Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Imprinting knots in a spinor Bose-Einstein condensate via a Raman process without knotted optical fields

Zekai Chen*, Elisha Haber, and Nicholas P. Bigelow†

  • Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA and Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA

  • *Current address: Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, 6020 Innsbruck, Austria.
  • †nicholas.bigelow@rochester.edu

Phys. Rev. Research 4, 043109 – Published 15 November, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.043109

Abstract

We propose a dynamical imprinting scheme to create nodal lines of torus and lemniscate knots via a Raman process in a dilute spinor Bose-Einstein condensate. We calculate the desired parameters and the necessary spatial profiles of the Raman laser fields that couple a realistic multilevel atomic system, and demonstrate the imprinting results via a numerical calculation. Additionally, we show the capability of our method to adjust the size and the aspect ratio of the knotted nodal lines by tuning the parameters of Raman lasers that propagate along different directions.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (39)

  1. C. F. Barenghi, Knots and unknots in superfluid turbulence, Milan J. Math. 75, 177 (2007).
  2. R. G. Cooper, M. Mesgarnezhad, A. W. Baggaley, and C. F. Barenghi, Knot spectrum of turbulence, Sci. Rep. 9, 10545 (2019).
  3. D. Proment, M. Onorato, and C. F. Barenghi, Vortex knots in a Bose-Einstein condensate, Phys. Rev. E 85, 036306 (2012).
  4. D.-L. Deng, S.-T. Wang, K. Sun, and L.-M. Duan, Probe knots and Hopf insulators with ultracold atoms, Chin. Phys. Lett. 35, 013701 (2017).
  5. W.-K. Bai, T. Yang, and W.-M. Liu, Topological transition from superfluid vortex rings to isolated knots and links, Phys. Rev. A 102, 063318 (2020).
  6. D.-L. Deng, S.-T. Wang, C. Shen, and L.-M. Duan, Hopf insulators and their topologically protected surface states, Phys. Rev. B 88, 201105(R) (2013).
  7. P. Sutcliffe, Skyrmion Knots in Frustrated Magnets, Phys. Rev. Lett. 118, 247203 (2017).
  8. D. Kleckner and W. T. Irvine, Creation and dynamics of knotted vortices, Nat. Phys. 9, 253 (2013).
  9. W. R. Taylor, A deeply knotted protein structure and how it might fold, Nature (London) 406, 916 (2000).
  10. D. Han, S. Pal, Y. Liu, and H. Yan, Folding and cutting DNA into reconfigurable topological nanostructures, Nat. Nanotechnol. 5, 712 (2010).
  11. A. Suma and C. Micheletti, Pore translocation of knotted DNA rings, Proc. Natl. Acad. Sci. USA 114, E2991 (2017).
  12. T. Chen, X. Zheng, Q. Pei, D. Zou, H. Sun, and X. Zhang, Creation of electrical knots and observation of DNA topology, New J. Phys. 23, 093045 (2021).
  13. H. Larocque, A. D'Errico, M. F. Ferrer-Garcia, A. Carmi, E. Cohen, and E. Karimi, Optical framed knots as information carriers, Nat. Commun. 11, 5119 (2020).
  14. M. R. Dennis, R. P. King, B. Jack, K. O'holleran, and M. J. Padgett, Isolated optical vortex knots, Nat. Phys. 6, 118 (2010).
  15. D. Sugic and M. R. Dennis, Singular knot bundle in light, J. Opt. Soc. Am. A 35, 1987 (2018).
  16. B. Bode, M. R. Dennis, D. Foster, and R. P. King, Knotted fields and explicit fibrations for lemniscate knots, Proc. R. Soc. A 473, 20160829 (2017).
  17. H. Larocque, D. Sugic, D. Mortimer, A. J. Taylor, R. Fickler, R. W. Boyd, M. R. Dennis, and E. Karimi, Reconstructing the topology of optical polarization knots, Nat. Phys. 14, 1079 (2018).
