Vorticity, Variance, and the Vigor of Many-Body Phenomena in Ultracold Quantum Systems: MCTDHB and MCTDH-X

  • Ofir E. Alon
  • Raphael Beinke
  • Lorenz S. Cederbaum
  • Matthew J. Edmonds
  • Elke Fasshauer
  • Mark A. Kasevich
  • Shachar Klaiman
  • Axel U. J. Lode
  • Nick G. Parker
  • Kaspar Sakmann
  • Marios C. Tsatsos
  • Alexej I. Streltsov
Conference paper


During the past year of the MCTDHB project at the HLRS, we continued to strive and conquest further applications, developments, and expansion of the MultiConfigurational Time-Dependent Hartree for Bosons (MCTDHB) method in the context of ultracold atomic systems. We also announce the MCTDH-X package, the Multiconfigurational Time-Dependent Hartree for Indistinguishable Particles X package, which is able to treat identical bosons and fermions, with or without spin/internal degrees of freedom, alike. Here we report on a plethora of results and versatile applications which include: (i) single-shot imaging of fluctuating vortices in a fragmented Bose-Einstein condensate (BEC); (ii) the many-body tunneling and fragmetnation of vortices in 2D trapped BECs; (iii) the transition from vortices to solitonic vortices in 2D trapped BECs; (iv) the variance of a many-particle system being very sensitive to correlations even in the infinite-particle limit; (v) the consequences of the latter on the out-of-equilibrium uncertainty product of an evolving BEC; (vi) the mechanism of tunneling to open space of a few interacting polarized fermions; and (vii) composite fragmentation of multi-components BECs (i.e., with internal degrees of freedom). These are all exciting results made throughout the allocation of computer time by the HLRS to the MCTDHB project. Finally, further perspectives and future research plans are briefly discussed.



Financial support by the Deutsche Forschungsgemeinschaft (DFG) is gratefully acknowledged. OEA acknowledges funding by the Israel Science Foundation (Grant No. 600/15). RB acknowledges support from the Heidelberg Graduate School of Fundamental Physics (HGSFP). MJE and NGP acknowledge support by EPSRC (UK) Grant No. EP/M005127/1. EF gratefully acknowledges funding from the Research Council of Norway (RCN) through CoE Grant No. 179568/V30 (CTCC). AUJL acknowledges financial support by the Swiss SNF and the NCCR Quantum Science and Technology. KS acknowledges support through the Karel Urbanek Postodcoral Research Fellowship from the Applied Physics Department of Stanford University. MCT acknowledges funding by FAPESP and CePOF at IFSC-University of São Paulo.


  1. 1.
    Streltsov, A.I., Alon, O.E., Cederbaum, L.S.: General variational many-body theory with complete self-consistency for trapped bosonic systems. Phys. Rev. A 73, 063626 (2006)CrossRefGoogle Scholar
  2. 2.
    Streltsov, A.I., Alon, O.E., Cederbaum, L.S.: Role of excited states in the splitting of a trapped interacting bose-einstein condensate by a time-dependent barrier. Phys. Rev. Lett. 99, 030402 (2007)CrossRefGoogle Scholar
  3. 3.
    Alon, O.E., Streltsov, A.I., Cederbaum, L.S.: Unified view on multiconfigurational time propagation for systems consisting of identical particles. J. Chem. Phys. 127, 154103 (2007)CrossRefGoogle Scholar
  4. 4.
    Alon, O.E., Streltsov, A.I., Cederbaum, L.S.: Multiconfigurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems. Phys. Rev. A 77, 033613 (2008)CrossRefGoogle Scholar
  5. 5.
    Sakmann, K., Streltsov, A.I., Alon, O.E., Cederbaum, L.S.: Exact quantum dynamics of a bosonic Josephson junction. Phys. Rev. Lett. 103, 220601 (2009)CrossRefGoogle Scholar
  6. 6.
    Lode, A.U.J., Sakmann, K., Alon, O.E., Cederbaum, L.S., Streltsov, A.I.: Numerically exact quantum dynamics of bosons with time-dependent interactions of harmonic type. Phys. Rev. A 86, 063606 (2012)CrossRefGoogle Scholar
  7. 7.
