The frequency of the breathing mode of a two-dimensional Fermi gas with zero-range interactions in a harmonic confinement is fixed by the scale invariance of the Hamiltonian. Scale invariance is broken in the quantized theory by introducing the two-dimensional scattering length as a regulator. This is an example of a quantum anomaly in the field of ultracold atoms and leads to a shift of the frequency of the collective breathing mode of the cloud. In this work, we study this anomalous frequency shift for a two-component Fermi gas in the strongly interacting regime. We measure significant upwards shifts away from the scale-invariant result that show a strong interaction dependence. This observation implies that scale invariance is broken anomalously in the strongly interacting two-dimensional Fermi gas.

中文翻译：

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二维费米气体中尺度不变性的异常破坏

在哈密尔顿量表的尺度不变性下，谐波约束下具有零范围相互作用的二维费米气体的呼吸模式频率是固定的。通过引入二维散射长度作为调节器，在量化理论中打破了尺度不变性。这是超冷原子领域中量子异常的一个例子，并导致云集体呼吸模式的频率发生偏移。在这项工作中，我们研究了在强相互作用状态下两组分费米气体的这种异常频移。我们测量了远离尺度不变结果的显着向上偏移，尺度不变结果显示出强烈的交互依赖性。该观察结果暗示在强烈相互作用的二维费米气体中尺度不变性被异常破坏。