  18. L. S. Leslie, A. Hansen, K. C. Wright, B. M. Deutsch, and N. P. Bigelow, Creation and Detection of Skyrmions in a Bose-Einstein Condensate, Phys. Rev. Lett. 103, 250401 (2009).
  19. J. T. Schultz, A. Hansen, J. D. Murphree, M. Jayaseelan, and N. P. Bigelow, Creating full-Bloch Bose–Einstein condensates with Raman q-plates, J. Opt. 18, 064009 (2016).
  20. A. Hansen, J. T. Schultz, and N. P. Bigelow, Singular atom optics with spinor Bose-Einstein condensates, Optica 3, 355 (2016).
  21. W. Lee, A. H. Gheorghe, K. Tiurev, T. Ollikainen, M. Möttönen, and D. S. Hall, Synthetic electromagnetic knot in a three-dimensional skyrmion, Sci. Adv. 4, eaao3820 (2018).
  22. Y. Kawaguchi, M. Nitta, and M. Ueda, Knots in a Spinor Bose-Einstein Condensate, Phys. Rev. Lett. 100, 180403 (2008).
  23. D. S. Hall, M. W. Ray, K. Tiurev, E. Ruokokoski, A. H. Gheorghe, and M. Möttönen, Tying quantum knots, Nat. Phys. 12, 478 (2016).
  24. T. Ollikainen, A. Blinova, M. Möttönen, and D. S. Hall, Decay of a Quantum Knot, Phys. Rev. Lett. 123, 163003 (2019).
  25. C. W. Duncan, C. Ross, N. Westerberg, M. Valiente, B. J. Schroers, and P. Öhberg, Linked and knotted synthetic magnetic fields, Phys. Rev. A 99, 063613 (2019).
  26. J. Ruostekoski and Z. Dutton, Engineering vortex rings and systems for controlled studies of vortex interactions in Bose-Einstein condensates, Phys. Rev. A 72, 063626 (2005).
  27. F. Maucher, S. Gardiner, and I. Hughes, Excitation of knotted vortex lines in matter waves, New J. Phys. 18, 063016 (2016).
  28. K. Brauner, Das verhalten der funktionen in der umgebung ihrer verzweigungsstellen, in Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (Springer, Berlin, 1928), Vol. 6, pp. 1–55.
  29. R. P. King, Knotting of optical vortices, Ph.D. thesis, University of Southampton, 2010.
  30. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-VCH, Berlin, 1998).
  31. K. C. Wright, L. S. Leslie, and N. P. Bigelow, Raman coupling of Zeeman sublevels in an alkali-metal Bose-Einstein condensate, Phys. Rev. A 78, 053412 (2008).
  32. D. A. Steck, Rubidium 87 d line data (2001).
  33. V. Lerner, D. Shwa, Y. Drori, and N. Katz, Shaping Laguerre-Gaussian laser modes with binary gratings using a digital micromirror device, Opt. Lett. 37, 4826 (2012).
  34. Y.-X. Ren, Z.-X. Fang, L. Gong, K. Huang, Y. Chen, and R.-D. Lu, Digital generation and control of Hermite-Gaussian modes with an amplitude digital micromirror device, J. Opt. 17, 125604 (2015).
  35. J. T. Schultz, Singular atom optics via stimulated Raman interactions in Spinor Bose-Einstein condensates, Ph.D. thesis, University of Rochester, 2016.
  36. A. Hansen, Topological spin textures in Spinor Bose-Einstein condensates generated by stimulated Raman interactions, Ph.D. thesis, University of Rochester, 2016.
  37. Z. Chen, H. Yao, E. Haber, and N. P. Bigelow, Momentum dependent optical lattice induced by an artificial gauge potential, Phys. Rev. Res. 4, 013124 (2022).
  38. P. Treutlein, T. W. Hänsch, J. Reichel, A. Negretti, M. A. Cirone, and T. Calarco, Microwave potentials and optimal control for robust quantum gates on an atom chip, Phys. Rev. A 74, 022312 (2006).
  39. M. Singh, M. Volk, A. Akulshin, A. Sidorov, R. McLean, and P. Hannaford, One-dimensional lattice of permanent magnetic microtraps for ultracold atoms on an atom chip, J. Phys. B: At. Mol. Opt. Phys. 41, 065301 (2008).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation