Therefore, in this study, we consider the propagation of a massless scalar in the bulk of the paper. Based on our understanding of the Einstein equivalence principle, we expect that studying a massless scalar field theory also captures some features of a photon’s propagation in curved spacetime geometry. In flat spacetime geometry, the propagation of each polarisation of photon is isomorphic to the propagation of a massless scalar field.
Here, we present a computationally simple method to calculate the distortion by the curvature of any spacetime geometry on any localised wavepacket.
19 do not take into consideration all the multi-polar modes required to calculate the effects of the curvature at the vicinity of the Earth. On the surface of the earth, a narrow beam with an initial width of 10 cm and a large value of Rayleigh range requires taking into account the contribution of multi-polar modes up to at least ℓ = 10 9. 19, all the multi-polar ℓ modes are presented only at the level of the equations however, the upper value of ℓ = 100 on the multi-polar modes is considered to compute the solution. 19 has not been taken into account, therefore, 17, 18 cannot claim to reproduce all the effects of a curved spacetime geometry. 17, the second term on the left-hand side of Eq. For instance, the four-dimensional Klein-Gordon equation is approximated to a simple two-dimensional partial differential equation by ignoring all the multi-polar modes 17, 18. Different methods are used to tackle this study. We explore the propagation of relativistic wavepackets along an arbitrary null geodesic in a general curved spacetime geometry, and show how the curvature of the spacetime geometry distorts the wavepacket as it travels along the null geodesic. Effects associated to the change of the geodesic due to a mass distribution, such as Shapiro time-delay 10, gravitational lensing 11 and frame dragging 12, are well studied and observed 13, 14, 15, 16. satellites, airplanes, submersibles 1, 2, 3, 4, 5, requires the optical beam to not only traverse through a medium, but in a few cases, also in the fabric of the spacetime geometry, where general relativistic effects manifest 6, 7, 8, 9. Sharing information with a longer range or with moving objects, e.g. Therefore, the alteration to those degrees of freedom for any communication channel needs to be considered and well examined. through fibre, air or underwater channels, causes these photonic degrees of freedom to be altered, and thus causes undesired errors on the shared information. In optical communication, the sender and the receiver, namely Alice and Bob, use one or several internal photonic degrees of freedom, such as wavelength, polarisation, transverse mode or time-bins, to share information, including a ciphertext and the secret key to decrypt the ciphertext. Understanding how these optical properties are altered upon propagation is a key element for any optical communication network. These traits are governed by Maxwell’s equations, which are the relativistic quantum field theory of the U(1) gauge connection. group and phase velocity, wavelength, linear and optical angular momentum, are modified inside or during propagation through a linear or a nonlinear medium.
Photons, electromagnetic waves, are widely used in classical and quantum communication since they do not possess electric charge or rest mass.
Our finding shows that this gravitational distortion is significant, and it needs to be either pre- or post-corrected at the sender or receiver to retrieve the information. For instance, the spacetime curvature causes a 0.10 radian phase-shift for communication between Earth and the International Space Station on a monochromatic laser beam and quadrupole astigmatism can cause a 12.2% cross-talk between structured modes traversing through the solar system. Furthermore, we investigate this distortion for anti de Sitter and Schwarzschild geometries. An explicit expression for the distortion onto the carrier wavefunction in terms of the Riemann curvature is obtained. Here, we report how the curvature of spacetime geometry affects the propagation of information carriers along an arbitrary geodesic. The well-studied general relativistic effects include Shapiro time-delay, gravitational lensing, and frame dragging which all are due to how a mass distribution alters geodesics. The current race in quantum communication – endeavouring to establish a global quantum network – must account for special and general relativistic effects.
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