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Quantum mechanical rotation of a photon polarization by Earth’s gravitational field

Hansol Noh, Paul M. Alsing, Doyeol Ahn, Warner A. Miller, Namkyoo Park

Published Nov 18, 2021• 6 citations
Publisher

Abstract

Abstract We describe the quantum mechanical rotation of a photon state, the Wigner rotation—a quantum effect that couples a transformation of a reference frame to a particle’s spin, to investigate geometric phases induced by Earth’s gravitational field for observers in various orbits. We find a potentially measurable quantum phase of the Wigner rotation angle in addition to the rotation of standard fame, the latter of which is computed and agrees well with the geodetic rotation. When an observer is in either a circular or a spiraling orbit containing non-zero angular momentum, the additional quantum phase contributes 10−6 degree to 10−4 degree respectively, depending on the altitude of the Earth orbit. In the former case, the additional quantum phase is dominant over the near-zero classical geodetic rotation. Our results show that the Wigner rotation represents a non-trivial semi-classical effect of quantum field theory on a background classical gravitational field.

DOI
10.1038/s41534-021-00471-6

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gr-qcCross-listedarXiv:2605.15600•May 18, 2026
Abstract We describe the quantum mechanical rotation of a photon state, the Wigner rotation—a quantum effect that couples a transformation of a reference frame to a particle’s spin, to investigate geometric phases induced by Earth’s gravitational field for observers in various orbits. We find a potentially measurable quantum phase of the Wigner rotation angle in addition to the rotation of standard fame, the latter of which is computed and agrees well with the geodetic rotation. When an observer is in either a circular or a spiraling orbit containing non-zero angular momentum, the additional quantum phase contributes 10−6 degree to 10−4 degree respectively, depending on the altitude of the Earth orbit. In the former case, the additional quantum phase is dominant over the near-zero classical geodetic rotation. Our results show that the Wigner rotation represents a non-trivial semi-classical effect of quantum field theory on a background classical gravitational field.
We revisit polarization rotation due to gravity, known as the gravitational Faraday effect, with a view on its role in quantum communications with Earth-orbiting satellites. In a static spherically symmetric gravitational field Faraday rotation is purely a reference frame (gauge) effect. This is so also in the leading post-Newtonian expansion of the Earth's gravitational field. However, establishing the local reference frame with respect to distant stars leads to the nonzero Faraday phase. In communications between a ground station and an Earth-orbiting spacecraft this phase is of the order of ${10}^{\ensuremath{-}10}$. Under the same conditions the Wigner phase of special relativity is typically of the order ${10}^{\ensuremath{-}4}\ensuremath{-}{10}^{\ensuremath{-}5}$. These phases lead to the physical lower bound on communication errors. However, both types of errors can be simultaneously mitigated. Moreover, they are countered by a fully reference frame independent scheme that also handles arbitrary misalignments between the reference frames of sender and receiver.
Unification of gravity with quantum mechanics is still a terra incognita. Photon polarization measurements offer a unique window for probing the interaction between these two fundamental forces. We have revealed that non-reciprocity in the photon polarization angle can arise by tailoring the quantization axis, which corresponds to the direction of polarizer. Due to this non-reciprocity, the measured polarization angle can become ten times larger than that of gravitationally induced frame rotation in both near-Earth and black hole environments. To verify this finding, we propose an astronomical interferometer composed of satellites with the tailored quantization axis, challenging the conventional view of their triviality in closed paths of a photon. Notably, this non-reciprocity can extend to any rotation in the polarization plane, irrespective of the origins, all of which can dictate polarization rotation. Our findings could offer new opportunities for testing fundamental principles in physics.
We investigate in a covariant manner the spin-induced non-geodesic motion of massive spin 1/2 particles in an arbitrary gravitational field for trajectories that are initially geodesic when spin is ignored. Using the WKB approximation for the wave function in curved spacetime, we compute the O(hbar) correction to the Wigner rotation of the spin 1/2 particle, whose O(1) contribution is zero on timelike geodesics. We develop conditions for the motion of observers in which the Wigner rotation is null. For the spherically symmetric Schwarzschild metric, we consider specific examples of particle motion in the equatorial plane for (i) circular orbits and (ii) radially infalling trajectories. For the former case we consider the entanglement for a perfectly anti-correlated EPR entangled pair of spins as the separate qubits traverse the circular orbit in same direction.
The effect of a classical gravitational field on the spin entanglement of a system of two spin- particles moving in the curved spacetime is discussed. The system is described by a two-particle Gaussian wave packet represented in the momentum space and both the acceleration of the system and the curvature of the spacetime produce a Wigner rotation acting on the wave packet as it moves along a path in the curved spacetime. By calculating the reduced density operator at a final point, we focus on the spin entanglement of the system. In a spherically symmetric and static gravitational field, for example a charged black hole, there can be particular paths on which the Wigner rotation is trivial and so the initial reduced density matrix remains intact. This causes the spin entanglement to be invariant during the motion. The spin entanglement descends to zero by increasing the angular velocity of the mean centroid of the system as well as increasing the proper time during which the centroid moves on its circular path around the center.
The preparation of quantum systems and the execution of quantum information tasks between distant users are always affected by gravitational and relativistic effects. In this work, we quantitatively analyze how the curved space-time background of the Earth affects the classical and quantum correlations between photon pairs that are initially prepared in a two-mode squeezed state. More specifically, considering the rotation of the Earth, the space-time around the Earth is described by the Kerr metric. Our results show that these state correlations, which initially increase for a specific range of satellite's orbital altitude, will gradually approach a finite value with increasing height of satellite's orbit (when the special relativistic effects become relevant). More importantly, our analysis demonstrates that the changes of correlations generated by the total gravitational frequency shift could reach the level of [Formula: see text] within the satellite's height at geostationary Earth orbits.
We study the rotation of the polarization due to the gravitational field in the Kerr spacetime and the possibility of estimating the specific angular momentum that parameterizes this metric. Our approach is based on a geodesic interferometer, that is, a Mach-Zehnder interferometer whose arms are defined by null geodesics, and a single photon propagating within it. We show that the detection probability at the output ports of the interferometer is a function of two phase differences, one arising from the gravitational time delay and the other from the polarization rotation, both computed under the slow rotation and weak field approximations. Thereby, the interferometric visibility is a signature of two relativistic effects. Using the detection probability, we obtain an estimate for the specific angular momentum and characterize its uncertainty.