Skip to main content
Log in

Casimir Force of Two-Component Bose–Einstein Condensates Confined by a Parallel Plate Geometry

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

Using field theory we calculate the Casimir energy and Casimir force of two-component Bose-Einstein condensates restricted between two parallel plates, in which Dirichlet and periodic boundary conditions applied. Our results show that, in one-loop approximation, the Casimir force equals to summation of the one of each component and it is vanishing in some cases: (i) inter-distance between two plates becomes large enough; (ii) intraspecies interaction is zero; (iii) interspecies interaction is full strong segregation.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Casimir, H.B.G., Polder, D.: The influences of retardation on the London-van der Waals forces. Phys. Rev. 73, 360 (1948)

    Article  MATH  ADS  Google Scholar 

  2. Casimir, H.B.G.: On the attraction between two perfectly conducting plates. Proc. K. Ned. Akad. Wet. 51, 793 (1948)

    MATH  Google Scholar 

  3. Edery, A.: Multidimensional cut-off technique, odd-dimensional Epstein zeta functions and Casimir energy of massless scalar fields. J. Phys. A 39, 685 (2006)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  4. Phat, T.H., Thu, N.V.: Finite-size effect of linear sigma model in compactified space-time. Int. J. Mod. Phys. A 29, 1450078 (2014)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  5. Recati, A., Fuchs, J.N., Peca, C.S., Zwerger, W.: Casimir forces between defects in one-dimensional quantum liquids. Phys. Rev. A 72, 023616 (2005)

    Article  ADS  Google Scholar 

  6. Bordag, M., Mohideen, U., Mostepanenko, V.M.: New developments in the Casimir effect. Phys. Rep. 353, 1 (2001)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  7. Biswas, S.: Bose–Einstein condensation and the Casimir effect for an ideal Bose gas confined between two slabs. J. Phys. A 40, 9969 (2007)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  8. Biswas, S.: Bose–Einstein condensation and Casimir effect of trapped ideal Bose gas in between two slabs. Eur. Phys. J. D 42, 109 (2007)

    Article  ADS  Google Scholar 

  9. Biswas, S., Bhattacharjee, J.K., Majumder, D., Saha, K., Chakravarty, N.: Casimir force on an interacting Bose–Einstein condensates. J. Phys. B 43, 085305 (2010)

    Article  ADS  Google Scholar 

  10. Schiefele, J., Henkel, C.: Casimir energy of a BEC: from moderate interactions to the ideal gas. J. Phys. A 42, 045401 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Martin, P.A., Zagrebnov, V.A.: The Casimir effect for the Bose-gas in slabs. Europhys. Lett. 73, 15 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  12. Harber, D.M., Obrecht, J.M., McGuirk, J.M., Cornell, E.A.: Measurement of the Casimir–Polder force through center-of-mass oscillations of a Bose–Einstein condensate. Phys. Rev. A 72, 033610 (2005)

    Article  ADS  Google Scholar 

  13. Van Thu, N.: Static properties of Bose–Einstein condensate mixtures in semi-infinite space. Phys. Lett. A 380, 2920 (2016)

    Article  MathSciNet  ADS  Google Scholar 

  14. Van Thu, N., Phat, T.H., Song, P.T.: Finite-size effects of surface tension in two segregated BECs confined by two hard walls. J. Low Temp. Phys. 186, 127 (2017)

    Article  ADS  Google Scholar 

  15. Indekeu, J.O., Lin, C.-Y., Thu, N.V., Van Schaeybroeck, B., Phat, T.H.: Static interfacial properties of Bose–Einstein-condensate mixtures. Phys. Rev. A 91, 033615 (2015)

    Article  ADS  Google Scholar 

  16. Deng, Z., Schaeybroeck, B.V., Lin, C.-Y., Thu, N.V., Indekeu, J.O.: Interfacial tension and wall energy of a Bose–Einstein condensate binary mixture: triple-parabola approximation. Physica A 444, 1027 (2016)

    Article  MathSciNet  ADS  Google Scholar 

  17. Mazets, I.E.: Waves on an interface between two phase-separated Bose–Einstein condensates. Phys. Rev. 65, 033618 (2002)

    Article  ADS  Google Scholar 

  18. Indekeu, J.O., Thu, N.V., Lin, C.-Y., Phat, T.H.: Capillary wave dynamics and interface structure modulation in binary Bose–Einstein condensate mixtures. Submitted to Phys. Rev. A (2016)

  19. Takahashi, D.A., Kobayashi, M., Nitta, M.: Nambu-Goldstone modes propagating along topological defects: Kelvin and ripple modes from small to large systems. Phys. Rev. B 91, 184501 (2015)

    Article  ADS  Google Scholar 

  20. Lipowsky, R.: Random Fluctuations and Pattern Growth (H. Stanley, N. Ostrowsky, ed.). NATO ASI Series E, vol. 157, pp. 227–245. Kluwer Academic Publishers, Dordrecht (1988) and references herein

  21. Phat, T.H., Hoa, L.V., Anh, N.T., Long, N.V.: Bose-Einstein condensation in binary mixture of Bose gases. Ann. Phys. 324, 2074 (2009)

    Article  MATH  ADS  Google Scholar 

  22. Pethick, C.J., Smith, H.: Bose–Einstein Condensation in Dilute Gases. Cambridge University Press, Cambridge (2008)

    Book  Google Scholar 

  23. Pethick, C.J., Smith, H.: Contemporary concepts of condensed matter science. In: Levin, K., Fetter, A.L., Stamper-Kurn, D.M. (eds.) Ultracold Bosonic and Fermionic Gases. Elsevier, Amsterdam (2012)

    Google Scholar 

  24. Ao, P., Chui, S.T.: Binary Bose–Einstein condensate mixtures in weakly and strongly segregated phases. Phys. Rev. A 58, 4836 (1998)

    Article  ADS  Google Scholar 

  25. Pitaevskii, L., Stringari, S.: Bose–Einstein Condensation. Oxford University Press, Oxford (2003)

    MATH  Google Scholar 

  26. Andersen, J.O.: Theory of the weakly interacting Bose gas. Rev. Mod. Phys. 76, 599 (2004)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  27. Saharian, A.A.: The generalized Abel–Plana formula with applications to Bessel functions and Casimir effect. arXiv:0708.1187

  28. Inouye, S., Andrews, M.R., Stenger, J., Miesner, H.-J., Stamper-Kurn, D.M., Ketterle, W.: Observation of Feshbach resonances in a Bose–Einstein condensate. Nature (London) 392, 151 (1998)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

It is our pleasure to acknowledge valuable discussions with Prof. Tran Huu Phat, Jurgen Schiefele, Shyamal Biswas and Nguyen Thi Tham.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nguyen Van Thu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Van Thu, N., Theu, L.T. Casimir Force of Two-Component Bose–Einstein Condensates Confined by a Parallel Plate Geometry. J Stat Phys 168, 1–10 (2017). https://doi.org/10.1007/s10955-017-1800-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-017-1800-4

Keywords

Mathematics Subject Classification

Navigation