Experimental band structure spectroscopy along a synthetic dimension

Abstract

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.

Mode-Locked Topological Insulator Laser Utilizing Synthetic Dimensions

“…[38]. The synthetic dimension can be constructed in the rings by using electro-optic modulators [61,62] modulating the refractive index. To match the modulation rate to the spacing between adjacent modes of the ring, the ring radius can be about 200 μm for a modulation rate of 80 GHz, which is accessible with current technology [61].…”

Topological phases in ring resonators: recent progress and future prospects

“…The first photonic topological insulator in a synthetic dimension was demonstrated using an array of multimode waveguides, where modulation of the refractive index along the waveguide axis played the role of the dynamic modulation [129]. The dynamically modulated resonator has also been implemented in the fibre-based ring experiments incorporating commercial electro-optic modulators [130,131], where band structures associated with one-dimensional synthetic lattices along the frequency axis of light have been measured [132]. Based on this experimental set-up, one can use the clockwise/ counterclockwise modes of a single ring as another degree of freedom to construct a synthetic Hall ladder with two independent physical synthetic dimensions, as shown in Figure 6 [128].…”

Photonic Gauge Potential in One Cavity with Synthetic Frequency and Orbital Angular Momentum Dimensions

“…Loss in the cavity includes transmissions through the input/output channels (mirrors), as well as intrinsic losses associated with reflections on mirrors, modulations in the EOM and SLMs, and also travelling through the additional path. One can compensate for the loss and tune γ i [42] by placing an amplifier in the optical path inside the main cavity, operated with a lower gain without inducing lasing, which dramatically increase the quality factor of the optical cavity [47].…”