Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122, Australia.
Department of Physics and State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China.
Phys Rev Lett. 2019 Feb 22;122(7):070401. doi: 10.1103/PhysRevLett.122.070401.
A two-dimensional (2D) harmonically trapped interacting Fermi gas is anticipated to exhibit a quantum anomaly and possesses a breathing mode at frequencies different from a classical scale-invariant value ω_{B}=2ω_{⊥}, where ω_{⊥} is the trapping frequency. The predicted maximum quantum anomaly (∼10%) has not been confirmed in experiments. Here, we theoretically investigate the zero-temperature density equation of state and the breathing mode frequency of an interacting Fermi superfluid at the dimensional crossover from three to two dimensions. We find that the simple model of a 2D Fermi gas with a single s-wave scattering length is not adequate to describe the experiments in the 2D limit, as commonly believed. A more complete description of quasi-2D leads to a much weaker quantum anomaly, consistent with the experimental observations. We clarify that the reduced quantum anomaly is due to the significant confinement-induced effective range of interactions.
二维（2D）简谐束缚相互作用费米气体预计会表现出量子反常，并在与经典标度不变值 ω_{B}=2ω_{⊥}不同的频率下具有呼吸模式，其中 ω_{⊥}是囚禁频率。预言的最大量子反常（约 10%）尚未在实验中得到证实。在这里，我们从三维到二维的维度交叉处理论上研究了相互作用费米超流的零温密度状态方程和呼吸模式频率。我们发现，通常认为，具有单一 s 波散射长度的二维费米气体的简单模型不足以描述二维极限中的实验，需要更完整的准二维描述才能得到弱得多的量子反常，这与实验观测结果一致。我们澄清了减少的量子反常是由于显著的约束诱导相互作用有效范围。
