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Reflection, transmission, and trapping of an ultracold atomic soliton at an attractive contact impurity

A. Isacsson*

C. E. Cruz-Roman

R. Cabrera-Trujillo

  • *Contact author: andreas.isacsson@chalmers.se
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APS Open Sci. 1, 000113 – Published 28 August, 2026

DOI: https://doi.org/10.1103/gv5l-zp57

Abstract

Reflection and transmission (tunneling) reveal the wave nature of ultracold matter when scattered from an impurity and are of great importance in atomtronics technology. Using the time-dependent Gross-Pitaevskii equation (GPE), we investigate the trapping, reflection, and transmission of a bright soliton in an ultracold-atom gas propagating through a one-dimensional waveguide with a contact defect. This allows us to analyze the dynamics of the scattering as a function of soliton velocity v, the strength of the contact impurity V0, and the intensity of the attractive nonlinear coupling g<0. We evolve the GPE numerically with the contact defect modeled as a δ sequence for the Dirac delta function. We find a universal behavior in terms of v/V0 and |g|/V0, thus reducing the dimension of the parameter space. Our analysis identifies four distinct regions of nonlinear coupling |g|/V0 that govern scattering dynamics, delimited by |g|/V0≈2, 4, and 6. Particularly, we observe distinct parameter dependent onsets between the soliton character and highly radiative-dispersive wave packets for the scattering products. To quantify the nature of the scattering products, we use the differential and Fisher information-theoretical measures to determine the degree of localization of the scattering products. The implications of these findings are discussed in the context of both fundamental quantum mechanics and potential experimental setups.

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References (73)

