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Femtosecond laser direct writing has made recent progress in the study of Bloch oscillation phenomena in optical Floquet lattices

author:Yangtze River Delta G60 Laser Alliance

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据悉,华中科技大学武汉光电国家研究中心舒学文教授团队与香港中文大学孙贤开教授团队合作在《光:科学与应用》(Light: Science & Applications)发表最新研究进展“Visual observation of photonic Floquet–Blochoscillations”。

Femtosecond laser direct writing has made recent progress in the study of Bloch oscillation phenomena in optical Floquet lattices

Bloch oscillation is a classical coherent quantum transport phenomenon characterized by periodic oscillations of quantum particles in a periodic potential field under the action of an applied constant force. As a basic physical effect, Bloch oscillation has been discovered and studied in a variety of systems, such as semiconductor superlattices, ultracold atoms, coupled waveguide arrays, and synthetic dimension photonic lattices, etc., which not only promote the development of basic physics research, but also provide new ideas and methods for flexibly manipulating the evolution of wave functions. However, the research on the Bloch oscillation phenomenon mainly focuses on the static system, and the Bloch oscillation phenomenon in the periodic drive (Floquet) system needs to be further explored.

Femtosecond laser direct writing has made recent progress in the study of Bloch oscillation phenomena in optical Floquet lattices

Figure 1. (a) Schematic diagram of femtosecond laser direct-writing waveguide array. (b) Cross-sectional photographs of the experimentally prepared samples. (c) Top-down view of the experimentally prepared sample.

In order to solve this problem, the Bloch oscillation phenomenon in the Froge system was studied by using a one-dimensional curved waveguide array prepared by femtosecond laser direct writing, and the general theory of the Bloch oscillation phenomenon in the optical Floquet lattice was proposed, and the optical Floquet-Bloch oscillation phenomenon was experimentally visualized. As shown in Figure 1, the bending trajectory of the waveguide in the array is a composite trajectory composed of circular bending and superimposed periodic bending. Under the paraxial approximation, the wave equation describing the propagation evolution of light in the waveguide array is mathematically equivalent to the Schrödinger equation, which describes the evolution of electrons in the periodic potential field with time under the action of an applied electric field, and the direction of light propagation in the waveguide array is equivalent to the time term of the Schrödinger equation. The curvature of the waveguide's bending trajectory is seen as the equivalent electric field force acting on the transmitted light waves, where the arc bending trajectory produces the equivalent constant electric field force that causes the Bloch oscillation, and the periodic bending trajectory produces the equivalent periodic electric field force introduced into Floquet modulation. Therefore, the waveguide array can be used to observe the Bloch oscillation phenomenon in the optical Floke lattice.

Femtosecond laser direct writing has made recent progress in the study of Bloch oscillation phenomena in optical Floquet lattices

Figure 2. (a)-(d) Experimental observations of single waveguide excitation. (e)-(h) Experimental observations at wide beam excitation.

In this study, waveguide fluorescence microscopy was used to visualize and observe the continuous propagation and evolution of light waves in the waveguide array. Figure 2 illustrates the breathing and oscillation modes of the Bloch oscillation phenomenon in the optical Floquet lattice under single-wave infusion emission and wide beam incidence, respectively. When the Floquet modulation period ɅFL is not equal to any integer multiple of the Bloch oscillation period ɅBO, the Floquet dispersion is constant equal to 0, and an optical Floquet-Bloch oscillation with period ɅFBO being the least common multiple of ɅFL and ʌbo will occur. In the rest of the cases, the Floquet dispersion is no longer constant equal to 0, and the transmission of light usually behaves as diffusion diffraction. In addition, the researchers studied the influence of Floquet modulation parameters on the optical Floquet-Bloch oscillation in combination with theory and experiments, and revealed the unique evolutionary properties of the phenomenon, including the fractal spectral characteristics related to the Floquet modulation period and the fractional-order Floquet tunneling characteristics related to the Floquet modulation amplitude.

Femtosecond laser direct writing has made recent progress in the study of Bloch oscillation phenomena in optical Floquet lattices

Figure 3. (a) Fractal spectral characteristics of optical Floquet-Bloch oscillations. (b) Fractional-order Floquet tunneling characteristics of optical Floquet-Bloch oscillations.

The visual observation of optical Floquet-Bloch oscillations reveals a novel wave function evolution mechanism, which is of great significance in both basic research and practical application. In terms of basic research, the theoretical model and experimental platform support further exploration of novel phenomena generated by the combination of Floquet-Bloch oscillation and the design and regulation of binary lattice, non-Hermitian lattice, optical nonlinearity, etc. In terms of practical applications, optical Floquet-Bloch oscillation is essentially a coherent transport phenomenon, so it can be generalized to multiple research platforms such as synthetic frequency-domain lattice, cold atom, space-time crystal, and quantum walking, and is expected to be used to realize frequency conversion, precision measurement, and transmission manipulation of various waves.

Zhang Zhen, a doctoral student at Wuhan National Research Center for Optoelectronics, and Li Yuan, a doctoral student at Chinese University of Hong Kong, are the co-first authors of the paper. Professor Shu Xuewen from Wuhan National Research Center for Optoelectronics and Professor Sun Xiankai from the University of Hong Kong Chinese are the co-corresponding authors of the paper. Wuhan National Research Center for Optoelectronics is the first unit of the paper.

Paper link: https://www.nature.com/articles/s41377-024-01419-z

Article source: Huazhong University of Science and Technology official website

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