    Meyer, H.-D., Gatti, F., Worth, G. A. (eds.): Multidimensional Quantum Dynamics: MCTDH Theory and Applications. Wiley-VCH, Weinheim (2009)Google Scholar
  8. 8.
    Proukakis, N.P., Gardiner, S.A., Davis, M.J., Szymanska, M.H. (eds.): Quantum Gases: Finite Temperature and Non-equilibrium Dynamics. Cold Atoms Series, vol. 1. Imperial College Press, London (2013)Google Scholar
  9. 9.
    Streltsov, A.I., Sakmann, K., Lode, A.U.J., Alon, O.E., Cederbaum, L.S.: The Multiconfigurational Time-Dependent Hartree for Bosons Package, version 2.3. Heidelberg (2013)Google Scholar
  10. 10.
    Streltsov, A.I., Cederbaum, L.S., Alon, O.E., Sakmann, K., Lode, A.U.J., Grond, J., Streltsova, O.I., Klaiman, S.: The Multiconfigurational Time-Dependent Hartree for Bosons Package, version 3.x. Heidelberg (2006-Present). http://mctdhb.org
  11. 11.
    Streltsov, A.I., Streltsova, O.I.: The Multiconfigurational Time-Dependent Hartree for Bosons Laboratory, version 1.5 (2015) http://MCTDHB-lab.org; http://QDlab.org
  12. 12.
    Lode, A.U.J., Tsatsos, M.C., Fasshauer, E.: The Multiconfigurational Time-Dependent Hartree for Indistinguishable Particles X Package (2015) http://mctdhx.org; http://ultracold.org; http://schroedinger.org; http://mctdh.bf
  13. 13.
    Lode, A.U.J., Sakmann, K., Doganov, R.A., Grond, J., Alon, O.E., Streltsov, A.I., Cederbaum, L.S.: Numerically-exact schrödinger dynamics of closed and open many-boson systems with the MCTDHB package. In: Nagel, W.E., Kröner, D.H., Resch, M.M. (eds.) High Performance Computing in Science and Engineering ’13: Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2013, pp. 81–92. Springer, Heidelberg (2013)Google Scholar
  14. 14.
    Klaiman, S., Lode, A.U.J., Sakmann, K., Streltsova, O.I., Alon, O.E., Cederbaum, L.S., Streltsov, A.I.: Quantum many-body dynamics of trapped bosons with the MCTDHB package: towards new horizons with novel physics. In: Nagel, W.E., Kröner, D.H., Resch, M.M. (eds.) High Performance Computing in Science and Engineering ’14: Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2014, pp. 63–86. Springer, Heidelberg (2015)Google Scholar
  15. 15.
    Alon, O.E., Bagnato, V.S., Beinke, R., Brouzos, I., Calarco, T., Caneva, T., Cederbaum, L.S., Kasevich, M.A., Klaiman, S., Lode, A.U.J., Montangero, S., Negretti, A., Said, R.S., Sakmann, K., Streltsova, O.I., Theisen, M., Tsatsos, M.C., Weiner, S.E., Wells, T., Streltsov, A.I.: MCTDHB physics and technologies: excitations and vorticity, single-shot detection,measurement of fragmentation, and optimal control in correlated ultra-cold bosonic many-body systems. In: Nagel, W.E., Kröner, D.H., Resch, M.M. (eds.) High Performance Computing in Science and Engineering ’15: Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2015, pp. 23–50. Springer, Heidelberg (2016)Google Scholar
  16. 16.
    Sakmann, K., Kasevich, M.: Single-shot simulations of dynamic quantum many-body systems. Nat. Phys. 12, 451 (2016)CrossRefGoogle Scholar
  17. 17.
    Beinke, R., Klaiman, S., Cederbaum, L.S., Streltsov, A.I., Alon, O.E.: Many-body tunneling dynamics of Bose-Einstein condensates and vortex states in two spatial dimensions. Phys. Rev. A 92, 043627 (2015)CrossRefGoogle Scholar
  18. 18.
    Tsatsos, M.C., Edmonds, M.J., Parker, N.G.: Transition from vortices to solitonic vortices in trapped atomic Bose-Einstein condensates. Phys. Rev. A 94, 023627 (2016)CrossRefGoogle Scholar
  19. 19.
