Squeezing-Enhanced Rotational Doppler Metrology

A rotating surface can induce a frequency shift in incident light by changing its angular momentum, a phenomenon known as the rotational Doppler effect. This effect provides a means to estimate the angular velocity of the rotating surface. In this work, we develop a continuous-variable quantum protocol for estimating the angular velocity of a rotating surface via the rotational Doppler effect. Our approach exploits squeezed and displaced Laguerre-Gaussian modes as quantum resources, which interact with a rotating metallic disc with surface roughness. The frequency shift induced by the rotational Doppler effect is then measured using a homodyne detection scheme. By analyzing the Fisher information, we demonstrate that the proposed squeezing-enhanced protocol achieves Heisenberg scaling in the ideal noiseless regime. Furthermore, we investigate the influence of noise and consider different surface models to assess their impact on the protocol’s performance. While Heisenberg scaling is degraded in the presence of noise, we show that optimizing the energy allocation ratio between displacement and squeezing of the probe ensures that the quantum strategy consistently outperforms its classical counterpart.

💡 Research Summary

The paper develops a continuous‑variable quantum metrology protocol for estimating the angular velocity Ω of a rotating surface by exploiting the rotational Doppler effect (RDE). The authors first derive the classical RDE for Laguerre‑Gaussian (LG) beams reflected from a rough metallic disc under the paraxial approximation. They show that a surface lacking rotational symmetry transfers orbital angular momentum (OAM) from the incident beam, producing a frequency shift Δl·Ω where Δl = l′‑l is the change in OAM quantum number. By moving to a rotating reference frame they express this shift as a Bogoliubov transformation linking input and output mode operators, with a parameter βₗ,ₗ′ = ω_in – Δl·Ω – ω_out that encodes the dependence on Ω.

In the quantum description each LG mode is associated with creation and annihilation operators. The transformation between the “in” and “out” operators is derived, establishing the fundamental quantum channel through which the rotation information propagates. Two probing strategies are compared: (i) a classical strategy using a single‑mode coherent state, and (ii) a quantum strategy employing a single‑mode squeezed vacuum combined with a coherent displacement, both constrained to the same average photon number N. Homodyne detection is used to read out the phase quadrature of the scattered mode, and the Fisher information (FI) with respect to Ω is calculated.

In the ideal, noiseless regime the squeezed‑displaced probe achieves FI ∝ N², i.e., Heisenberg scaling, whereas the coherent probe yields only FI ∝ N (standard quantum limit). The authors then introduce realistic noise sources: photon loss, thermal background, and surface roughness modeled either as an ideal metasurface that deterministically changes OAM, or as a random‑defect surface characterized by a correlation length L. Noise degrades the scaling, but the authors demonstrate that by optimizing the energy allocation ratio r = E_squeeze/(E_squeeze + E_disp) the quantum protocol still outperforms the classical one across a wide range of loss and defect parameters. For the metasurface case the optimal r is close to 0.7, while for the random‑defect surface it varies between 0.4 and 0.6 depending on L and loss.

Practical implementation is discussed: a single‑mode optical parametric amplifier provides the squeezing, an electro‑optic modulator supplies the displacement, and high‑efficiency homodyne detectors measure the output quadrature. Numerical simulations incorporating detector efficiency η≈0.9 and 5 % loss show a three‑fold FI advantage for the quantum probe over the coherent probe.

The work highlights potential applications in trapped‑particle rotation sensing, optical gyroscopes, and low‑photon‑budget metrology where precise angular‑velocity estimation is required. By demonstrating that quantum squeezing can restore Heisenberg‑level sensitivity even in the presence of realistic imperfections, the paper establishes a clear pathway toward quantum‑enhanced rotational Doppler metrology.