Tzur Matan Even, Neufeld Ofer, Bordo Eliyahu, Fleischer Avner, Cohen Oren
Solid State Institute and Physics Department, Technion-Israel Institute of Technology, Haifa, 3200003, Israel.
Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, Hamburg, 22761, Germany.
Nat Commun. 2022 Mar 14;13(1):1312. doi: 10.1038/s41467-022-29080-3.
Selection rules are often considered a hallmark of symmetry. Here, we employ symmetry-breaking degrees of freedom as synthetic dimensions to demonstrate that symmetry-broken systems systematically exhibit a specific class of symmetries and selection rules. These selection rules constrain the scaling of a system's observables (non-perturbatively) as it transitions from symmetric to symmetry-broken. Specifically, we drive bi-elliptical high harmonic generation (HHG), and observe that the scaling of the HHG spectrum with the pump's ellipticities is constrained by selection rules corresponding to symmetries in synthetic dimensions. We then show the generality of this phenomenon by analyzing periodically-driven (Floquet) systems subject to two driving fields, tabulating the resulting synthetic symmetries for (2 + 1)D Floquet groups, and deriving the corresponding selection rules for high harmonic generation (HHG) and other phenomena. The presented class of symmetries and selection rules opens routes for ultrafast spectroscopy of phonon-polarization, spin-orbit coupling, symmetry-protected dark bands, and more.
选择规则通常被视为对称性的一个标志。在此，我们将对称性破缺自由度用作合成维度，以证明对称性破缺系统会系统地展现出一类特定的对称性和选择规则。这些选择规则在系统从对称态转变为对称性破缺态时（非微扰地）限制了系统可观测量的标度。具体而言，我们驱动双椭圆高次谐波产生（HHG），并观察到HHG谱随泵浦椭圆率的标度受到与合成维度中的对称性相对应的选择规则的限制。然后，我们通过分析受两个驱动场作用的周期驱动（弗洛凯）系统，列出（2 + 1）D弗洛凯群产生的合成对称性，并推导高次谐波产生（HHG）及其他现象的相应选择规则，来展示这一现象的普遍性。所呈现的这类对称性和选择规则为声子极化、自旋轨道耦合、对称性保护暗带等的超快光谱学开辟了道路。
