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How gravitational waves change photon orbital angular momentum quantum states

Haorong Wu, Xilong Fan, Lixiang Chen

TL;DR

This work addresses how gravitational waves (GWs) can alter photon orbital angular momentum (OAM) states and whether such effects can enable GW sensing. It combines linearized gravity with a 3+1 Green's-function formalism in cylindrical coordinates, a perturbative treatment of vortex beams modeled as massless scalar fields, and a Bogoliubov transformation to connect flat-spacetime and GW-mode quantization, yielding explicit OAM-transition amplitudes. The authors find that a photon initially in |l⟩ can transition to |l'⟩ with Δl ∈ {−2, −1, 0, +1, +2}, with probabilities that depend on GW amplitudes A_+, A_×, geometry θ, and kinematic factors; in a circular polarization basis the selection rules clarify angular-momentum exchange with the GW, revealing polarization-dependent transfers. Based on these dynamics, a photonic single-arm detector is proposed that leverages OAM transitions to generate detectable signal photons, offering a potential pathway to mid-frequency GW detection with insensitivity to seismic noise, albeit with substantial experimental challenges such as generating high-purity OAM beams and controlling noise budgets.

Abstract

We explore the evolution of vortex light in the presence of gravitational waves (GWs) and demonstrate that the quantized orbital angular momentum (OAM) states can make transitions to other states due to the GWs. The interaction is calculated based on the framework of the wave propagation in linearized gravity theory and canonical quantization of the light field in curved spacetime. It is found that when a photon possessing OAM of $l$ interacts with GWs, the OAM modes of $l\pm1$ and $l\pm2$ may be excited with probabilities of $P_{l\pm1}\sim 10^{-17}$ and $P_{l\pm2}\sim 10^{-20}$, respectively. Higher probabilities of the transitions can be achieved when the photon radial wave vector or the propagation distance is increased, or when the photons encounter GWs with stronger amplitudes or smaller frequencies. Thus, a new GW detection technique is proposed, which may exhibit good performance in a wide range of GW frequencies. Furthermore, the detector is insensitive to seismic noise and is more advantageous for determining the distance of the source compared to current interferometer detectors.

How gravitational waves change photon orbital angular momentum quantum states

TL;DR

This work addresses how gravitational waves (GWs) can alter photon orbital angular momentum (OAM) states and whether such effects can enable GW sensing. It combines linearized gravity with a 3+1 Green's-function formalism in cylindrical coordinates, a perturbative treatment of vortex beams modeled as massless scalar fields, and a Bogoliubov transformation to connect flat-spacetime and GW-mode quantization, yielding explicit OAM-transition amplitudes. The authors find that a photon initially in |l⟩ can transition to |l'⟩ with Δl ∈ {−2, −1, 0, +1, +2}, with probabilities that depend on GW amplitudes A_+, A_×, geometry θ, and kinematic factors; in a circular polarization basis the selection rules clarify angular-momentum exchange with the GW, revealing polarization-dependent transfers. Based on these dynamics, a photonic single-arm detector is proposed that leverages OAM transitions to generate detectable signal photons, offering a potential pathway to mid-frequency GW detection with insensitivity to seismic noise, albeit with substantial experimental challenges such as generating high-purity OAM beams and controlling noise budgets.

Abstract

We explore the evolution of vortex light in the presence of gravitational waves (GWs) and demonstrate that the quantized orbital angular momentum (OAM) states can make transitions to other states due to the GWs. The interaction is calculated based on the framework of the wave propagation in linearized gravity theory and canonical quantization of the light field in curved spacetime. It is found that when a photon possessing OAM of interacts with GWs, the OAM modes of and may be excited with probabilities of and , respectively. Higher probabilities of the transitions can be achieved when the photon radial wave vector or the propagation distance is increased, or when the photons encounter GWs with stronger amplitudes or smaller frequencies. Thus, a new GW detection technique is proposed, which may exhibit good performance in a wide range of GW frequencies. Furthermore, the detector is insensitive to seismic noise and is more advantageous for determining the distance of the source compared to current interferometer detectors.

Paper Structure

This paper contains 6 sections, 57 equations, 3 figures.

Table of Contents

  1. Introduction
  2. 3+1 dimensional Green's function in cylindrical coordinates
  3. Perturbation of vortex beams in GWs
  4. Evolution of quantum states in GWs
  5. Photonic single-arm GW detectors
  6. Conclusion

Figures (3)

  • Figure 1: The path for integral with respect to $k_0$ in Eq. \ref{['eq.GreenFunctionIntegral']}. The contour is closed in the lower half plane.
  • Figure 2: The phase for Bessel beams with $l=0$, 1, and 2, respectively. The brightness indicates field intensity.
  • Figure 3: The rate of detected photon ($N$) for different GW frequencies ($10^{-2}$ to $10^3$ Hz) with a typical strain $A=10^{-21}$. The inset plot shows the behavior of $N$ between the GW frequency of 50 Hz and 150 Hz for the case where $L=1\times 10^4$ m and $n=560$, that can be achieved in a LIGO-like single-arm detector.