  1. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Observation of Bose-Einstein condensation in a dilute atomic vapor, Science 269, 198 (1995).
  2. K. B. Davis, M. O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Bose-Einstein condensation in a gas of sodium atoms, Phys. Rev. Lett. 75, 3969 (1995).
  3. N. Proukakis, A century of Bose-Einstein condensation, Commun. Phys. 8, 264 (2025).
  4. L. Amico, M. Boshier, G. Birkl, A. Minguzzi, C. Miniatura, L.-C. Kwek, D. Aghamalyan, V. Ahufinger, D. Anderson, N. Andrei, et al., Roadmap on atomtronics: State of the art and perspective, AVS Quantum Sci. 3, 039201 (2021).
  5. L. Amico, D. Anderson, M. Boshier, J.-P. Brantut, L.-C. Kwek, A. Minguzzi, and W. von Klitzing, Colloquium: Atomtronic circuits: From many-body physics to quantum technologies, Rev. Mod. Phys. 94, 041001 (2022).
  6. B. T. Seaman, M. Krämer, D. Z. Anderson, and M. J. Holland, Atomtronics: Ultracold-atom analogs of electronic devices, Phys. Rev. A 75, 023615 (2007).
  7. C. Cassens, B. Meyer-Hoppe, E. Rasel, and C. Klempt, Entanglement-enhanced atomic gravimeter, Phys. Rev. X 15, 011029 (2025).
  8. J. Polo, W. J. Chetcuti, E. C. Domanti, P. Kitson, A. Osterloh, F. Perciavalle, V. P. Singh, and L. Amico, Perspective on new implementations of atomtronic circuits, Quantum Sci. Technol. 9, 030501 (2024).
  9. R. Calviac, A. Rouxel, S. Charlot, D. Bourrier, A. Arnoult, A. Monmayrant, O. Gauthier-Lafaye, A. Gauguet, and B. Allard, Bose-Einstein-condensate source on an optical-grating-based atom chip for quantum sensor applications, Phys. Rev. Appl. 23, L011001 (2025).
  10. P. Kitson, T. Haug, A. La Magna, O. Morsch, and L. Amico, Rydberg atomtronic devices, Phys. Rev. A 110, 043304 (2024).
  11. C. Baroni, G. Lamporesi, and M. Zaccanti, Quantum mixtures of ultracold gases of neutral atoms, Nat. Rev. Phys. 6, 736 (2024).
  12. S. Abend, B. Allard, A. S. Arnold, T. Ban, L. Barry, B. Battelier, A. Bawamia, Q. Beaufils, S. Bernon, A. Bertoldi, et al., Technology roadmap for cold-atoms based quantum inertial sensor in space, AVS Quantum Sci. 5, 019201 (2023).
  13. M. T. Reeves, W. W. Wasserman, R. A. Harrison, I. Marinković, N. Luu, A. Sawadsky, Y. L. Sfendla, G. I. Harris, W. P. Bowen, and C. G. Baker, Nonlinear wave dynamics on a chip, Science 390, 371 (2025).
  14. E. P. Gross, Structure of a quantized vortex in boson systems, Nuovo Cimento 20, 454 (1961).
  15. L. P. Pitaevskii, Vortex lines in an imperfect Bose gas, Sov. Phys. JETP 13, 451 (1961).
  16. C. J. Pethick and H. Smith, Bose–Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, UK, 2008).
  17. B. T. Seaman, L. D. Carr, and M. J. Holland, Effect of a potential step or impurity on the Bose-Einstein condensate mean field, Phys. Rev. A 71, 033609 (2005).
  18. B. A. Malomed, Soliton models: Traditional and novel, one- and multidimensional, Low Temp. Phys. 48, 856 (2022).
  19. K. E. Strecker, G. B. Partridge, A. G. Truscott, and R. G. Hulet, Formation and propagation of matter-wave soliton trains, Nature (London) 417, 150 (2002).
  20. L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, and C. Salomon, Formation of a matter-wave bright soliton, Science 296, 1290 (2002).
  21. S. L. Cornish, S. T. Thompson, and C. E. Wieman, Formation of bright matter-wave solitons during the collapse of attractive Bose-Einstein condensates, Phys. Rev. Lett. 96, 170401 (2006).
  22. J. H. V. Nguyen, P. Dyke, D. Luo, B. A. Malomed, and R. G. Hulet, Collisions of matter-wave solitons, Nat. Phys. 10, 918 (2014).
  23. J. H. V. Nguyen, D. Luo, and R. G. Hulet, Formation of matter-wave soliton trains by modulational instability, Science 356, 422 (2017).
  24. A. Marchant, T. Billam, T. Wiles, M. Yu, S. Gardiner, and S. Cornish, Controlled formation and reflection of a bright solitary matter-wave, Nat. Commun. 4, 1865 (2013).
  25. S. Lepoutre, L. Fouché, A. Boissé, G. Berthet, G. Salomon, A. Aspect, and T. Bourdel, Production of strongly bound K39 bright solitons, Phys. Rev. A 94, 053626 (2016).
