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, and underestimates 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.

我们考虑一维谐波陷阱中的两个玻色子，通过接触势相互作用，并使用多构型时间相关 Hartree (MCTDH) 方法将该问题的精确解与自洽数值解进行比较。因此，我们用少体问题对 MCTDH 方法的预测进行了基准测试，该问题具有超冷量子气体中最常见的实验实现的相互作用势的解析解。发现精确的基态能量和一阶相关性被 MCTDH 准确地再现，直到与磁性捕获的超冷稀释 Bose 气体的典型背景散射长度相对应的中间无量纲耦合强度。对于较大的耦合，例如通过（组合）Feshbach 共振和光阱建立，MCTDH 方法高估了位置空间中一阶相关的陷阱诱导的相关下降的深度，并低估了碎片，定义为除能量最低的轨道之外的轨道的平均相对占据。我们预计，对于较大的粒子数，相关函数中的性质相似的特征可能会出现，这为通过超冷原子实验定量评估 MCTDH 的准确性铺平了道路。