    Klaiman, S., Alon, O.E.: Variance as a sensitive probe of correlations. Phys. Rev. A 91, 063613 (2015)CrossRefGoogle Scholar
  20. 20.
    Klaiman, S., Streltsov, A.I., Alon, O.E.: Uncertainty product of an out-of-equilibrium many-particle system. Phys. Rev. A 93, 023605 (2016)CrossRefGoogle Scholar
  21. 21.
    Fasshauer, E., Lode, A.U.J.: Multiconfigurational time-dependent Hartree method for fermions: implementation, exactness, and few-fermion tunneling to open space. Phys. Rev. A 93, 033635 (2016)CrossRefGoogle Scholar
  22. 22.
    Lode, A.U.J.: The multiconfigurational time-dependent Hartree method for bosons with internal degrees of freedom: theory and composite fragmentation of multi-component Bose-Einstein condensates. Phys. Rev. A 93, 063601 (2016)CrossRefGoogle Scholar
  23. 23.
    Penrose, O., Onsager, L.: Bose-Einstein condensation and liquid helium. Phys. Rev. 104, 576 (1956)CrossRefMATHGoogle Scholar
  24. 24.
    Javanainen, J., Yoo, S.M.: Quantum phase of a Bose-Einstein condensate with an arbitrary number of atoms. Phys. Rev. Lett. 76, 161 (1996)CrossRefGoogle Scholar
  25. 25.
    Castin, Y., Dalibard, J.: Relative phase of two Bose-Einstein condensates. Phys. Rev. A 55, 4330 (1997)CrossRefGoogle Scholar
  26. 26.
    Dziarmaga, J., Karkuszewski, Z.P., Sacha, K.: Images of the dark soliton in a depleted condensate. J. Phys. B 36, 1217 (2003)CrossRefGoogle Scholar
  27. 27.
    Dagnino, D., Barberán, N., Lewenstein, M.: Vortex nucleation in a mesoscopic Bose superfluid and breaking of the parity symmetry. Phys. Rev. A 80, 053611 (2009)CrossRefGoogle Scholar
  28. 28.
    Streltsov, A.I., Alon, O.E., Cederbaum, L.S.: General mapping for bosonic and fermionic operators in fock space. Phys. Rev. A 81, 022124 (2010)CrossRefGoogle Scholar
  29. 29.
    Fetter, A.L.: Rotating trapped Bose-Einstein condensates. Rev. Mod. Phys. 81, 647 (2009)CrossRefGoogle Scholar
  30. 30.
    Dagnino, D., Barberán, N., Lewenstein, M., Dalibard, J.: Vortex nucleation as a case study of symmetry breaking in quantum systems. Nat. Phys. 5, 431 (2009)CrossRefGoogle Scholar
  31. 31.
    Weiner, S.E., Tsatsos, M.C., Cederbaum, L.S., Lode, A.U.J.: Angular momentum in interacting many-body systems hides in phantom vortices. arXiv:1409.7670Google Scholar
  32. 32.
    Nozières, P., James, D.S.: Particle vs. pair condensation in attractive Bose liquids. J. Phys. (Fr.) 43, 1133 (1982)Google Scholar
  33. 33.
    Martin, A.M., Scott, R.G., Fromhold, T.M.: Transmission and reflection of Bose-Einstein condensates incident on a Gaussian tunnel barrier. Phys. Rev. A 75, 065602 (2007)CrossRefGoogle Scholar
  34. 34.
    Arovas, D.P., Auerbach, A.: Quantum tunneling of vortices in two-dimensional superfluids. Phys. Rev. B 78, 094508 (2008)CrossRefGoogle Scholar
  35. 35.
    Salgueiro, J.R., Zacarés, M., Michinel, H., Ferrando, A.: Vortex replication in Bose-Einstein condensates trapped in double-well potentials. Phys. Rev. A 79, 033625 (2009)CrossRefGoogle Scholar
  36. 36.
    Fialko, O., Bradley, A.S., Brand, J.: Quantum tunneling of a vortex between two pinning potentials. Phys. Rev. Lett. 108, 015301 (2012)CrossRefGoogle Scholar
  37. 37.
    Garcia-March, M.A., Carr, L.D.: Vortex macroscopic superpositions in ultracold bosons in a double-well potential. Phys. Rev. A 91, 033626 (2015)CrossRefGoogle Scholar
  38. 38.