  26. A. Di Carli, C. D. Colquhoun, G. Henderson, S. Flannigan, G.-L. Oppo, A. J. Daley, S. Kuhr, and E. Haller, Excitation modes of bright matter-wave solitons, Phys. Rev. Lett. 123, 123602 (2019).
  27. O. V. Marchukov, B. A. Malomed, V. A. Yurovsky, M. Olshanii, V. Dunjko, and R. G. Hulet, Splitting of nonlinear-Schrödinger-equation breathers by linear and nonlinear localized potentials, Phys. Rev. A 99, 063623 (2019).
  28. J. L. Helm, T. P. Billam, and S. A. Gardiner, Bright matter-wave soliton collisions at narrow barriers, Phys. Rev. A 85, 053621 (2012).
  29. J. L. Helm, S. J. Rooney, C. Weiss, and S. A. Gardiner, Splitting bright matter-wave solitons on narrow potential barriers: Quantum to classical transition and applications to interferometry, Phys. Rev. A 89, 033610 (2014).
  30. T. A. Pasquini, Y. Shin, C. Sanner, M. Saba, A. Schirotzek, D. E. Pritchard, and W. Ketterle, Quantum reflection from a solid surface at normal incidence, Phys. Rev. Lett. 93, 223201 (2004).
  31. Y. S. Kivshar', A. M. Kosevich, and O. A. Chubykalo, Point-defect scattering of bound quasiparticles as a soliton problem (onedimensional case), Zh. Eksp. Teor. Fiz. 93, 968 (1987) [Sov. Phys. JETP 66, 545 (1987)].
  32. C. Lee and J. Brand, Enhanced quantum reflection of matter-wave solitons, Europhys. Lett. 73, 321 (2006).
  33. A. I. Streltsov, O. E. Alon, and L. S. Cederbaum, Scattering of an attractive Bose-Einstein condensate from a barrier: Formation of quantum superposition states, Phys. Rev. A 80, 043616 (2009).
  34. C. Weiss and Y. Castin, Creation and detection of a mesoscopic gas in a nonlocal quantum superposition, Phys. Rev. Lett. 102, 010403 (2009).
  35. B. Gertjerenken, T. P. Billam, L. Khaykovich, and C. Weiss, Scattering bright solitons: Quantum versus mean-field behavior, Phys. Rev. A 86, 033608 (2012).
  36. A. Boissé, G. Berthet, L. Fouché, G. Salomon, A. Aspect, S. Lepoutre, and T. Bourdel, Nonlinear scattering of atomic bright solitons in disorder, Europhys. Lett. 117, 10007 (2017).
  37. Y. Kivshar, A. Kosevich, and O. Chubykalo, Resonant and non-resonant soliton scattering by impurities, Phys. Lett. A 125, 35 (1987).
  38. O. J. Wales, A. Rakonjac, T. P. Billam, J. L. Helm, S. A. Gardiner, and S. L. Cornish, Splitting and recombination of bright-solitary-matter waves, Commun. Phys. 3, 51 (2020).
  39. R. Eid, A. Hammond, L. Lavoine, and T. Bourdel, Ultracold-atom quantum tunneling through single and double optical barriers, Phys. Rev. A 110, 043316 (2024).
  40. F. Lorenzi and L. Salasnich, Atomic soliton transmission and induced collapse in scattering from a narrow barrier, Sci. Rep. 14, 4665 (2024).
  41. S. Watabe and Y. Kato, Reflection and refraction of Bose-Einstein-condensate excitations, Phys. Rev. A 78, 063611 (2008).
  42. F. Lingua, L. Lepori, F. Minardi, V. Penna, and L. Salasnich, Collision of impurities with Bose–Einstein condensates, New J. Phys. 20, 045001 (2018).
  43. J. Holmer, J. Marzuola, and M. Zworski, Fast soliton scattering by delta impurities, Commun. Math. Phys. 274, 187 (2007).
  44. K. Forinash, M. Peyrard, and B. Malomed, Interaction of discrete breathers with impurity modes, Phys. Rev. E 49, 3400 (1994).
  45. X. D. Cao and B. A. Malomed, Soliton-defect collisions in the nonlinear Schrödinger equation, Phys. Lett. A 206, 177 (1995).
  46. K. T. Stoychev, M. T. Primatarowa, and R. S. Kamburova, Resonant scattering of nonlinear Schrödinger solitons from potential wells, Phys. Rev. E 70, 066622 (2004).
  47. R. H. Goodman, P. J. Holmes, and M. I. Weinstein, Strong NLS soliton–defect interactions, Physica D 192, 215 (2004).
  48. H. Sakaguchi and M. Tamura, Scattering and trapping of nonlinear Schrödinger solitons in external potentials, J. Phys. Soc. Jpn. 73, 503 (2004).
  49. T. Ernst and J. Brand, Resonant trapping in the transport of a matter-wave soliton through a quantum well, Phys. Rev. A 81, 033614 (2010).
