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Evidence for an oscillating soliton/vortex ring by density engineering of a Bose–Einstein condensate

Abstract

When two Bose–Einstein condensates collide with high collisional energy, the celebrated matter-wave interference pattern appears1. For lower collisional energies, the repulsive interaction energy becomes significant, and the interference pattern evolves into an array of grey solitons2,3. But the lowest collisional energies, producing a single pair of solitons, have not been probed so far. Here, we report on experiments using density engineering on the healing length scale3,4 to produce such a pair of solitons. We see evidence that the solitons evolve periodically between vortex rings and solitons. The stable, periodic evolution is in sharp contrast to the behaviour seen in previous experiments5,6 in which the solitons decay irreversibly into vortex rings through the so-called snake instability7,8,9,10,11,12,13. The evolution can be understood in terms of conservation of mass and energy in a narrow condensate.

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Figure 1: Solitons and matter-wave interference fringes.
Figure 2: Simulation of the periodic soliton/vortex ring.
Figure 3: In situ images of the vortex rings and solitons.
Figure 4: The speed of the periodic soliton/vortex ring.

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References

  1. Andrews, M. R. et al. Observation of interference between two Bose condensates. Science 275, 637–641 (1997).

    Article  Google Scholar 

  2. Scott, T. F., Ballagh, R. J. & Burnett, K. Formation of fundamental structures in Bose–Einstein condensates. J. Phys. B 31, L329–L335 (1998).

    Article  ADS  Google Scholar 

  3. Carr, L. D., Brand, J., Burger, S. & Sanpera, A. Dark-soliton creation in Bose–Einstein condensates. Phys. Rev. A 63, 051601(R) (2001).

    Article  ADS  Google Scholar 

  4. Reinhardt, W. P. & Clark, C. W. Soliton dynamics in the collisions of Bose–Einstein condensates: An analogue of the Josephson effect. J. Phys. B 30, L785–L789 (1997).

    Article  ADS  Google Scholar 

  5. Anderson, B. P. et al. Watching dark solitons decay into vortex rings in a Bose–Einstein condensate. Phys. Rev. Lett. 86, 2926–2929 (2001).

    Article  ADS  Google Scholar 

  6. Dutton, Z., Budde, M., Slowe, C. & Hau, L. V. Observation of quantum shock waves created with ultra-compressed slow light pulses in a Bose–Einstein condensate. Science 293, 663–668 (2001).

    Article  ADS  Google Scholar 

  7. Kadomtsev, B. B. & Petviashvili, V. I. On the stability of solitary waves in weakly dispersing media. Sov. Phys. Dokl. 15, 539–541 (1970).

    ADS  MATH  Google Scholar 

  8. Jones, C. A., Putterman, S. J. & Roberts, P. H. Motions in a Bose condensate: V. Stability of solitary wave solutions of non-linear Schrödinger equations in two and three dimensions. J. Phys. A 19, 2991–3011 (1986).

    Article  ADS  Google Scholar 

  9. Josserand, C. & Pomeau, Y. Generation of vortices in a model of superfluid 4He by the Kadomtsev–Petviashvili instability. Europhys. Lett. 30, 43–48 (1995).

    Article  ADS  Google Scholar 

  10. Feder, D. L., Pindzola, M. S., Collins, L. A., Schneider, B. I. & Clark, C. W. Dark-soliton states of Bose–Einstein condensates in anisotropic traps. Phys. Rev. A 62, 053606 (2000).

    Article  ADS  Google Scholar 

  11. Brand, J. & Reinhardt, W. P. Solitonic vortices and the fundamental modes of the ‘snake instability’: Possibility of observation in the gaseous Bose–Einstein condensate. Phys. Rev. A 65, 043612 (2002).

    Article  ADS  Google Scholar 

  12. Theocharis, G., Frantzeskakis, D. J., Kevrekidis, P. G., Malomed, B. A. & Kivshar, Y. S. Ring dark solitons and vortex necklaces in Bose–Einstein condensates. Phys. Rev. Lett. 90, 120403 (2003).

    Article  ADS  Google Scholar 

  13. Mamaev, A. V., Saffman, M. & Zozulya, A. A. Propagation of dark stripe beams in nonlinear media: Snake instability and creation of optical vortices. Phys. Rev. Lett. 76, 2262–2265 (1996).

