Valdés-Curiel A, Trypogeorgos D, Marshall E E, Spielman I B
Joint Quantum Institute, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, United States of America.
New J Phys. 2017 Mar;19:033025. doi: 10.1088/1367-2630/aa6279. Epub 2017 Mar 16.
We describe a Fourier transform spectroscopy technique for directly measuring band structures, and apply it to a spin-1 spin-orbit coupled Bose-Einstein condensate. In our technique, we suddenly change the Hamiltonian of the system by adding a spin-orbit coupling interaction and measure populations in different spin states during the subsequent unitary evolution. We then reconstruct the spin and momentum resolved spectrum from the peak frequencies of the Fourier transformed populations. In addition, by periodically modulating the Hamiltonian, we tune the spin-orbit coupling strength and use our spectroscopy technique to probe the resulting dispersion relation. The frequency resolution of our method is limited only by the coherent evolution timescale of the Hamiltonian and can otherwise be applied to any system, for example, to measure the band structure of atoms in optical lattice potentials.
我们描述了一种用于直接测量能带结构的傅里叶变换光谱技术，并将其应用于自旋为1的自旋轨道耦合玻色-爱因斯坦凝聚体。在我们的技术中，通过添加自旋轨道耦合相互作用，我们突然改变系统的哈密顿量，并在随后的幺正演化过程中测量不同自旋态的布居数。然后，我们从傅里叶变换后的布居数的峰值频率重建自旋和动量分辨谱。此外，通过周期性地调制哈密顿量，我们调节自旋轨道耦合强度，并使用我们的光谱技术来探测由此产生的色散关系。我们方法的频率分辨率仅受哈密顿量的相干演化时间尺度限制，并且在其他方面可应用于任何系统，例如，用于测量光学晶格势中原子的能带结构。
