We present an experimental investigation of collective oscillations in harmonically trapped Fermi gases through the crossover from two to three dimensions. Specifically, we measure the frequency of the radial monopole oscillation or breathing mode in highly oblate gases with tunable interactions. The breathing mode frequency is set by the adiabatic compressibility and probes the thermodynamic equation of state. In 2D, a dynamical scaling symmetry for atoms interacting via a $\delta$ potential predicts the breathing mode to occur at exactly twice the harmonic confinement frequency. However, a renormalized quantum treatment introduces a new length scale which breaks this classical scale invariance resulting in a so-called quantum anomaly. Our measurements deep in the 2D regime lie above the scale-invariant prediction for a range of interaction strengths providing evidence for the quantum anomaly and signifying the breakdown of an elementary $\delta$-potential model of atomic interactions. By varying the atom number we can tune the chemical potential and see the breathing mode frequency evolve smoothly between the 2D to 3D thermodynamic limits.

中文翻译：

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强相互作用费米气体中的量子异常和2D-3D穿越

我们提出了从二维到三维分频的谐波捕获费米气体中集体振荡的实验研究。具体来说，我们在具有可调相互作用的高度扁平气体中测量径向单极振动或呼吸模式的频率。呼吸模式频率由绝热可压缩性设置，并探查热力学状态方程。在2D中，原子通过原子相互作用的动态缩放对称性$\delta$电势可预测呼吸模式的发生频率正好是谐波限制频率的两倍。然而，重新归一化的量子处理引入了新的长度尺度，该尺度打破了这种经典的尺度不变性，从而导致了所谓的量子异常。我们在2D区域深处的测量值超出了尺度不变性预测，从而预测了一系列相互作用强度，从而为量子异常提供了证据，并表明了基本元素的分解。$\delta$原子相互作用的潜在模型。通过改变原子数，我们可以调节化学势，并观察呼吸模式频率在2D到3D热力学极限之间平稳发展。