Benchmarking the multiconfigurational Hartree method by the exact wavefunction of two harmonically trapped bosons with contact interaction

Abstract

We consider two bosons in a one-dimensional harmonic trap, interacting by a contact potential, and compare the exact solution of this problem to a self-consistent numerical solution by using the multiconfigurational time-dependent Hartree (MCTDH) method. We thereby benchmark the predictions of the MCTDH method with a few-body problem that has an analytical solution for the most commonly experimentally realized interaction potential in ultracold quantum gases. It is found that exact ground state energy and first order correlations are accurately reproduced by MCTDH up to the intermediate dimensionless coupling strengths corresponding to typical background scattering lengths of magnetically trapped ultracold dilute Bose gases. For larger couplings, established for example by (a combination of) Feshbach resonances and optical trapping, the MCTDH approach overestimates the depth of the trap-induced correlation dip of first order correlations in position space, as well as overestimates the fragmentation, defined as the average relative occupation of orbitals other than the energetically lowest one. We anticipate that qualitatively similar features in the correlation function may arise for larger particle numbers, paving the way for a quantitative assessment of the accuracy of MCTDH by experiments with ultracold atoms.

16 pages, 5 figures

References in corpus (18)

• The multi-configurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems
• Fragmentation of Bose-Einstein Condensates
• Multiconfigurational time-dependent Hartree approaches for indistinguishable particles
• Exact quantum dynamics of bosons with finite-range time-dependent interactions of harmonic type
• Analytical solutions for the dynamics of two trapped interacting ultracold atoms
• The multiconfigurational time-dependent Hartree method for bosons with internal degrees of freedom: Theory and composite fragmentation of multi-component Bose-Einstein condensates
• Two-point phase correlations of a one-dimensional bosonic Josephson junction
• Fragmented Superradiance of a Bose-Einstein Condensate in an Optical Cavity
• Parametric Excitation of a Bose-Einstein Condensate: From Faraday Waves to Granulation
• Condensate fragmentation as a sensitive measure of the quantum many-body behavior of bosons with long-range interactions
• MCTDH-X: The multiconfigurational time-dependent Hartree method for indistinguishable particles software
• Variance as a sensitive probe of correlations enduring the infinite particle limit
• Overlap of exact and Gross-Pitaevskii wavefunctions in Bose-Einstein condensates of dilute gases
• Variance of an anisotropic Bose-Einstein condensate
• The BBGKY hierarchy for ultracold bosonic systems: II. Applications
• Self-consistent determination of the many-body state of ultracold bosonic atoms in a one-dimensional harmonic trap
• Reply to the correspondence of Drummond and Brand [arXiv:1610.07633]
• Correspondence on "Single-shot simulations of dynamic quantum many-body systems"

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• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• A modular implementation of an effective interaction approach for harmonically trapped fermions in 1D
• Classical and quantum metrology of the Lieb-Liniger model
• Dynamics and transport of Bose-Einstein condensates in bent potentials