Interacting bosons in external traps: Theory, computational methods and applications beyond standard mean-field
Final Report Abstract
We have successfully fullfilled and accomplished all the objectives, aims, and goals defined in this proposal. Scientifically, we have developed a complete set of theories beyond Gross-Pitaevskii mean-field capable to attack different problems appearing in the context of ultra-cold atomic systems consisting of singleand multi-component, attractive and repulsive BECs, mixture thereof, spinors etc. The main theoretical agenda was to solve the time-(in)dependent many-particle Schrödinger equation numerically as precisely as possible. On our way to this goal we have developed a number of intermediate theoretical methods, i.e., BMF, TDMF, MCHB, which can be considered as limiting cases of the MCTDHB theory. On the other hand, they have been developed together with the evolution of our understanding of the role which the many-body physics plays in static and dynamics of ultra-cold bosonic systems. The MCTDHB method can solve the many-boson statics and dynamics numerically exactly. Its applicability is currently restricted by the size of the many-body Fock space which we have to deal with, practicaly up to 40,000,000 (the next generation of the interconnections will allow us to go till 400,000,000). This restriction does not hold for our multi-orbital mean-field approaches which, hence, can be applied to study qualitative and even quantitative statics and dynamics of systems with large particle numbers in external traps of very complicated topologies, including OLs. As a practical outcome we have created a (i) hybrid MPI-OpenMP parallel MCT-DHB package operating on supercomputers; (ii) serial, fully-documented OpenMCTDHB package to run on standard working stations; (iii) analysis tools to monitor and visualize evolutions of the properties (densities in real and momentum spaces, correlation functions, etc.) of the many-boson wavefunctions in a form of figures and movies. The major physical goal of our project was defined as: “to describe the many-body physics accompanying ground and excited-state fragmentation and quantum phase transitions in traps, and many-body dynamics of condensate immersed in different traps and upon their release.” We have demonstrated that fragmentation is a phenomenon widely accompanying condensation of the repulsive BECs in simple multi-well traps and in OLs where it corresponds to Mott-insulator phenomena. In attractive BECs it can persist by itself, i.e., without traps and leads to a number of dramatic physical phenomena which can be verified experimentally: e.g. postpone of the collapse in 3D; swift loss of the coherence of soliton trains, and formation of the “Fragmentons” and “Catons” at low dimensions. We hope that our predictions will stimulate experiments.
Publications
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Interferences in the Density of Two Bose-Einstein Condensates Consisting of Identical or Different Atoms, Phys. Rev. Lett. 98, 110405 (2007)
L. S. Cederbaum, A. I. Streltsov, Y. B. Band, and O. E. Alon
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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)
A. I. Streltsov, O. E. Alon, and L. S. Cederbaum
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Formation and Dynamics of Many- Boson Fragmented States in One-Dimensional Attractive Ultracold Gases, Phys. Rev. Lett. 100, 130401 (2008)
A. I. Streltsov, O. E. Alon, and L. S. Cederbaum
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Multiconfigurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems, Phys. Rev. A 77, 033613 (2008)
O. E. Alon, A. I. Streltsov, and L. S. Cederbaum
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Exact Quantum Dynamics of a Bosonic Josephson Junction, Phys. Rev. Lett. 103, 220601 (2009)
K. Sakmann, A. I. Streltsov, O. E. Alon, and L. S. Cederbaum
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Swift loss of coherence of soliton trains in attractive Bose-Einstein condensates, Phys. Rev. Lett. 106, 240401 (2011)
A. I. Streltsov, O. E. Alon, and L. S. Cederbaum
