Introduction to gravitational redshift of quantum photons propagating in curved spacetime

Abstract

Gravitational redshift is discussed in the context of quantum photons propagating in curved spacetime. A brief introduction to modelling realistic photons is first presented and the effect of gravity on the spectrum computed for photons largely confined along the direction of propagation. It is then shown that redshift-induced transformations on photon operators with sharp momenta are not unitary, while a unitary transformation can be constructed for realistic photons with finite bandwidth. The unitary transformation obtained is then characterized as a multimode mixing operation, which is a generalized rotation of the Hilbert-space basis. Finally, applications of these results are discussed with focus on performance of quantum communication protocols, exploitation of the effects for quantum metrology and sensing, as well as potential for tests of fundamental science.

A Simple Quantum Picture of the Relativistic Doppler Effect

“…[69] for gravitationally redshifted photons, this amplitude change occurs as the transformation between monochromatic excitations cannot be unitary. It was also shown in this reference, however, that a unitary transformation can be constructed for realistic photon operators when a suitable transformation for the frequency of the photon is introduced [69,70]. Whilst the transformation given in Equation ( 51) is very simple, it clearly shows that excitations do not have the same momenta in all reference frames.…”

Entanglement‐Enhanced Quantum Ranging in Near‐Earth Spacetime

“…Ω A , which is known as the gravitational redshift. [36,37,43] It is feasible to utilize the relation between the annihilation operator to derive the relation between the wave packet before and after propagation, [30,33]…”

“…It is important to note that the propagation pulse is affected via changing their frequency distribution in center and shape in the near-Earth curved spacetime. [30][31][32][33][34][35][36][37][38] The Earth's gravity has been found to make observable effects on entanglement and fidelity of quantum communication, [30,31] the accuracy of quantum metrology, [33][34][35] and the reliability of quantum clock synchronization. [32] Therefore, it is crucial to consider the gravitational field of the Earth in practical quantum ranging tasks.…”