Quantum Many-Body Dynamics of Trapped Bosons with the MCTDHB Package: Towards New Horizons with Novel Physics

  • Shachar Klaiman
  • Axel U. J. Lode
  • Kaspar Sakmann
  • Oksana I. Streltsova
  • Ofir E. Alon
  • Lorenz S. Cederbaum
  • Alexej I. Streltsov
Conference paper


The MCTDHB package has been applied to study the physics of trapped interacting many-boson systems by solving the underlying time-dependent (as well as the time-independent) many-boson Schrödinger equation. Here we report on four studies where novel physical ideas and phenomena have been proposed and discovered: (a) Universality of the fragmentation dynamics in double wells – at long propagation times properties of the evolving system saturate to some asymptotic values; (b) Novel many-body spectral features in trapped systems – the newly-developed linear-response theory on-top of MCTDHB predicts the existence of low-lying excitations not described so far by the standard theory even in harmonic potentials; (c) Efficient protocol to control the many-particle tunneling dynamics to open space, by combining the effects of a threshold potential and inter-particle interaction; (d) Physics behind the formation of patterns in the ground states of trapped bosonic systems with strong finite- and long-range repulsive interactions and the origin of their dynamical stability. From the perspective of the required computational resources and numerical algorithms applied, each of these numerically-demanding studies has challenged different aspects of computational physics and mathematics: Long-time propagation – stability of the numerical methods used to integrate the MCTDHB equations-of-motion; Control of the tunneling dynamics – a very detailed study where an interplay of the parameters controlling the decay by tunneling dynamics is accompanied by a long-time propagation on huge spatial grids, which are needed to simulate open systems; Excited states of many-body systems – construction and diagonalization of complex non-hermitian linear-response matrices; Finite- and long-range interactions in 1D, 2D, and 3D setups – efficient methods and techniques for evaluation of involved high-dimensional integrals. Implications and further perspectives and future plans are briefly discussed and addressed.


Interparticle Interaction Natural Orbital Harmonic Trap Fragmentation Phenomenon Tunneling Dynamic 
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  1. 1.
    Aikawa, K., Frisch, A., Mark, M., Baier, S., Rietzler, A., Grimm, R., Ferlaino, F.: Bose-Einstein Condensation of Erbium. Phys. Rev. Lett. 108, 210401 (2012)CrossRefGoogle Scholar
  2. 2.
    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
  3. 3.
    Alon, O.E., Streltsov, A.I., Cederbaum, L.S.: Unified view on linear response of interacting identical and distinguishable particles from multiconfigurational time-dependent Hartree methods. J. Chem. Phys. 140, 034108 (2014)CrossRefGoogle Scholar
  4. 4.
    Astrakharchik, G.E., Girardeau, M.D.: Exact ground-state properties of a one-dimensional Coulomb gas. Phys. Rev. B 83, 153303 (2011)CrossRefGoogle Scholar
  5. 5.
    Baranov, M.A.: Theoretical progress in many-body physics with ultracold dipolar gases. Phys. Rep. 464, 71 (2008)CrossRefGoogle Scholar
  6. 6.
    B\(\check{\mathrm{r}}\) ezinová, I., Lode, A.U.J., Streltsov, A.I., Alon, O.E., Cederbaum, L.S., Burgdörfer, J.: Wave chaos as signature for depletion of a Bose-Einstein condensate. Phys. Rev. A 86, 013630 (2012)Google Scholar
  7. 7.
    B\(\check{\mathrm{r}}\) ezinová, I., Lode, A.U.J., Streltsov, A.I., Cederbaum, L.S., Alon, O.E., Collins, L.A., Schneider, B.I., Burgdörfer, J.: Elastic scattering of a Bose-Einstein condensate at a potential landscape. J. Phys. Conf. Ser. 488, 012032 (2014)Google Scholar
  8. 8.
    bwGRiD, member of the German D-grid initiative, funded by the Ministry for Education and Research (Bundesministerium für Bildung und Forschung) and the Ministry for Science, Research and Arts Baden-Württemberg (Ministerium für Wissenschaft, Forschung und Kunst Baden-Württemberg).
