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摘要

利用Bogoliubov理论研究了自由空间中可调自旋-轨道耦合玻色-爱因斯坦凝聚体(Bose-Einstein condensates, BECs)的激发谱. 通过高频近似得到具有两体相互作用时与时间无关的有效Floquet哈密顿量, 从而获得一种可调的自旋-轨道耦合和一种可由周期驱动拉曼耦合调控的有效两体相互作用. 基于系统有效的Floquet哈密顿量, 得到凝聚体具有相互作用时的色散关系, 发现周期驱动强度可以有效地调控色散关系的结构, 即周期驱动的拉曼耦合可以调控系统在零动量相与平面波相之间的相变. 进一步利用Bogoliubov理论得到系统的Bogoliubov-de-Gennes (BdG)方程, 分别研究了凝聚体在零动量相和平面波相中的激发谱. 发现零动量相中的激发谱均为声子激发, 且激发谱随周期驱动强度的增加表现出贝塞尔函数的行为; 平面波相中的激发谱存在声子激发和旋子激发, 当周期驱动强度增加时, 旋子模出现软化现象. 因此, 可以通过周期驱动拉曼耦合实时地调控自旋-轨道耦合BECs激发谱中的声子激发和旋子激发.

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Abstract

In a recent experiment, the excitation spectrum of spin-orbit (SO) coupled Bose-Einstein condensates (BECs) of $^{87}{\rm{Rb}}$ atoms was studied by using Bragg spectroscopy, and the roton-maxon structure was found to exist in the excitation spectrum of magnetized phase. In addition, the roton-mode and its softening phenomenon are obtained by using various artificial SO couplings such as Rashba SO coupling and spin-orbital-angular-momentum coupling. However, the SO coupling strength in previous studies could not be controlled in real time, which limits the further study and precise regulation of the excitation spectrum of condensate. Thus, it is still an important topic to study how to regulate the SO coupling strength of the system through an external driving field, and further regulate the excitation spectrum of SO coupled BECs. In this work, the excitation spectrum of a tunable SO coupled BECs in free space is studied by using Bogoliubov theory. The time-independent effective Floquet Hamiltonian with two-body interaction is obtained in the high frequency approximation, and then a tunable SO coupling and an effective two-body interaction that can be regulated by the periodic driving of Raman coupling are obtained. Based on the effective Floquet Hamiltonian of the system, the dispersion relation of the BECs with interactions is numerically calculated. It is found that the periodic driving can effectively regulate the structure of the dispersion relation, which indicates that the periodic driving can regulate the phase transition between the zero-momentum phase and the plane wave phase. Then, the Bogoliubov-de-Gennes (BdG) equation of the system is obtained by using Bogoliubov theory. Moreover, the excitation spectrum of the BECs in the zero momentum phase and the plane wave phase are studied, respectively. Only the phonon excitation exists in the excitation spectrum of the zero momentum phase, and the excitation spectrum behaves as a Bessel function with the increase of the periodic driving strength. The phonon and roton excitations exist in the excitation spectrum of the plane wave phase, and the roton mode gradually softens with the increase of periodically driving strength. Therefore, the phonon and roton excitations in the excitation spectrum of SO coupled BECs can be regulated in real time by periodically driving Raman coupling.

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作者及机构信息

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通信作者:薛具奎,xuejk@nwnu.edu.cn

基金项目:国家自然科学基金(批准号: 12164042, 12264045, 11764039, 11865014, 11847304)、甘肃省自然科学基金(批准号: 17JR5RA076, 20JR5RA526)和甘肃省高等学校创新能力提升项目(批准号: 2020A-146, 2022A-011)资助的课题

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Corresponding author:Xue Ju-Kui,xuejk@nwnu.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant Nos. 12164042, 12264045, 11764039, 11865014, 11847304), the Natural Science Foundation of Gansu Province, China (Grant Nos. 17JR5RA076, 20JR5RA526), and the Innovation Capability Enhancement Project of Higher Education of Gansu Province, China (Grant Nos. 2020A-146, 2022A-011)

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施引文献

下载: 全尺寸图片幻灯片

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