Dikopoltsev Alex, Sharabi Yonatan, Lyubarov Mark, Lumer Yaakov, Tsesses Shai, Lustig Eran, Kaminer Ido, Segev Mordechai
Physics Department, Technion-Israel Institute of Technology, Haifa 32000, Israel.
Electrical Engineering Department, Technion-Israel Institute of Technology, Haifa 32000, Israel.
Proc Natl Acad Sci U S A. 2022 Feb 8;119(6). doi: 10.1073/pnas.2119705119.
Photonic time-crystals (PTCs) are spatially homogeneous media whose electromagnetic susceptibility varies periodically in time, causing temporal reflections and refractions for any wave propagating within the medium. The time-reflected and time-refracted waves interfere, giving rise to Floquet modes with momentum bands separated by momentum gaps (rather than energy bands and energy gaps, as in photonic crystals). Here, we present a study on the emission of radiation by free electrons in PTCs. We show that a free electron moving in a PTC spontaneously emits radiation, and when associated with momentum-gap modes, the electron emission process is exponentially amplified by the modulation of the refractive index. Moreover, under strong electron-photon coupling, the quantum formulation reveals that the spontaneous emission into the PTC bandgap experiences destructive quantum interference with the emission of the electron into the PTC band modes, leading to suppression of the interdependent emission. Free-electron physics in PTCs offers a platform for studying a plethora of exciting phenomena, such as radiating dipoles moving at relativistic speeds and highly efficient quantum interactions with free electrons.
光子时间晶体（PTCs）是空间均匀的介质，其电磁极化率随时间周期性变化，导致在该介质中传播的任何波发生时间反射和折射。时间反射波和时间折射波相互干涉，产生具有由动量间隙分隔的动量带的弗洛凯模式（而不是像光子晶体那样的能带和能隙）。在此，我们展示了一项关于PTCs中自由电子辐射发射的研究。我们表明，在PTC中移动的自由电子会自发发射辐射，并且当与动量间隙模式相关联时，电子发射过程会因折射率的调制而呈指数放大。此外，在强电子 - 光子耦合下，量子理论表明，向PTC带隙的自发发射与电子向PTC带模式的发射经历相消量子干涉，导致相互依赖发射的抑制。PTCs中的自由电子物理为研究大量令人兴奋的现象提供了一个平台，例如以相对论速度移动的辐射偶极子以及与自由电子的高效量子相互作用。
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