  9. 9.
    Castin, Y., Dum, R.: Low-temperature Bose-Einstein condensates in time-dependent traps: Beyond the U(1) symmetry-breaking approach. Phys. Rev. A 57, 3008 (1998)CrossRefGoogle Scholar
  10. 10.
    Comparat, D., Pillet, P.: Dipole blockade in a cold Rydberg atomic sample [Invited]. J. Opt. Soc. Am. B 6, A208 (2010)CrossRefGoogle Scholar
  11. 11.
    Cray XE6 cluster Hermit and NEC Nehalem cluster Luki at the High Performance Computing Center Stuttgart (HLRS).
  12. 12.
    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
  13. 13.
    Esry, B.D.: Hartree-Fock theory for Bose-Einstein condensates and the inclusion of correlation effects. Phys. Rev. A 55, 1147 (1997)CrossRefGoogle Scholar
  14. 14.
    Fetter, A.L., Walecka, J.D.A.: Quantum Theory of Many-Particle Systems. McGraw-Hill, New York (1971)Google Scholar
  15. 15.
    Gardiner, C.W.:Particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas. Phys. Rev. A 56, 1414 (1997)Google Scholar
  16. 16.
    Girardeau, M.: Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension. J. Math. Phys. 1, 516 (1960)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Griesmaier, A., Werner, J., Hensler, S., Stuhler, J., Pfau, T.: Bose-Einstein Condensation of Chromium. Phys. Rev. Lett. 94, 160401 (2005)CrossRefGoogle Scholar
  18. 18.
    Grond, J., Schmiedmayer, J., Hohenester, U.: Optimizing number squeezing when splitting a mesoscopic condensate. Phys. Rev. A 79, 021603(R) (2009)Google Scholar
  19. 19.
    Grond, J., Betz, T., Hohenester, U., Mauser, N.J., Schmiedmayer, J., Schumm, T., New J.: Shapiro effect in atomchip-based bosonic Josephson junctions. Phys. 13, 065026 (2011)Google Scholar
  20. 20.
    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
  21. 21.
    Heimsoth, M., Hochstuhl, D., Creffield, C.E., Carr, L.D., Sols, F.: Effective Josephson dynamics in resonantly driven Bose-Einstein condensates. New J. Phys. 15, 103006 (2013)CrossRefGoogle Scholar
  22. 22.
    Henkel, N., Nath, R., Pohl, T.: Three-Dimensional Roton Excitations and Supersolid Formation in Rydberg-Excited Bose-Einstein Condensates. Phys. Rev. Lett. 104, 195302 (2010)CrossRefGoogle Scholar
  23. 23.
    Henkel, N., Cinti, F., Jain, P., Pupillo, G., Pohl, T.: Supersolid Vortex Crystals in Rydberg-Dressed Bose-Einstein Condensates. Phys. Rev. Lett. 108, 265301 (2012)CrossRefGoogle Scholar
  24. 24.
    Hochstuhl, D., Hinz, C.M., Bonitz, M.: Time-dependent multiconfiguration methods for the numerical simulation of photoionization processes of many-electron atoms. Eur. Phys. J. Spec. Top. 223, 177 (2014)CrossRefGoogle Scholar
  25. 25.
    Hofferberth, S., Lesanovsky, I., Fischer, B., Verdu, J., Schmiedmayer, J.: Radiofrequency-dressed-state potentials for neutral atoms. Nat. Phys. 2, 710 (2006)CrossRefGoogle Scholar
  26. 26.
    Hybrid computing complex K100 (Keldysh Institute of Applied Mathematics, RAS).
  27. 27.
    Johnson, J.E., Rolston, S.L.: Interactions between Rydberg-dressed atoms. Phys. Rev. A 82, 033412 (2010)CrossRefGoogle Scholar
  28. 28.