  50. T. L. Belyaeva and V. N. Serkin, Wave-particle duality of solitons and solitonic analog of the Ramsauer-Townsend effect, Eur. Phys. J. D 66, 153 (2012).
  51. S. Damgaard Hansen, N. Nygaard, and K. Mølmer, Scattering of matter wave solitons on localized potentials, Appl. Sci. 11, 2294 (2021).
  52. C.-H. Wang, T.-M. Hong, R.-K. Lee, and D.-W. Wang, Particle-wave duality in quantum tunneling of a bright soliton, Opt. Express 20, 22675 (2012).
  53. U. Al Khawaja, Critical soliton speed for quantum reflection by a reflectionless potential well, Phys. Rev. E 103, 062202 (2021).
  54. L. Al Sakkaf and U. Al Khawaja, Bound-states spectrum of the nonlinear Schrödinger equation with Pöschl-Teller and square-potential wells, Phys. Rev. E 106, 024206 (2022).
  55. A. Debnath, A. Khan, and B. Malomed, Interaction of one-dimensional quantum droplets with potential wells and barriers, Commun. Nonlinear Sci. Numer. Simul. 126, 107457 (2023).
  56. A. Brattley, H. Huang, and K. K. Das, Quantum scattering states in a nonlinear coherent medium, Phys. Rev. A 108, 023314 (2023).
  57. G. Koutsokostas, I. Moseley, T. Horikis, and D. Frantzeskakis, Particle and wave dynamics of nonlocal solitons in external potentials, Phys. Lett. A 518, 129683 (2024).
  58. Z. Almualla, L. Al Sakkaf, and U. Al Khawaja, Resonant soliton scattering by topological states of a finite array of reflectionless potential wells, Phys. Lett. A 552, 130646 (2025).
  59. A. L. Marchant, T. P. Billam, M. M. H. Yu, A. Rakonjac, J. L. Helm, J. Polo, C. Weiss, S. A. Gardiner, and S. L. Cornish, Quantum reflection of bright solitary matter waves from a narrow attractive potential, Phys. Rev. A 93, 021604(R) (2016).
  60. Y. Linzon, R. Morandotti, M. Volatier, V. Aimez, R. Ares, and S. Bar-Ad, Nonlinear scattering and trapping by local photonic potentials, Phys. Rev. Lett. 99, 133901 (2007).
  61. X. Hu, Z. Li, Y. Guo, Y. Chen, and X. Luo, Scattering of one-dimensional quantum droplets by a reflectionless potential well, Phys. Rev. A 108, 053306 (2023).
  62. J. Garnier and F. K. Abdullaev, Transmission of matter-wave solitons through nonlinear traps and barriers, Phys. Rev. A 74, 013604 (2006).
  63. K. L. Jensen, J. Riga, A. Shabaev, M. Osofsky, and J. C. Prestigiacomo, A delta barrier in a well and the exact time evolution of its eigenstates, J. Appl. Phys. 133, 174402 (2023).
  64. D. Griffiths and D. Schroeter, Introduction to Quantum Mechanics (Cambridge University Press, Cambridge, UK, 2018).
  65. R. Cabrera-Trujillo, C. E. de la C. Roman, and C. E. Teran-Cisneros, Ionization, excitation, protonium formation, and energy loss of antiprotons colliding with atomic hydrogen, Phys. Rev. A 108, 012817 (2023).
  66. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, Cambridge, UK, 2010).
  67. C. E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27, 379 (1948).
  68. L. J. Savage, On rereading R. A. Fisher, Ann. Stat. 4, 441 (1976).
  69. C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, Urbana, IL, 1949).
  70. R. A. Fisher, Statistical methods for research workers, in Breakthroughs in Statistics: Methodology and Distribution, edited by S. Kotz and N. L. Johnson (Springer New York, New York, NY, 1992), pp. 66–70.
  71. M. W. J. Bromley and B. D. Esry, Classical aspects of ultracold atom wave packet motion through microstructured waveguide bends, Phys. Rev. A 69, 053620 (2004).
  72. S. E. Kooning and D. C. Meredith, Computational Physics, Fortran Version (Perseus Books, Reading, MA, 1990).
  73. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge University Press, New York, 1992).

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APS Open Sci. 1, 000113– Published 28 August, 2026
Vol. 1
  • Received 19 March 2026
  • Revised 18 June 2026
  • Accepted 17 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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