    Kevrekidis, P.G., Frantzeskakis, D.J., Carretero-González, R. (eds.): Emergent Nonlinear Phenomena in Bose-Einstein Condensates. Springer, Berlin (2008)MATHGoogle Scholar
  39. 39.
    Becker, C., Sengstock, K., Schmelcher, P., Kevrekidis, P.G., Carretero-González, R.: Inelastic collisions of solitary waves in anisotropic Bose-Einstein condensates: sling-shot events and expanding collision bubbles. New J. Phys. 15, 113028 (2013)CrossRefGoogle Scholar
  40. 40.
    Donadello, S., Serafini, S., Tylutki, M., Pitaevskii, L.P., Dalfovo, F., Lamporesi, G., Ferrari, G.: Observation of solitonic vortices in Bose-Einstein condensates. Phys. Rev. Lett. 113, 065302 (2014)CrossRefGoogle Scholar
  41. 41.
    Ku, M.J.H., Ji, W., Mukherjee, B., Guardado-Sanchez, E., Cheuk, L.W., Yefsah, T., Zwierlein, M.W.: Motion of a solitonic vortex in the BEC-BCS crossover. Phys. Rev. Lett. 113, 065301 (2014)CrossRefGoogle Scholar
  42. 42.
    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)CrossRefGoogle Scholar
  43. 43.
    Cohen-Tannoudji, C., Diu, B., Laloë, F.: Quantum Mechanics, vol. 1. Wiley, New York (1977)MATHGoogle Scholar
  44. 44.
    Dalfovo, F., Giorgini, S., Pitaevskii, L.P., Stringari, S.: Theory of Bose-Einstein condensation in trapped gases. Rev. Mod. Phys. 71, 463 (1999)CrossRefGoogle Scholar
  45. 45.
    Leggett, A.J.: Bose-Einstein condensation in the alkali gases: some fundamental concepts. Rev. Mod. Phys. 73, 307 (2001)CrossRefGoogle Scholar
  46. 46.
    Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885 (2008)CrossRefGoogle Scholar
  47. 47.
    Pitaevskii, L., Stringari, S.: Bose-Einstein Condensation. Oxford University Press, Oxford (2003)MATHGoogle Scholar
  48. 48.
    Leggett, A.J.: Quantum Liquids: Bose Condensation and Cooper Pairing in Condensed Matter Systems. Oxford University Press, Oxford (2006)CrossRefGoogle Scholar
  49. 49.
    Pethick, C.J., Smith, H.: Bose-Einstein Condensation in Dilute Gases, 2nd edn. Cambridge University Press, Cambridge (2008)CrossRefGoogle Scholar
  50. 50.
    Lieb, E.H., Seiringer, R., Yngvason, J.: Bosons in a trap: a rigorous derivation of the Gross-Pitaevskii energy functional. Phys. Rev. A 61, 043602 (2000)CrossRefGoogle Scholar
  51. 51.
    Lieb, E.H., Seiringer, R.: Proof of Bose-Einstein condensation for dilute trapped gases. Phys. Rev. Lett. 88, 170409 (2002)CrossRefGoogle Scholar
  52. 52.
    Erdős, L., Schlein, B., Yau, H.-T.: Rigorous derivation of the Gross-Pitaevskii equation. Phys. Rev. Lett. 98, 040404 (2007)CrossRefGoogle Scholar
  53. 53.
    Brazhnyi, V.A., Kamchatnov, A.M., Konotop, V.V.: Hydrodynamic flow of expanding Bose-Einstein condensates. Phys. Rev. A 68, 035603 (2003)CrossRefGoogle Scholar
  54. 54.
    Serwane, F., Zürn, G., Lompe, T., Ottenstein, T.B., Wenz, A.N., Jochim, S.: Deterministic preparation of a tunable few-fermion system. Science 332, 6027 (2011)CrossRefGoogle Scholar
  55. 55.
