High-dimensional band measurement in the synthetic frequency dimension

Synthetic dimensions

Dimension is the basic concept of physics, and many unique physical phenomena only exist in high-dimensional systems. In order to study these high-dimensional systems, the researchers proposed the concept of “optical synthesis dimension”: the intrinsic degree of freedom of photons as an additional dimension. These intrinsic degrees of freedom can be frequencies, spatial patterns, orbital angular momentum, etc. They are physically equivalent to the spatial dimensions as we know them. Therefore, we can introduce these additional “synthetic dimensions” to explore physical phenomena in high-dimensional systems using simpler experimental platforms.

Can band measurement

In the band structure of high-dimensional systems, there is a wealth of physical information. With band measurement, we can predict and regulate the physical behavior of the system. However, in the study of synthetic frequency dimension, existing band measurement methods have their limitations. Researchers can only measure the band structure of a one-dimensional system or perform one-dimensional sampling of high-dimensional band structures. This is not conducive to interpreting the complete information in the structure of the high-dimensional band.

Recently, the team of Professor Shanhui Fan of Stanford University proposed a new method that can achieve complete high-dimensional band measurement in the frequency dimension of optical synthesis. This discovery will help deepen the understanding of unique physical phenomena in high-dimensional systems, and is expected to have applications in optical device design, quantum information processing and other fields.

The results were published in Light: Science & Applications under the title “Multi-dimensional band structure spectroscopy in the synthetic frequency dimension.” Dali Cheng is the first author of the paper, and Professor Shanhui Fan is the corresponding author of the paper.

The experimental platform used by the team is a dynamically modulated optical resonant ring, as shown in Figure 1. If multiple frequencies are included in the modulated signal, the frequency patterns in the resonant loop can form a high-dimensional lattice. The resonant ring is excited by a laser with an adjustable wavelength. By changing the laser wavelength and analyzing the transmission spectrum of the resonant ring, researchers can obtain the energy of the lattice. The team proposed that by adjusting the relative phase of different frequencies in the modulated signal, the complete high-dimensional band structure of the crystal lattice could be measured. This is the main innovation of the method.

Figure 1: Experimental platform for high-dimensional band measurements. The laser is input from the left, and the transmission spectrum output from the right is used to extract the band structure.

The team used this new method to measure the two-dimensional band structure of a non-Ermi system, as shown in Figure 2. The band structure of the system contains non-trivial topological properties that are related to the non-Ermie skin effect. The non-Ermi skin effect is a novel physical phenomenon that means that in a non-Ermi system, the energy eigenstates can not be a pattern of periodic Bloch waves, but are localized on the boundary of the system. These measurements deepen our understanding of non-Amime systems.

Figure 2: Measurement results of a non-ermi band structure. The left side is the energy real part, and the right side is the energy imaginary part. Experimental (colored data points) are consistent with theoretical (gray surfaces) results.


In the research of physics and optical engineering, high-dimensional band measurement is an important tool, which has both basic research value and practical application significance. In the future, the team hopes to apply this tool to more complex lattice systems to deepen our understanding of the laws of physics in high-dimensional systems. At the same time, this tool is expected to be used in the fields of optical device design and quantum information processing. (Source: China Optics)

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