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Experimental Observation of Single- and Multisite Matter-Wave Solitons in an Optical Accordion Lattice

Robbie Cruickshank1, Francesco Lorenzi2,3, Arthur La Rooij1, Ethan F. Kerr1, Timon Hilker1, Stefan Kuhr1, Luca Salasnich2,4,3,5, and Elmar Haller1

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Phys. Rev. Lett. 135, 263404 – Published 23 December, 2025

DOI: https://doi.org/10.1103/sh72-wnmv

Abstract

We report the experimental observation of discrete bright matter-wave solitons with attractive interaction in an optical lattice. Using an accordion lattice with adjustable spacing, we prepare a Bose-Einstein condensate of cesium atoms across a defined number of lattice sites. By quenching the interaction strength and the trapping potential, we generate both single-site and multisite solitons. Our results reveal the existence and characteristics of these solitons across a range of lattice depths and spacings. We identify stable regions of the solitons based on interaction strength and lattice properties, and compare these findings with theoretical predictions. The experimental results qualitatively agree with a Gaussian variational model and match quantitatively with numerical simulations of the three-dimensional Gross-Pitaevskii equation extended with a quintic term to account for the loss of atoms. Our results provide insights into the quench dynamics and collapse mechanisms, paving the way for further studies of transport and dynamical properties of matter-wave solitons in lattices.

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An Accordion Lattice Playing a Soliton Tune

Published 13 January, 2026

Decades after their experimental realization, wave patterns known as discrete solitons continue to fascinate.

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References (74)

