Dutt Avik, Minkov Momchil, Lin Qian, Yuan Luqi, Miller David A B, Fan Shanhui
Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA, 94305, USA.
Department of Applied Physics, Stanford University, Stanford, CA, 94305, USA.
Nat Commun. 2019 Jul 16;10(1):3122. doi: 10.1038/s41467-019-11117-9.
There has been significant recent interest in synthetic dimensions, where internal degrees of freedom of a particle are coupled to form higher-dimensional lattices in lower-dimensional physical structures. For these systems, the concept of band structure along the synthetic dimension plays a central role in their theoretical description. Here we provide a direct experimental measurement of the band structure along the synthetic dimension. By dynamically modulating a resonator at frequencies commensurate with its mode spacing, we create a periodically driven lattice of coupled modes in the frequency dimension. The strength and range of couplings can be dynamically reconfigured by changing the modulation amplitude and frequency. We show theoretically and demonstrate experimentally that time-resolved transmission measurements of this system provide a direct readout of its band structure. We also realize long-range coupling, gauge potentials and nonreciprocal bands by simply incorporating additional frequency drives, enabling great flexibility in band structure engineering.
最近，人们对合成维度产生了浓厚兴趣，在合成维度中，粒子的内部自由度相互耦合，在低维物理结构中形成高维晶格。对于这些系统，沿合成维度的能带结构概念在其理论描述中起着核心作用。在此，我们提供了沿合成维度的能带结构的直接实验测量。通过以与其模式间距相称的频率动态调制谐振器，我们在频率维度中创建了一个耦合模式的周期性驱动晶格。通过改变调制幅度和频率，可以动态重新配置耦合的强度和范围。我们从理论上表明并通过实验证明，该系统的时间分辨传输测量提供了其能带结构的直接读数。我们还通过简单地加入额外的频率驱动实现了长程耦合、规范势和非互易能带，从而在能带结构工程中实现了极大的灵活性。
