Skip to main content
SpringerLink
Log in

Antibunching of photons in a coherent radiation field coupled to a non-degenerate parametric oscillator beyond rotating wave approximation

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

Under the classical (strong) pump condition, the Hamiltonian involving the signal and the idler modes of a non-degenerate parametric oscillator is exhibited. Without using the usual rotating wave approximation (RWA), the analytical solutions of the field operators are used to investigate the antibunching of photons of the input radiation field coupled to the non-degenerate parametric oscillator. By using the symbolic calculation, the antibunching of photons for both the signal and idler modes are investigated. In particular, the effects of the inclusion of rotating wave approximated terms on the antibunching of photons are clearly indicated. To substantiate the analytical results, the temporal evolution of signal photon and idler photons, and the antibunching effects of the signal and idler modes are investigated numerically by using the QuTip 3.1.0. The exact numerical results obtained by QuTip 3.1.0 matches extremely well with those of the analytical results. The present article and hence the analytical method might be of use for investigating the situations of having ultra-strongly and deep-strongly coupled systems where the possibilities of using RWA is completely ruled out.

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
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. R W Boyd, Nonlinear optics, 2nd edn (Academic Press, New York, 2006).

    Google Scholar 

  2. A Yariv, Quantum electronics, 3rd edn (John Wiley & Sons, New York, 1988)

  3. J Perina, Z Hradil and J Branislav, Quantum optics and fundamentals of physics (Kluwer Academic Publishers, Dordrecht, 1994)

    Google Scholar 

  4. Z Ficek and M R B Wahiddin, Quantum optics: Fundamentals and applications (International Islamic University Malaysia, Kuala Lumpur, 2004)

    MATH  Google Scholar 

  5. Z Ficek and M R B Wahiddin, Quantum optics for beginners (Pan Stanford Publishing, Singapore, 2014)

    MATH  Google Scholar 

  6. P A Franken, A E Hills, C W Peters and G Weinreich, Phys. Rev. Lett. 7, 118 (1961)

    Article  ADS  Google Scholar 

  7. D R White and W H Louisell, Phys. Rev. A 1, 1347 (1970)

    Article  ADS  Google Scholar 

  8. A Yariv and W H Louisell, IEEE J. Quant. Electron. QE-2, 418 (1966)

    Article  ADS  Google Scholar 

  9. L-A Wu, M Xiao and H J Kimble, J. Opt. Soc. Am. B 10, 1465 (1987)

    Article  ADS  Google Scholar 

  10. N Bloembergen and Y R Shen, Phys. Rev. A 133, 37 (1964).

    Article  ADS  Google Scholar 

  11. W H Louisell, A Yariv and A E Siegman, Phys. Rev. 124, 1646 (1961)

    Article  ADS  Google Scholar 

  12. Y Zhang, Fron. Phys. China 3, 126 (2008)

    Article  ADS  Google Scholar 

  13. N C Wong, Phys. Rev. A 45, 3176 (1992)

    Article  ADS  Google Scholar 

  14. L Allen and J H Eberly, Optical resonance and two-level atoms (Dover Publications, New York, 1987)

  15. J Larson, Phys. Rev. Lett. 108, 033601 (2012)

    Article  ADS  Google Scholar 

  16. M Janowicz and A Orlowski, Rep. Math. Phys. 54, 71 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  17. M Mirzaee and M Batavani, Chin. Phys. B 24, 040306 (2015)

    Article  ADS  Google Scholar 

  18. A Moroz, Ann. Phys. 340, 252 (2014)

    Article  ADS  Google Scholar 

  19. F Yoshihara, T Fuse, S Ashhab, K Kakuyanagi, S Saito and K Semba, Nat. Phys. 13, 44 (2017)

    Article  Google Scholar 

  20. A Le Boite, M-J Hwang, H Nha and M B Plenio, Phys. Rev. A 94, 033827 (2016)

    Article  ADS  Google Scholar 

  21. P Forn-Díaz, J J García-Ripoll, B Peropadre, J-L Orgiazzi, M A Yurtalan, R Belyansky, C M Wilson and A Lupascu, Nat. Phys. 13, 39 (2017)