    Article  ADS  Google Scholar 

  14. Jo, G.-B. et al. Phase-sensitive recombination of two Bose–Einstein condensates on an atom chip. Phys. Rev. Lett. 98, 180401 (2007).

    Article  ADS  Google Scholar 

  15. Pitaevskii, L. & Stringari, S. Bose–Einstein condensation Sects 5.4 and 5.5 (Oxford Univ. Press, 2003).

    MATH  Google Scholar 

  16. Jackson, A. D., Kavoulakis, G. M. & Pethick, C. J. Solitary waves in clouds of Bose–Einstein condensed atoms. Phys. Rev. A 58, 2417–2422 (1998).

    Article  ADS  Google Scholar 

  17. Burger, S. et al. Dark solitons in Bose–Einstein condensates. Phys. Rev. Lett. 83, 5198–5201 (1999).

    Article  ADS  Google Scholar 

  18. Denschlag, J. et al. Generating solitons by phase engineering of a Bose–Einstein condensate. Science 287, 97–101 (2000).

    Article  ADS  Google Scholar 

  19. Becker, C. et al. Oscillations and interactions of dark and dark-bright solitons in Bose–Einstein condensates. Nature Phys. 4, 496–501 (2008).

    Article  ADS  Google Scholar 

  20. Muryshev, A. E., van Linden van den Heuvell, H. B. & Shlyapnikov, G. V. Stability of standing matter waves in a trap. Phys. Rev. A 60, R2665–R2668 (1999).

    Article  ADS  Google Scholar 

  21. Carr, L. D., Clark, C. W. & Reinhardt, W. P. Stationary solutions of the one-dimensional nonlinear Schrödinger equation. I. Case of repulsive nonlinearity. Phys. Rev. A 62, 063610 (2000).

    Article  ADS  Google Scholar 

  22. Komineas, S. & Papanicolaou, N. Nonlinear waves in a cylindrical Bose–Einstein condensate. Phys. Rev. A 67, 023615 (2003).

    Article  ADS  Google Scholar 

  23. Donnelly, R. J. Quantized Vortices in Helium II Chs 1, 4 (Cambridge Univ. Press, 1991).

    Google Scholar 

  24. Rayfield, G. W. & Reif, F. Quantized vortex rings in superfluid helium. Phys. Rev. 136, A1194–A1208 (1964).

    Article  ADS  Google Scholar 

  25. Guilleumas, M., Jezek, D. M., Mayol, R., Pi, M. & Barranco, M. Generating vortex rings in Bose–Einstein condensates in the line-source approximation. Phys. Rev. A 65, 053609 (2002).

    Article  ADS  Google Scholar 

  26. Andrews, M. R. et al. Propagation of sound in a Bose–Einstein condensate. Phys. Rev. Lett. 79, 553–556 (1997).

    Article  ADS  Google Scholar 

  27. Zaremba, E. Sound propagation in a cylindrical Bose-condensed gas. Phys. Rev. A 57, 518–521 (1998).

    Article  ADS  Google Scholar 

  28. Snyder, A. W., Hewlett, S. J. & Mitchell, D. J. Periodic solitons in optics. Phys. Rev. E 51, 6297–6300 (1995).

    Article  ADS  Google Scholar 

  29. Weller, A. et al. Experimental observation of oscillating and interacting matter wave dark solitons. Phys. Rev. Lett. 101, 130401 (2008).

    Article  ADS  Google Scholar 

  30. Levy, S., Lahoud, E., Shomroni, I. & Steinhauer, J. The a.c. and d.c. Josephson effects in a Bose–Einstein condensate. Nature 449, 579–583 (2007).

    Article  ADS  Google Scholar 

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Acknowledgements

We thank A. Soffer, M. Segev, W. Ketterle, A. Minguzzi and R. Ozeri for helpful discussions. This work was supported by the Israel Science Foundation.

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Correspondence to J. Steinhauer.

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Shomroni, I., Lahoud, E., Levy, S. et al. Evidence for an oscillating soliton/vortex ring by density engineering of a Bose–Einstein condensate. Nature Phys 5, 193–197 (2009). https://doi.org/10.1038/nphys1177

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