Rotational Doppler shift of the phase-conjugated photon

TL;DR

This paper demonstrates that the rotational Doppler shift of photons with orbital angular momentum is enhanced in a phase-conjugating interferometer with Dove prisms, enabling detection of rotation through vortex pattern shifts at the single-photon level.

Contribution

It introduces a novel phase-conjugating interferometer setup that amplifies rotational Doppler shifts for photons with orbital angular momentum, enabling sensitive rotation detection.

Findings

Rotational Doppler shift is an even multiple of the frame's angular frequency.

The interferometer's shift scales with the number of Dove prisms and photon angular momentum.

Rotation of vortex interference patterns can be detected via phase conjugation effects.

Abstract

The rotational Doppler shift of a photon with orbital angular momentum $\pm \ell \hbar$ is shown to be an even multiple of the angular frequency $\Omega$ of the reference frame rotation when photon is reflected from the phase-conjugating mirror. We consider the one-arm phase-conjugating interferometer which contains $N$ Dove prisms or other angular momentum altering elements rotating in opposite directions. When such interferometer is placed in the rotating vehicle the $\delta \omega=4 (N+1/2) \ell \cdot \Omega$ rotational Doppler shift appears and rotation of the helical interference pattern with angular frequency $\delta \omega /{2 \ell}$ occurs. The accumulation of angular Doppler shift via successive passage through the $N$ image-inverting prisms is due to the phase conjugation, for conventional parabolic retroreflector the accumulation is absent. The features of such a vortex phase conjugating interferometry at the single photon level are discussed.