Skip to main content
SpringerLink
Log in

Curl forces and their role in optics and ion trapping

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

The position dependent nonconservative forces are called curl forces introduced recently by M.V. Berry, P. Shukla, J. Phys. A 45, 305201 (2012). In this article, we elucidate the role of curl forces in classical and quantum optics. At first we review the work of A. Ashkin and demonstrate the existence of curl force. We then discuss the role of curl force in ion trapping theory and map it to rotating saddle potential. Finally we show the connection between the two level atom problem, curl forces and their connection to Pais-Uhlenbeck oscillator.

Graphical abstract

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

Similar content being viewed by others

References

  1. L.L. Landau, E.M. Lifshitz Lifshitz, Mechanics. 3rd edn. (Heinemann, Butterworth, 1993)

  2. M.V. Berry, P. Shukla, J. Phys. A 45, 305201 (2012)

    MathSciNet  Google Scholar 

  3. M.V. Berry, P. Shukla, Proc. R. Soc. A 471, 20150002 (2015)

    ADS  Google Scholar 

  4. M.V. Berry, P. Shukla, J. Phys. A 46, 422001 (2013)

    MathSciNet  Google Scholar 

  5. P.C. Chaumet, M. Nieto-Vesperinas, Opt. Lett. 25, 1065 (2000)

    ADS  Google Scholar 

  6. S. Albaladejo, M.I. Marqués, M. Laroche, J.J. Sáenz, Phys. Rev. Lett 102, 113602 (2009)

    ADS  Google Scholar 

  7. Y. Shimizu, H. Sasada, Am. J. Phys. 66, 960 (1998)

    ADS  Google Scholar 

  8. M.C. Gutzwiller, J. Math. Phys. 14, 139 (1973)

    ADS  Google Scholar 

  9. R.L. Devaney, J. Diff. Equat. 29, 253 (1978)

    ADS  Google Scholar 

  10. J.E. Marsden, T.S. Ratiu, An Introduction to Mechanics and Symmetry, Texts in Applied Mathematics (Springer-Verlag, Berlin, Heidelberg, New York, 1994)

