Many-body density and coherence of trapped cold bosons

Camille Lévêque; Fritz Diorico; Jörg Schmiedmayer; Axel U. J. Lode

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arXiv · 2006.10755

Many-body density and coherence of trapped cold bosons

Camille Lévêque·Fritz Diorico·Jörg Schmiedmayer·Axel U. J. Lode

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Abstract

Many-body densities and correlation functions are of paramount importance for understanding quantum many-body physics. Here, we present a method to compute them; our approach is general and based on the action of bosonic or fermionic annihilation field operators on the many-body wavefunction. We analyze $N = 6$ quasi-one-dimensional harmonically-trapped bosons with weak to strong contact interaction strength up to the Tonks-Girardeau limit with infinite repulsion using the MultiConfigurational Time-Dependent Hartree method for indistinguishable particles (MCTDH-X). We compare our MCTDH-X solutions to the analytical ones in the infinite repulsion regime as well as to the so-called correlated pair wavefunction approach and find a good agreement. Since numerical approximations are not bound to the cases where analytical solutions are known, we thus demonstrate a general method to investigate high-order reduced density matrices and correlation functions in systems for which analytical solutions are unknown. We trace the build-up of correlation features in the crossover from weak interactions to the Tonks-Girardeau limit and find that the higher-order correlation functions and densities resemble those in the Tonks-Girardeau limit for way smaller interactions than anticipated from just the one-body density.

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Camille Lévêque, Fritz Diorico, Jörg Schmiedmayer, Axel U. J. Lode. 2020-06-18. Many-body density and coherence of trapped cold bosons. https://arxiv.org/abs/2006.10755

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