Quantum Metric and Nonlinear Hall Effect of Photons
TLDR
This paper shows photons possess a quantum metric, leading to a nonlinear Hall effect of light and corrections to gravitational lensing.
Key contributions
- Photons possess a nontrivial quantum metric in momentum space, derived via path-integral formalism.
- Quantum metric induces a nonlinear Hall effect of light in media with varying refractive index.
- It also causes nonlinear corrections to gravitational lensing in curved spacetime.
- This gravitational effect arises from the interplay of position and momentum space geometry.
Why it matters
This research uncovers fundamental properties of photons, showing they possess a quantum metric. This discovery could lead to new insights into light manipulation and a deeper understanding of light's interaction with complex media and gravity.
Original Abstract
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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