  11. O. Kirillov, M. Levi, Am. J. Phys. 84, 26 (2016)

    ADS  Google Scholar 

  12. O. Kirillov, M. Levi, Nonlinearity 30, 1109 (2017)

    ADS  MathSciNet  Google Scholar 

  13. P. Guha, Eur. Phys. J. Plus 133, 536 (2018)

    Google Scholar 

  14. S. Earnshaw, Trans. Cambridge Philos. Soc. 7, 97 (1842)

    ADS  Google Scholar 

  15. W. Paul, Rev. Mod. Phys. 62, 531 (1990)

    ADS  Google Scholar 

  16. A. Stephenson, Philos. Mag. 6, 233 (1908)

    Google Scholar 

  17. P.L. Kapitsa, Soviet Phys. JETP. 21, 588 (1951)

    MathSciNet  Google Scholar 

  18. P.L. Kapitsa, Usp. Fiz. Nauk. 44, 7 (1951)

    ADS  Google Scholar 

  19. M. Knoop, N. Madsen, R.C. Thompson, in Physics with Trapped Charged Particles (2013), Chap. 1

  20. R.S. Van DyckJr, P.B. Schwinberg, H.G. Dehmelt, Phys. Rev. Lett. 38, 310 (1977)

    ADS  Google Scholar 

  21. W. Nagourney, J. Sandberg, H.G. Dehmelt, Phys. Rev. Lett. 56, 2797 (1986)

    ADS  Google Scholar 

  22. H.G. Dehmelt, Rev. Mod. Phys. 62, 525 (1990)

    ADS  Google Scholar 

  23. J. Byrne, P.S. Farago, Proc. Phys. Soc. 86, 801 (1965)

    ADS  Google Scholar 

  24. B.G. Gräff, E. Klempt, Z. Naturforsch. A 22, 1960 (1967)

    ADS  Google Scholar 

  25. A.A. Sokolov, YuG Pavlenko, Opt. Spectrosc. 22, 1 (1967)

    ADS  Google Scholar 

  26. H.J. Metcalf, P. van der Straten, Laser Cooling and Trapping. 2nd edn. (Springer, 2002)

  27. C.M. Bender, M. Gianfreda, B. Peng, S.K. Özdemir, L. Yang, Phys. Rev. A 88, 062111 (2013)

    ADS  Google Scholar 

  28. M.V. Berry, P. Shukla, New J. Phys. 18, 063018 (2016)

    ADS  Google Scholar 

  29. A. Ghose-Choudhury, P. Guha, A. Paliathanasis, P.G.L. Leach, Int. J. Geom. Methods Mod. Phys. 14, 1750018 (2017)

    MathSciNet  Google Scholar 

  30. P.L. Kapitsa, Zhur. Tekhn. Fiz. 9, 124 (1939)

    Google Scholar 

  31. D.R. Merkin, Gyroscopic systems (Nauka, Moscow, 1956) [in Russian]

  32. D.R. Merkin, Introduction to the theory of stability (Springer-Verlag, New York, 1997)

  33. A. Ashkin, Phys. Rev. Lett. 24, 156 (1970)

    ADS  Google Scholar 

  34. A. Ashkin, J.P. Gordon, Opt. Lett. 8, 511 (1983)

    ADS  Google Scholar 

  35. A. Ashkin, J.M. Dziedzic, J.E. Bjorkholm, S. Chu, Opt. Lett. 11, 288 (1986)

    ADS  Google Scholar 

  36. S. Albaladejo, M.I. Marqués, M. Laroche, J.J. Saenz, Phys. Rev. Lett. 102, 113602 (2009)

    ADS  Google Scholar 

  37. S. Chu, J.E. Bjorkholm, A. Ashkin, A. Cable, Phys. Rev. Lett. 57, 314 (1986)

    ADS  Google Scholar 

  38. A. Khein, D.F. Nelson, Am. J. Phys. 61, 170 (1993)

    ADS  Google Scholar 

  39. H. Bateman, Phys. Rev. 38, 815 (1931)

    ADS  Google Scholar 

  40. C.M. Bender, M. Gianfreda, N. Hassanpour, H.F. Jones, J. Math. Phys. 57, 084101 (2016)

    ADS  MathSciNet  Google Scholar 

  41. L. Yang, B.Peng Özdemir, Reported in the conference Pseudo-Hermitian Hamiltonians in Quantum Physics 12, Istanbul, Turkey, July 2013,

  42. I.I. Rabi, Phys. Rev. 51, 652 (1937)

    ADS  Google Scholar 

  43. M. Cariglia, C. Duval, G.W. Gibbons, P.A. Horvathy, Ann. Phys. 373, 631 (2016)

    ADS  Google Scholar 

  44. R. Krechetnikov, J.E. Marsden, Rev. Mod. Phys. 79, 519 (2007)

    ADS  Google Scholar 

  45. D. Sinha, P. Ghosh, Eur. Phys. J. Plus 132, 460 (2017)

    Google Scholar 

  46. M.J. Ablowitz, P.A. Clarkson, , Solitons, Nonlinear evolution equations and inverse Scattering, in London Mathematical Society Lecture Note Series (Cambridge University Press, 1991), Vol. 149

  47. O. Babelon, D. Bernard, M. Talon, Introduction to Classical Integrable Systems (Cambridge University Press, 2003)

  48. H. Ziegler, Z. Angew, Math. Phys. 4, 89 (1953)

    Google Scholar 

  49. C.R. Galley, Phys. Rev. Lett. 110, 174301 (2013)

    ADS  Google Scholar 

  50. C.R. Galley, D. Tsang, L.C. Stein, https://arXiv:1412.3082 (2014)

  51. A. Pais, G.E. Uhlenbeck, Phys. Rev. 79, 145 (1950)

    ADS  MathSciNet  Google Scholar 

  52. A. Mostafazadeh, Phys. Lett. A 375, 93 (2010)

    ADS  MathSciNet  Google Scholar 

  53. P. Pavsic, Mod. Phys. Lett. A 28, 1350165 (2013)

    ADS  Google Scholar 

  54. A. Ghose-Choudhury, P. Guha, Acta Mech. 230, 2267 (2019)

    MathSciNet  Google Scholar 

  55. S.K. Pal, P. Nandi, B. Chakraborty, Phys. Rev. A 97, 062110 (2018)

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. SN Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata, 700106, India

    Partha Guha

Authors
  1. Partha Guha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Partha Guha.

Additional information

Publisher’s Note

The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guha, P. Curl forces and their role in optics and ion trapping. Eur. Phys. J. D 74, 99 (2020). https://doi.org/10.1140/epjd/e2020-100462-6

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2020-100462-6

Keywords

Search

Navigation