光子的量子度量与非线性霍尔效应
Quantum Metric and Nonlinear Hall Effect of Photons
AI总结：
研究光子在动量空间中的量子度量，揭示其非线性霍尔效应及引力透镜效应的修正机制
摘要：
利用路径积分方法，我们证明光子在动量空间中具有非平凡的量子度量。通过考虑量子度量，推导出半经典作用量和运动方程。在折射率随空间变化的介质中，量子度量导致光轨迹在二阶导数项下发生偏移，可视为光的非线性霍尔效应。量子度量还导致曲时空中的引力透镜效应在非线性阶的修正。这种引力非线性霍尔效应源于位置空间与动量空间几何的相互作用。
英文摘要：
Using the path-integral formalism, we show that photons possess a nontrivial quantum metric in momentum space. We derive the semiclassical action and equations of motion by taking into account the quantum metric. In media with a spatially varying refractive index $n(\mathbf{x})$, the quantum metric induces a shift in the trajectory of light at second order in derivatives of $n$, which may be regarded as a nonlinear Hall effect of light. The quantum metric also gives rise to corrections to gravitational lensing in curved spacetime at the nonlinear order in wavelength. This gravitational nonlinear Hall effect results from the interplay between the geometry of position space and that of momentum space.
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