近日，美国加州大学的Chih-Chun Chien及其研究团队取得一项新进展。他们提出了基于哈特里近似的开放系统玻色子输运的三次量子化方法。相关研究成果已于2024年12月24日在国际知名学术期刊《物理评论A》上发表。

据悉，玻色子的三次量子化（3rd Q），为具有二次哈密顿量的林德布拉德方程提供了精确的稳态解。

通过根据哈特里近似分解玻色-哈伯德模型（BHM）的相互作用，该研究团队提出一种自洽的形式主义，用于求解弱相互作用下，开放系统玻色子林德布拉德方程的稳态解。结合哈特里近似的三次量子化（3rd Q）考虑了玻色子的无限福克空间，同时其资源需求随系统大小呈多项式增长。

研究人员通过分析玻色-哈伯德模型的三个实例来检验该方法，包括均匀链、相互作用诱导的二极管效应以及苏-施里弗-赫格-哈伯德模型。与小型系统中限制玻色子数量的模拟相比，结合哈特里近似的三次量子化捕捉到了定性行为，并给出了稳态值的上界。

有限尺寸缩放证实了结合哈特里近似的，第三次量子化的结果向热力学极限收敛。因此，这种可管理的方法使研究人员能够表征和预测，与冷原子实验相关的相互作用玻色子系统中量子输运的大系统行为。

附：英文原文

Title: Third quantization with Hartree approximation for open-system bosonic transport

Author: Fernando Espinoza-Ortiz and Chih-Chun Chien*

Issue&Volume: 2024-12-24

Abstract: The third quantization (3rd Q) for bosons provides the exact steady-state solution of the Lindblad equation with quadratic Hamiltonians. By decomposing the interaction of the Bose-Hubbard model (BHM) according to Hartree approximation, we present a self-consistent formalism for solving the open-system bosonic Lindblad equation with weak interactions in the steady state. The 3rd Q with Hartree approximation takes into account the infinite Fock space of bosons, while its demand of resource scales polynomially with the system size. We examine the method by analyzing three examples of the BHM, including the uniform chain, interaction-induced diode effect, and Su-Schrieffer-Heeger Hubbard model. When compared with the simulations with capped boson numbers for small systems, the 3rd Q with Hartree approximation captures the qualitative behavior and suggests an upper bound of the steady-state value. Finite-size scaling confirms the results from the 3rd Q with Hartree approximation converging towards the thermodynamic limit. Thus, the manageable method allows us to characterize and predict large-system behavior of quantum transport in interacting bosonic systems relevant to cold-atom experiments.

DOI: 10.1103/PhysRevA.110.063323

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.063323