quantum operations on classical states. J. Phys. B: At. Mol. Opt. Phys. 45, 205501 (2012)

    Article  ADS  Google Scholar 

  16. Xu, X.-X., Yuan, H.-C., Hu, L.-Y., Fan, H.-Y.: Statistical properties of a generalized photon-modulated thermal state. J. Phys. A: Math. Theor. 44, 445306 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  17. Agarwal, G.S., Tara, K.: Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics. Phys. Rev. A 46, 485–488 (1992)

    Article  ADS  Google Scholar 

  18. Walls, D.F., Zoller, P.: Reduced quantum fluctuations in resonance fluorescence. Phys. Rev. Lett. 47, 709–711 (1981)

    Article  ADS  Google Scholar 

  19. Walls, D.F.: Squeezed states of light. Nat. 306, 141–146 (1983)

    Article  ADS  Google Scholar 

  20. Cahill, K.E., Glauber, R.J.: Ordered expansions in boson amplitude operators. Phys. Rev. 177, 1857-1881 (1969); Cahill, K. E. and Glauber, R. J.: Density operators and quasiprobability distributions. Phys. Rev. 177, 1882–1902 (1969)

    ADS  Google Scholar 

  21. Lvovsky, A.I., Mlynek, J.: Quantum-Optical Catalysis: Generating Nonclassical States of Light by Means of Linear Optics. Phys. Rev. Lett. 88, 250401 (2002)

    Article  ADS  Google Scholar 

  22. Bartley, T.J., Donati, G., Spring, J.B., Jin, X.-M., Barbieri, M., Datta, A., Smith, B.J., Walmsley, I.A.: Multiphoton state engineering by heralded interference between single photons and coherent states. Phys. Rev. A 86, 043820 (2012)

    Article  ADS  Google Scholar 

  23. Cariñena, J.F., Perelomov, A.M., Rañada, M.F., Santander, M.: A quantum exactly solvable nonlinear oscillator related to the isotonic oscillator. J. Phys. A: Math. Theor. 41, 085301 (2008)

    Article  ADS  Google Scholar 

  24. Chithiika Ruby, V., Senthilvelan, M.: On the generalized intelligent states and certain related nonclassical states of a quantum exactly solvable nonlinear oscillator. J. Phys. A: Math. Theor. 43, 415301 (2010)

    Article  MathSciNet  Google Scholar 

  25. Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, series and products. Academic Press, New York (1980)

    MATH  Google Scholar 

  26. de Matos Filho, R.L., Vogel, W.: Nonlinear coherent states. Phys. Rev. A 54, 4560–4563 (1996)

    Article  ADS  Google Scholar 

  27. Barnett, S.M., Radmore, P.M.: Methods in theoretical quantum optics. Oxford University Press, New York (1997)

    Google Scholar 

  28. Obada, A. -S.F., Abd Al-Kader, G.M.: A class of nonlinear squeezed coherent states. J. Opt. B: Quantum Semiclass. Opt. 7, S635–S642 (2005)

    Article  ADS  Google Scholar 

  29. 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 (2010)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

VC wishes to thank the Council of Scientific and Industrial Research, Government of India for providing a Senior Research Fellowship.

Author information

Authors and Affiliations

  1. Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirappalli, 620024, Tamilnadu, India

    V. Chithiika Ruby & M. Senthilvelan

Authors
  1. V. Chithiika Ruby
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Senthilvelan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Senthilvelan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ruby, V.C., Senthilvelan, M. Photon Modulated Coherent States of a Generalized Isotonic Oscillator by Weyl Ordering and their Non-Classical Properties. Int J Theor Phys 53, 4338–4350 (2014). https://doi.org/10.1007/s10773-014-2183-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-014-2183-9

Keywords

Search

Navigation