    Köhler, T., Góral, K., Julienne, P.S.: Production of cold molecules via magnetically tunable Feshbach resonances. Rev. Mod. Phys. 78, 1311 (2006)CrossRefGoogle Scholar
  29. 29.
    Lahaye, T., Menotti, C., Santos, L., Lewenstein, M., Pfau, T.: The physics of dipolar bosonic quantum gases. Rep. Prog. Phys. 72, 126401 (2009)CrossRefGoogle Scholar
  30. 30.
    Leggett, A.J.: Bose-Einstein condensation in the alkali gases: Some fundamental concepts. Rev. Mod. Phys. 73, 307 (2001)CrossRefGoogle Scholar
  31. 31.
    Lode, A.U.J., Tsatsos, M.C.: The recursive multiconfigurational time-dependent Hartree for Bosons package.;; (2014)
  32. 32.
    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
  33. 33.
    Lode, A.U.J., Streltsov, A.I., Sakmann, K., Alon, O.E., Cederbaum, L.S.: How an interacting many-body system tunnels through a potential barrier to open space. Proc. Natl. Acad. Sci. USA 109, 13521 (2012)CrossRefGoogle Scholar
  34. 34.
    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, HLRS report for 2012. 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. Springer, Heidelberg (2013)Google Scholar
  35. 35.
    Lode, A.U.J., Klaiman, S., Alon, O.E., Streltsov, A.I., Cederbaum, L.S.: Controlling the velocities and the number of emitted particles in the tunneling to open space dynamics. Phys. Rev. A 89, 053620 (2014)CrossRefGoogle Scholar
  36. 36.
    Lu, M., Burdick, N.Q., Youn, S.H., Lev, B.L.: Strongly Dipolar Bose-Einstein Condensate of Dysprosium. Phys. Rev. Lett. 107, 190401 (2011)CrossRefGoogle Scholar
  37. 37.
    Meyer, H.-D., Gatti, F., Worth, G.A. (eds.): Multidimensional Quantum Dynamics: MCTDH Theory and Applications. Wiley-VCH, Weinheim (2009)Google Scholar
  38. 38.
    Milburn, G.J., Corney, J., Wright, E.M., Walls, D.F.: Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential. Phys. Rev. A 55, 4318 (1997)CrossRefGoogle Scholar
  39. 39.
    Mueller, E.J., Ho, T.-L., Ueda, M., Baym, G.: Fragmentation of Bose-Einstein condensates. Phys. Rev. A 74, 033612 (2006)CrossRefGoogle Scholar
  40. 40.
    Nest, M., Klamroth, T., Saalfrank, P.: Unified view on multiconfigurational time-propagation for systems consisting of identical particles. J. Chem. Phys. 127, 154103 (2005)Google Scholar
  41. 41.
    Nozières, P.: Some Comments on Bose-Einstein Condensation. In: Griffin, A., Snoke, D.W., Stringari, S. (eds.) Bose-Einstein Condensation. Cambridge University Press, Cambridge (1996)Google Scholar
  42. 42.
    Nozières, P., Saint James, D.: Particle vs. pair condensation in attractive Bose liquids. J. Phys. (Fr.) 43, 1133 (1982)Google Scholar
  43. 43.
    Olsen, J., Jørgensen, P.: Linear and nonlinear response functions for an exact state and for an MCSCF state. J. Chem. Phys. 82, 3235 (1985)CrossRefGoogle Scholar
  44. 44.
    Orzel, C., Tuchman, A.K., Fenselau, M.L., Yasuda, M., Kasevich, M.A.: Squeezed States in a Bose-Einstein Condensate. Science 291, 2386 (2001)CrossRefGoogle Scholar
  45. 45.
    Penrose, O., Onsager, L.: Bose-Einstein Condensation and Liquid Helium. Phys. Rev. 104, 576 (1956)CrossRefzbMATHGoogle Scholar
  46. 46.
