Ultracold atoms confined to periodic potentials have proven to be a powerful tool for quantum simulation of complex many-body systems. We confine fermions to one dimension to realize the Tomonaga-Luttinger liquid model, which describes the highly collective nature of their low-energy excitations. We use Bragg spectroscopy to directly excite either the spin or charge waves for various strengths of repulsive interaction. We observe that the velocity of the spin and charge excitations shift in opposite directions with increasing interaction, a hallmark of spin-charge separation. The excitation spectra are in quantitative agreement with the exact solution of the Yang-Gaudin model and the Tomonaga-Luttinger liquid theory. Furthermore, we identify effects of nonlinear corrections to this theory that arise from band curvature and back-scattering.

中文翻译：

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具有可调相互作用的一维费米气体中的自旋电荷分离

受限于周期性势的超冷原子已被证明是复杂多体系统量子模拟的有力工具。我们将费米子限制在一个维度以实现 Tomonaga-Luttinger 液体模型，该模型描述了它们的低能激发的高度集体性。我们使用布拉格光谱直接激发自旋波或电荷波，以获得各种强度的排斥相互作用。我们观察到随着相互作用的增加，自旋和电荷激发的速度向相反的方向移动，这是自旋电荷分离的标志。激发光谱与Yang-Gaudin模型和Tomonaga-Luttinger液体理论的精确解在定量上一致。此外，我们确定了由带曲率和反向散射引起的对该理论的非线性校正的影响。