  1. Y. S. Kivshar and B. A. Malomed, Dynamics of solitons in nearly integrable systems, Rev. Mod. Phys. 61, 763 (1989).
  2. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, Experimental observation of picosecond pulse narrowing and solitons in optical fibers, Phys. Rev. Lett. 45, 1095 (1980).
  3. Solitary Waves in Fluids, edited by R. Grimshaw, Advances in Fluid Mechanics (WIT Press, Southampton, 2007).
  4. F. Kh. Abdullaev, A. Gammal, A. M. Kamchatnov, and L. Tomio, Dynamics of bright matter wave solitons in a Bose–Einstein condensate, Int. J. Mod. Phys. B 19, 3415 (2005).
  5. C. C. Bradley, C. A. Sackett, and R. G. Hulet, Bose-Einstein condensation of lithium: Observation of limited condensate number, Phys. Rev. Lett. 78, 985 (1997).
  6. 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).
  7. 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).
  8. C. A. Sackett, H. T. C. Stoof, and R. G. Hulet, Growth and collapse of a Bose-Einstein condensate with attractive interactions, Phys. Rev. Lett. 80, 2031 (1998).
  9. J. M. Gerton, D. Strekalov, I. Prodan, and R. G. Hulet, Direct observation of growth and collapse of a Bose-Einstein condensate with attractive interactions, Nature (London) 408, 692 (2000).
  10. E. A. Donley, N. R. Claussen, S. L. Cornish, J. L. Roberts, E. A. Cornell, and C. E. Wieman, Dynamics of collapsing and exploding Bose-Einstein condensates, Nature (London) 412, 295 (2001).
  11. 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).
  12. A. S. Davydov and N. I. Kislukha, Solitary excitons in one-dimensional molecular chains, Phys. Status Solidi (b) 59, 465 (1973).
  13. We follow the convention of using the term “soliton” instead of “solitary wave” for our nonintegrable system, as suggested by B. A. Malomed, Soliton Management in Periodic Systems (Springer, New York, 2006), p. 19.
  14. B. A. Malomed, Soliton Management in Periodic Systems (Springer Science, New York, 2006).
  15. N. I. Kruglov, Solitons in quasi-one-dimensional molecular chains, J. Phys. C 17, L453 (1984).
  16. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Discrete spatial optical solitons in waveguide arrays, Phys. Rev. Lett. 81, 3383 (1998).
  17. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Dynamics of discrete solitons in optical waveguide arrays, Phys. Rev. Lett. 83, 2726 (1999).
  18. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Observation of discrete solitons in optically induced real time waveguide arrays, Phys. Rev. Lett. 90, 023902 (2003).
  19. B. A. Malomed and D. Mihalache, Nonlinear waves in optical and matter-wave media: A topical survey of recent theoretical and experimental results, Rom. J. Phys. 64, 106 (2019).
  20. A. Trombettoni and A. Smerzi, Discrete solitons and breathers with dilute Bose-Einstein condensates, Phys. Rev. Lett. 86, 2353 (2001).
  21. E. A. Ostrovskaya and Y. S. Kivshar, Matter-wave gap solitons in atomic band-gap structures, Phys. Rev. Lett. 90, 160407 (2003).
  22. B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, and M. K. Oberthaler, Bright Bose-Einstein gap solitons of atoms with repulsive interaction, Phys. Rev. Lett. 92, 230401 (2004).
  23. V. Ahufinger, A. Sanpera, P. Pedri, L. Santos, and M. Lewenstein, Creation and mobility of discrete solitons in Bose-Einstein condensates, Phys. Rev. A 69, 053604 (2004).
  24. B. B. Baizakov, B. A. Malomed, and M. Salerno, Multidimensional solitons in periodic potentials, Europhys. Lett. 63, 642 (2003).
  25. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices, Nature (London) 422, 147 (2003).
  26. V. A. Brazhnyi and B. A. Malomed, Dragging two-dimensional discrete solitons by moving linear defects, Phys. Rev. E 84, 016608 (2011).
  27. R. Franzosi, R. Livi, G.-L. Oppo, and A. Politi, Discrete breathers in Bose-Einstein condensates, Nonlinearity 24, R89 (2011).
  28. F. Kh. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, Nonlinear excitations in arrays of Bose-Einstein condensates, Phys. Rev. A 64, 043606 (2001).
  29. N. K. Efremidis and D. N. Christodoulides, Lattice solitons in Bose-Einstein condensates, Phys. Rev. A 67, 063608 (2003).
