宇称-时间对称谐振子势阱中Kohn振荡的相互作用诱导周期偏移

中文摘要 AI 辅助

在谐振子势阱中，玻色-爱因斯坦凝聚体的质心以阱频振荡，且与相互作用无关。在没有相互作用的情况下，宇称-时间对称的增益-损耗梯度不会改变这一频率，基态宽度的云团被刚性平移，同时原子数被周期性地调制。当存在相互作用时，这种保护性丧失，因为增益和损耗改变了原子数；被调制的原子数驱动云团的宽度，而宽度又反过来作用于质心。在较小增益下，周期随增益强度呈二次增长，其系数在托马斯-费米区域仅由云团的大小决定。从Kohn振荡延续而来的周期轨道族可以一直追踪到临界增益，在临界增益处，它与阱的高度激发态发生共振，并且在所计算的轨道族中，该临界增益随振荡幅度和云团大小的增加而减小。一个五变量矩模型在接近临界增益的轨道上几乎精确地再现了周期和云团宽度。

英文摘要

The center of mass of a Bose--Einstein condensate in a harmonic trap oscillates at the trap frequency independently of the interactions. Without interactions a parity-time-symmetric gain-loss gradient leaves this frequency unchanged, and a cloud of the ground-state width is translated rigidly while the atom number is periodically modulated. With interactions the protection is lost, because the gain and the loss change the number of atoms; the modulated atom number drives the width of the cloud, and the width acts back on the center of mass. At small gain the period grows quadratically with the gain strength, with a coefficient that in the Thomas--Fermi regime is set by the size of the cloud alone. The family of periodic orbits continued from the Kohn oscillation can be followed up to a critical gain, where it comes into resonance with highly excited states of the trap, and over the computed families this critical gain decreases with the amplitude of the oscillation and with the size of the cloud. A five-variable moment model reproduces the period and the width of the cloud along the orbits nearly up to the critical gain.

发表机构

• Hebei Key Laboratory of Physics and Energy Technology, Department of Mathematics and Physics, North China Electric Power University（华北电力大学数学与物理学院、河北省物理与能源技术重点实验室）

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