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Imaging and Applied Optics

Approaching the Quantum Limit of Wavefront Sensing with Spatial Mode Sorting

Jacob Trzaska, Amit Ashok

Published Jan 1, 2024• 1 citation
Publisher

Abstract

We describe a wavefront sensor that is asymptotically quantum-optimal in the limit of small phase error. The sensor could be used with an adaptive optics system to sense residual errors when in closed loop.
DOI
10.1364/cosi.2024.cf1b.2

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High-dimensional orbital-angular-momentum quantum key distribution (OAM-QKD) in free space is jointly limited by aperture-induced diffraction and turbulence-induced modal crosstalk. We develop a numerical framework that first selects an encoding for finite-aperture propagation and then addresses the breakdown of conventional adaptive optics (AO) in branch-point-rich turbulence. Comparing Laguerre–Gaussian, perfect Laguerre–Gaussian, and minimum-diffraction-loss (MDL) modes identifies MDL modes as the most robust of the tested encodings against diffraction-induced quantum dit error rate (QDER). Using this baseline, we introduce branch-cut-length-minimized AO: branch points are localized from beacon-wavefront slopes, equivalent hidden-phase representations are ranked by intensity-weighted branch-cut length, and the selected reconstruction is fitted to a finite-actuator deformable mirror. Under moderate-to-strong turbulence, conventional AO provides useful recovery only while the wavefront remains predominantly smooth, whereas branch-cut-length minimization reduces QDER once branch points become prevalent. For a five-dimensional MDL-encoded QKD link at r 0 = 0.01 m, the mean QDER over 500 turbulence realizations decreases from 0.5550 for traditional AO to 0.5302 after branch-cut-length minimization, compared with 0.4957 for the Ideal AO reference. Residual-error analysis further shows that the remaining QDER is most strongly associated with residual phase mismatch and out-of-subspace leakage. At the same time, receiver-plane amplitude scintillation remains inaccessible to phase-only AO. These results establish branch-cut-length minimization as a physically implementable route to extend beacon-based AO beyond smooth-wavefront conditions, while defining the residual limits imposed by the finite measurement subspace and amplitude distortion.
Orbital angular momentum of photons is an intriguing system for the storage and transmission of quantum information, but it is rapidly degraded by atmospheric turbulence. We explore the ability of adaptive optics to compensate for this disturbance by measuring and correcting cumulative phase shifts in the wavefront. These shifts can be represented as a sum of Zernike functions; we analyze the residual errors after correcting up to a certain number of Zernike modes when an orbital angular momentum state is transmitted through a turbulent atmosphere whose density fluctuations have a Kolmogorov spectrum. We approximate the superoperator map that represents these residual errors and find the solution in closed form. We illustrate with numerical examples how this perturbation depends on the the number of Zernike modes corrected and the orbital angular momentum state of the light.