  30. H. Sakaguchi and B. A. Malomed, Matter-wave solitons in nonlinear optical lattices, Phys. Rev. E 72, 046610 (2005).
  31. L. Salasnich, A. Cetoli, B. A. Malomed, and F. Toigo, Nearly-one-dimensional self-attractive Bose-Einstein condensates in optical lattices, Phys. Rev. A 75, 033622 (2007).
  32. A. Maluckov, L. Hadžievski, B. A. Malomed, and L. Salasnich, Solitons in the discrete nonpolynomial Schrödinger equation, Phys. Rev. A 78, 013616 (2008).
  33. Y. V. Kartashov, B. A. Malomed, and L. Torner, Solitons in nonlinear lattices, Rev. Mod. Phys. 83, 247 (2011).
  34. C. P. Rubbo, I. I. Satija, W. P. Reinhardt, R. Balakrishnan, A. M. Rey, and S. R. Manmana, Quantum dynamics of solitons in strongly interacting systems on optical lattices, Phys. Rev. A 85, 053617 (2012).
  35. P. Naldesi, J. P. Gomez, B. Malomed, M. Olshanii, A. Minguzzi, and L. Amico, Rise and fall of a bright soliton in an optical lattice, Phys. Rev. Lett. 122, 053001 (2019).
  36. P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Bose-Einstein condensates in optical lattices: Band-gap structure and solitons, Phys. Rev. A 67, 013602 (2003).
  37. M. Mitchell, A. Di Carli, G. Sinuco-León, A. La Rooij, S. Kuhr, and E. Haller, Floquet solitons and dynamics of periodically driven matter waves with negative effective mass, Phys. Rev. Lett. 127, 243603 (2021).
  38. L. Fallani, C. Fort, J. E. Lye, and M. Inguscio, Bose-Einstein condensate in an optical lattice with tunable spacing: Transport and static properties, Opt. Express 13, 4303 (2005).
  39. S. Al-Assam, R. A. Williams, and C. J. Foot, Ultracold atoms in an optical lattice with dynamically variable periodicity, Phys. Rev. A 82, 021604 (2010).
  40. J. L. Ville, T. Bienaimé, R. Saint-Jalm, L. Corman, M. Aidelsburger, L. Chomaz, K. Kleinlein, D. Perconte, S. Nascimbène, J. Dalibard, and J. Beugnon, Loading and compression of a single two-dimensional Bose gas in an optical accordion, Phys. Rev. A 95, 013632 (2017).
  41. H. Saito and M. Ueda, Mean-field analysis of collapsing and exploding Bose-Einstein condensates, Phys. Rev. A 65, 033624 (2002).
  42. S. K. Adhikari, Mean-field description of collapsing and exploding Bose-Einstein condensates, Phys. Rev. A 66, 013611 (2002).
  43. Y. Kagan, A. Muryshev, and G. Shlyapnikov, Collapse and Bose-Einstein condensation in a trapped Bose gas with negative scattering length, Phys. Rev. Lett. 81, 933 (1998).
  44. L. D. Carr and Y. Castin, Dynamics of a matter-wave bright soliton in an expulsive potential, Phys. Rev. A 66, 063602 (2002).
  45. N. G. Parker, S. L. Cornish, C. S. Adams, and A. M. Martin, Bright solitary waves and trapped solutions in Bose-Einstein condensates with attractive interactions, J. Phys. B 40, 3127 (2007).
  46. P. A. Ruprecht, M. J. Holland, K. Burnett, and M. Edwards, Time-dependent solution of the nonlinear Schrödinger equation for Bose-condensed trapped neutral atoms, Phys. Rev. A 51, 4704 (1995).
  47. V. M. Pérez-García, H. Michinel, J. I. Cirac, M. Lewenstein, and P. Zoller, Dynamics of Bose-Einstein condensates: Variational solutions of the Gross-Pitaevskii equations, Phys. Rev. A 56, 1424 (1997).
  48. L. Salasnich, A. Parola, and L. Reatto, Effective wave equations for the dynamics of cigar-shaped and disk-shaped Bose condensates, Phys. Rev. A 65, 043614 (2002).
  49. See Supplemental Material at http://link.aps.org/supplemental/10.1103/sh72-wnmv for additional information, which includes Refs. [50,51].
  50. R. A. Williams, J. D. Pillet, S. Al-Assam, B. Fletcher, M. Shotter, and C. J. Foot, Dynamic optical lattices: Two-dimensional rotating and accordion lattices for ultracold atoms, Opt. Express 16, 16977 (2008).
  51. T. C. Li, H. Kelkar, D. Medellin, and M. G. Raizen, Real-time control of the periodicity of a standing wave: An optical accordion, Opt. Express 16, 5465 (2008).
  52. T. Kraemer, J. Herbig, M. Mark, T. Weber, C. Chin, H.-C. Nägerl, and R. Grimm, Optimized production of a cesium Bose-Einstein condensate, Appl. Phys. B 79, 1013 (2004).
  53. A. Di Carli, C. D. Colquhoun, S. Kuhr, and E. Haller, Interferometric measurement of micro-g acceleration with levitated atoms, New J. Phys. 21, 053028 (2019).
