Many-body entropies, correlations, and emergence of statistical relaxation in interaction quench dynamics of ultracold bosons

• Published in: Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2015-09, Vol.92 (3), Article 033622
• Main Authors: Lode, Axel U. J., Chakrabarti, Barnali, Kota, Venkata K. B.
• Format: Article
• Language: English
• Subjects: Atomic and Molecular Clusters; Computational Physics; Condensed Matter; Physics; Quantum Gases; Quantum Physics
• ISSN: 1050-2947; 1094-1622
• DOI: 10.1103/PhysRevA.92.033622

We study the quantum many-body dynamics and the entropy production triggered by an interaction quench in a system of N = 10 interacting identical bosons in an external one-dimensional harmonic trap. The multiconfigura-tional time-dependent Hartree method for bosons (MCTDHB) is used for solving the time-dependent Schrödinger equation at a high level of accuracy. We consider many-body entropy measures such as the Shannon information entropy, number of principal components, and occupation entropy that are computed from the time-dependent many-body basis set used in MCTDHB. These measures quantify relevant physical features such as irregular or chaotic dynamics, statistical relaxation, and thermalization. We monitor the entropy measures as a function of time and assess how they depend on the interaction strength. For larger interaction strength, the many-body information and occupation entropies approach the value predicted for the Gaussian orthogonal ensemble of random matrices. This implies statistical relaxation. The basis states of MCTDHB are explicitly time-dependent and optimized by the variational principle in a way that minimizes the number of significantly contributing ones. It is therefore a non-trivial fact that statistical relaxation prevails in MCTDHB computations. Moreover, we demonstrate a fundamental connection between the production of entropy, the buildup of correlations and loss of coherence in the system. Our findings imply that mean-field approaches such as the time-dependent Gross-Pitaevskii equation cannot capture statistical relaxation and thermalization because they neglect correlations. Since the coherence and correlations are experimentally accessible, their present connection to many-body entropies can be scrutinized to detect statistical relaxation. In this work we use the recent recursive software implementation of the MCTDHB (R-MCTDHB).