    Article  Google Scholar 

  22. C Ciuti, G Bastard and I Carusotto, Phys. Rev. B 72, 115303 (2005)

    Article  ADS  Google Scholar 

  23. C Ciuti and I Carusotto, Phys. Rev. A 74, 033811 (2006)

    Article  ADS  Google Scholar 

  24. M Alam, S Mandal and M R B Wahiddin, Optik 157, 1035 (2018)

    Article  ADS  Google Scholar 

  25. M Alam, S Mandal and M R B Wahiddin, Opt. Commun. 398, 1 (2017)

    Article  ADS  Google Scholar 

  26. A H Nayfeh, Introduction to perturbation techniques (Wiley, New York, 1981)

    MATH  Google Scholar 

  27. A H Nayfeh and D T Mook, Non-linear oscillations (Wiley, New York, 1979)

    MATH  Google Scholar 

  28. C M Bender and L M A Bettencourt, Phys. Rev. Lett. 77, 4114 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  29. R Bellman, Methods of nonlinear analysis (Academic Press, New York, 1970) Vol. 1, p. 198

    Google Scholar 

  30. D F Walls, Nature 306, 141 (1983)

    Article  ADS  Google Scholar 

  31. R Loudon and P L Knight, J. Mod. Opt. 34, 709 (1987)

    Article  ADS  Google Scholar 

  32. D F Walls, Nature 280, 451 (1979)

  33. R Loudon, The quantum theory of light, 2nd edn (Oxford University Press, Oxford, 1983)

  34. H P Yuen, Phys. Rev. A 13, 2226 (1976)

  35. D Stoller, B E A Saleh and M C Teich, Opt. Acta 32, 345 (1985)

    Article  ADS  Google Scholar 

  36. C C Gerry, J. Mod. Opt. 40, 1053 (1993)

    Article  ADS  Google Scholar 

  37. J R Johansson, P D Nation and F Nori, Comput. Phys. Commun. 184, 1234 (2013)

  38. J R Johansson, P D Nation and F Nori, Comput. Phys. Commun. 183, 1760 (2012)

    Article  ADS  Google Scholar 

  39. S Fedortchenko, S Felicetti, D Markovic, S Jezouin, A Keller, T Coudreau, B Huard and P Milman, arXiv:1612.05542v1

Download references

Acknowledgements

Generous funding from the Malaysia Ministry of Education FRGS17-024-0590 is gratefully acknowledged. One of the authors (SM) thanks the University Grants Commission, New Delhi for financial support through a major research project (F.No.42-852/2013(SR)). SM also is thankful to the Council of Scientific and Industrial Research (CSIR), Government of India for financial support (03(1283)/13/EMR-II). MK is grateful to the UGC for the award of senior research fellowship (F1-17.1/2016-17/NFST-2015-17-ST-WES-878/(SA-III/Website).

Author information

Authors and Affiliations

  1. Department of Physics, Visva Bharati, Santiniketan, 731 235, India

    Swapan Mandal, Mohosin Alam & Monojit Kora

  2. Department of Computer Science, Kulliyyah of ICT, International Islamic University Malaysia, 53100, Kuala Lumpur, Malaysia

    Mohamed Ridza Wahiddin

Authors
  1. Swapan Mandal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohosin Alam
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Monojit Kora
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mohamed Ridza Wahiddin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Swapan Mandal.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mandal, S., Alam, M., Kora, M. et al. Antibunching of photons in a coherent radiation field coupled to a non-degenerate parametric oscillator beyond rotating wave approximation. Pramana - J Phys 95, 82 (2021). https://doi.org/10.1007/s12043-021-02121-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-021-02121-0

Keywords

PACS Nos

Search

Navigation