  54. M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, G. Rojas-Kopeinig, and H.-C. Nägerl, Control of interaction-induced dephasing of bloch oscillations, Phys. Rev. Lett. 100, 080404 (2008).
  55. M. Berninger, A. Zenesini, B. Huang, W. Harm, H.-C. Nägerl, F. Ferlaino, R. Grimm, P. S. Julienne, and J. M. Hutson, Feshbach resonances, weakly bound molecular states, and coupled-channel potentials for cesium at high magnetic fields, Phys. Rev. A 87, 032517 (2013).
  56. B. Peaudecerf, M. Andia, M. Brown, E. Haller, and S. Kuhr, Microwave preparation of two-dimensional fermionic spin mixtures, New J. Phys. 21, 013020 (2019).
  57. R. Cruickshank, A. L. Rooij, E. Kerr, T. Hilker, S. Kuhr, and E. Haller, Tunable optical lattices for the creation of matter-wave lattice solitons, arXiv:2509.22471.
  58. K. Winkler, G. Thalhammer, F. Lang, R. Grimm, J. Hecker Denschlag, A. J. Daley, A. Kantian, H. P. Büchler, and P. Zoller, Repulsively bound atom pairs in an optical lattice, Nature (London) 441, 853 (2006).
  59. A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates, Phys. Rev. Lett. 79, 4950 (1997).
  60. M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction, Phys. Rev. Lett. 95, 010402 (2005).
  61. B. J. Dabrowska-Wüster, S. Wüster, and M. J. Davis, Dynamical formation and interaction of bright solitary waves and solitons in the collapse of Bose-Einstein condensates with attractive interactions, New J. Phys. 11, 053017 (2009).
  62. A. I. Streltsov, O. E. Alon, and L. S. Cederbaum, Swift loss of coherence of soliton trains in attractive Bose-Einstein condensates, Phys. Rev. Lett. 106, 240401 (2011).
  63. A. D. Martin and J. Ruostekoski, Quantum dynamics of atomic bright solitons under splitting and recollision, and implications for interferometry, New J. Phys. 14, 043040 (2012).
  64. T. Weber, J. Herbig, M. Mark, H.-C. Nägerl, and R. Grimm, Three-body recombination at large scattering lengths in an ultracold atomic gas, Phys. Rev. Lett. 91, 123201 (2003).
  65. P.-T. Kraemer, Few-body interactions in an ultracold gas of cesium atoms, Ph.D. thesis, Leopold-Franzens-Universität Innsbruck, 2006.
  66. S. Flach and A. V. Gorbach, Discrete breathers—advances in theory and applications, Phys. Rep. 467, 1 (2008).
  67. G. Gligorić, A. Maluckov, L. Salasnich, B. A. Malomed, and Lj. Hadžievski, Two routes to the one-dimensional discrete nonpolynomial Schrödinger equation, Chaos 19, 043105 (2009).
  68. G. D. McDonald, C. C. N. Kuhn, K. S. Hardman, S. Bennetts, P. J. Everitt, P. A. Altin, J. E. Debs, J. D. Close, and N. P. Robins, Bright solitonic matter-wave interferometer, Phys. Rev. Lett. 113, 013002 (2014).
  69. J. L. Helm, S. L. Cornish, and S. A. Gardiner, Sagnac interferometry using bright matter-wave solitons, Phys. Rev. Lett. 114, 134101 (2015).
  70. J. Polo, P. Naldesi, A. Minguzzi, and L. Amico, The quantum solitons atomtronic interference device, Quantum Sci. Technol. 7, 015015 (2021).
  71. P. Naldesi, J. Polo, V. Dunjko, H. Perrin, M. Olshanii, L. Amico, and A. Minguzzi, Enhancing sensitivity to rotations with quantum solitonic currents, SciPost Phys. 12, 138 (2022).
  72. I. Tutunnikov, C. Chuang, and J. Cao, Coherent spatial control of wave packet dynamics on quantum lattices, J. Phys. Chem. Lett. 14, 11632 (2023).
  73. E. S. Sedov, A. P. Alodjants, S. M. Arakelian, Y.-L. Chuang, Y. Lin, W.-X. Yang, and R.-K. Lee, Tunneling-assisted optical information storage with lattice polariton solitons in cavity-QED arrays, Phys. Rev. A 89, 033828 (2014).
  74. R. Cruickshank, F. Lorenzi, A. La Rooij, E. Kerr, T. Hilker, S. Kuhr, L. Salasnich, and E. Haller, Data for experimental observation of single- and multi-site matter-wave solitons in an optical accordion lattice, University of Strathclyde, 2025, 10.15129/c78af204-a552-4213-a581-7cbdaa14a311.

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Phys. Rev. Lett. 135, 263404– Published 23 December, 2025
  • Received 15 April 2025
  • Accepted 16 October 2025
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