    Caillat, J., Zanghellini, J., Kitzler, M., Koch, O., Kreuzer, W., Scrinzi, A.: Correlated multielectron systems in strong laser fields: a multiconfiguration time-dependent Hartree-Fock approach. Phys. Rev. A 71, 012712 (2005); Zanghellini, J., Kitzler, M., Fabian, C., Brabec, T., Scrinzi, A.: An MCTDHF approach to multielectron dynamics in laser fields. Laser Phys. 13, 1064 (2003)Google Scholar
  56. 56.
    Kato, T., Kono, H.: Time-dependent multiconfiguration theory for electronic dynamics of molecules in an intense laser field. Chem. Phys. Lett. 392, 533 (2004)CrossRefGoogle Scholar
  57. 57.
    Nest, M., Klamroth, T., Saalfrank, P.: The multiconfiguration time-dependent Hartree-Fock method for quantum chemical calculations. J. Chem. Phys. 122, 124102 (2005)CrossRefGoogle Scholar
  58. 58.
    Grond, J., Streltsov, A.I., Lode, A.U.J., Sakmann, K., Cederbaum, L.S., Alon, O.E.: Excitation spectra of many-body systems by linear response: general theory and applications to trapped condensates. Phys. Rev. A 88, 023606 (2013)CrossRefGoogle Scholar
  59. 59.
    Alon, O.E., Streltsov, A.I., Cederbaum, L.S.: Unified view on linear response of interacting identical and distinguishableparticles from multiconfigurational time-dependent Hartree methods. J. Chem. Phys. 140, 034108 (2014)CrossRefGoogle Scholar
  60. 60.
    Alon, O.E.: Many-body excitation spectra of trapped bosons with general interaction by linear response. J. Phys. Conf. Ser. 594, 012039 (2015)CrossRefGoogle Scholar
  61. 61.
    Tsatsos, M.C., Tavares, P.E.S., Cidrim, A., Fritsch, A.R., Caracanhas, M.A., dos Santos, F.E.A., Barenghi, C.F., Bagnato, V.S.: Quantum turbulence in trapped atomic Bose-Einstein condensates. Phys. Rep. 622, 1 (2016)MathSciNetCrossRefGoogle Scholar
  62. 62.
    Lode, A.U.J., Chakrabarti, B., Kota, V.K.B.: Many-body entropies, correlations, and emergence of statistical relaxation in interaction quench dynamics of ultracold bosons. Phys. Rev. A 92, 033622 (2015)CrossRefGoogle Scholar
  63. 63.
    Gring, M., Kuhnert, M., Langen, T., Kitagawa, T., Rauer, B., Schreitl, M., Mazets, I., Adu Smith, D., Demler, E., Schmiedmayer, J.: Relaxation and prethermalization in an isolated quantum system. Science 337, 1318 (2012)CrossRefGoogle Scholar
  64. 64.
    von Stecher, J., Greene, C.H.: Spectrum and dynamics of the BCS-BEC crossover from a few-body perspective. Phys. Rev. Lett. 99, 090402 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Ofir E. Alon
    • 1
  • Raphael Beinke
    • 2
  • Lorenz S. Cederbaum
    • 2
  • Matthew J. Edmonds
    • 3
  • Elke Fasshauer
    • 4
  • Mark A. Kasevich
    • 5
  • Shachar Klaiman
    • 2
  • Axel U. J. Lode
    • 6
  • Nick G. Parker
    • 3
  • Kaspar Sakmann
    • 7
  • Marios C. Tsatsos
    • 8
  • Alexej I. Streltsov
    • 2
  1. 1.Department of PhysicsUniversity of Haifa at OranimTivonIsrael
  2. 2.Theoretische Chemie, Physikalisch-Chemisches InstitutUniversität HeidelbergHeidelbergGermany
  3. 3.Joint Quantum Centre (JQC) Durham-NewcastleSchool of Mathematics and Statistics, Newcastle UniversityNewcastle upon TyneEngland, UK
  4. 4.Department of Chemistry, University of Tromsø – The Arctic University of NorwayCentre for Theoretical and Computational ChemistryTromsøNorway
  5. 5.Department of PhysicsStanford UniversityStanfordUSA
  6. 6.Department of PhysicsUniversity of BaselBaselSwitzerland
  7. 7.Vienna Center for Quantum Science and TechnologyAtominstitut TU WienViennaAustria
  8. 8.Instituto de Física de São CarlosUniversidade de São PauloSão Carlos, São PauloBrazil

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