    Perrin, A., Chang, H., Krachmalnicoff, V., Schellekens, M., Boiron, D., Aspect, A., Westbrook, C.I.: Observation of Atom Pairs in Spontaneous Four-Wave Mixing of Two Colliding Bose-Einstein Condensates. Phys. Rev. Lett. 99, 150405 (2007)CrossRefGoogle Scholar
  47. 47.
    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
  48. 48.
    Pupillo, G., Micheli, A., Boninsegni, M., Lesanovsky, I., Zoller, P.: Strongly Correlated Gases of Rydberg-Dressed Atoms: Quantum and Classical Dynamics. Phys. Rev. Lett. 104, 223002 (2010)CrossRefGoogle Scholar
  49. 49.
    Ruprecht, P.A., Edwards, M., Burnett, K., Clark, C.W.: Probing the linear and nonlinear excitations of Bose-condensed neutral atoms in a trap. Phys. Rev. A 54, 4178 (1996)CrossRefGoogle Scholar
  50. 50.
    Sakmann, K., Streltsov, A.I., Alon, O.E., Cederbaum, L.S.: Reduced density matrices and coherence of trapped interacting bosons. Phys. Rev. A 78, 023615 (2008)CrossRefGoogle Scholar
  51. 51.
    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
  52. 52.
    Sakmann, K., Streltsov, A.I., Alon, O.E., Cederbaum, L.S.: Universality of fragmentation in the Schrdinger dynamics of bosonic Josephson junctions. Phys. Rev. A 89, 023602 (2014)CrossRefGoogle Scholar
  53. 53.
    Smerzi, A., Fantoni, S., Giovanazzi, S., Shenoy, S.R.: Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates. Phys. Rev. Lett. 79, 4950 (1997)CrossRefGoogle Scholar
  54. 54.
    Spekkens, R.W., Sipe, J.E.: Spatial fragmentation of a Bose-Einstein condensate in a double-well potential. Phys. Rev. A 59, 3868 (1999)CrossRefGoogle Scholar
  55. 55.
    Streltsov, A.I.: Quantum systems of ultracold bosons with customized interparticle interactions. Phys. Rev. A 88, 041602(R) (2013)Google Scholar
  56. 56.
    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
  57. 57.
    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
  58. 58.
    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)
  59. 59.
    Streltsova, O.I., Alon, O.E., Cederbaum, L.S., Streltsov, A.I.: Generic regimes of quantum many-body dynamics of trapped bosonic systems with strong repulsive interactions. Phys. Rev. A 89, 061602(R) (2014)Google Scholar
  60. 60.
    Stuhler, J., Griesmaier, A., Koch, T., Fattori, M., Pfau, T., Giovanazzi, S., Pedri, P., Santos, L.: Observation of Dipole-Dipole Interaction in a Degenerate Quantum Gas. Phys. Rev. Lett. 95, 150406 (2005)CrossRefGoogle Scholar
  61. 61.
    Viteau, M., Bason, M.G., Radogostowicz, J., Malossi, N., Ciampini, D., Morsch, O., Arimondo, E.: Rydberg Excitations in Bose-Einstein Condensates in Quasi-One-Dimensional Potentials and Optical Lattices. Phys. Rev. Lett. 107, 060402 (2011)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Shachar Klaiman
    • 1
  • Axel U. J. Lode
    • 2
  • Kaspar Sakmann
    • 3
  • Oksana I. Streltsova
    • 4
  • Ofir E. Alon
    • 5
  • Lorenz S. Cederbaum
    • 1
  • Alexej I. Streltsov
    • 1
  1. 1.Theoretische ChemieUniversität HeidelbergHeidelbergGermany
  2. 2.Condensed Matter Theory and Quantum Computing Group, Departement für PhysikUniversität BaselBaselSwitzerland
  3. 3.Department of PhysicsStanford UniversityStanfordUSA
  4. 4.Laboratory of Information TechnologiesJoint Institute for Nuclear ResearchDubnaRussia
  5. 5.Department of PhysicsUniversity of Haifa at OranimTivonIsrael

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