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Journal of Lightwave Technology

Fundamental Limits to the Measurement of the Polarization of Classical Light

Antonio Mecozzi, Cristian Antonelli, Mark Shtaif

Published Jan 14, 2021• 2 citations
Publisher

Abstract

We study the limits that quantum mechanics imposes on the accuracy of the measurement of the Stokes polarization-vector in the case of classical states. Using the apparatus of the conventional Stokes receiver, we propose an estimation method that allows not only to exceed the signal-to-noise limit that is achieved by a heterodyne measurement or after ideal phase-insensitive amplification, but also to achieve the quantum SNR limit for the measurement of classical light. We refer to this receiver scheme as the enhanced Stokes receiver.

DOI
10.1109/jlt.2021.3051855

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Any polarization state of light occupies intrinsic quantum uncertainties due to the noncommutative behavior of the Stokes operators, which are manifested as unavoidable quantum fluctuations in the corresponding classical Stokes parameters.In this thesis, we explore such quantum polarization uncertainties exhibited by vectorial light fields in Young's seminal double-slit interference experiment.As a main result, by adopting a proper Stokes operator representation of double-slit interference, we establish general quantum polarization uncertainty relations for the Stokes parameters in the observation plane.The relations show how the lower bounds of the polarization uncertainties are periodically varying across the observation screen and how they are affected by the polarization and coherence properties of the light at the two slits.We also present various noncommutative, interlinked connections between coherence and polarization in the slit plane which have not been considered earlier in the literature.Our work sets the fundamental precision limits imposed by quantum physics for characterizing any polarization state in double-slit interference, which could find use in photonic applications exploiting polarimetric and interferometric techniques for high-resolution quantum-enhanced sensing.
Abstract Classical polarimetry is a well-established discipline with diverse applications across different branches of science. The burgeoning interest in leveraging quantum resources to achieve highly sensitive measurements has spurred researchers to elucidate the behavior of polarized light within a quantum mechanical framework, thereby fostering the development of a quantum theory of polarimetry. In this work, drawing inspiration from polarimetric investigations in biological tissues, we investigate the precision limits of polarization rotation angle estimation about a known rotation axis, in a quantum polarimetric process, comprising three distinct quantum channels. The rotation angle to be estimated is induced by the retarder channel on the Stokes vector of the probe state. The diattenuator and depolarizer channels, acting on the probe state, can be thought of as effective noise processes. We explore the precision constraints inherent in quantum polarimetry by evaluating the quantum Fisher information for probe states of significance in quantum metrology, namely NOON, Kings of Quantumness, and Coherent states. The effects of the noise channels as well as their ordering is analyzed on the estimation error of the rotation angle to characterize practical and optimal quantum probe states for quantum polarimetry. Furthermore, we propose an experimental framework tailored for NOON state quantum polarimetry, aiming to bridge theoretical insights with empirical validation.
In this paper we discuss the estimation of parameters describing polarized and partially polarized light when radiation is collected with a receiver consisting of an array of incoherent detectors and registering light levels after passage through an array of retardation plates and analyzers. The results obtained in semiclassical limit include Poisson photon statistics. We obtain fundamental limits on estimation of parameters of interest as a function of the number of photons available, and determine the value of a priori knowledge for achieving the desired estimation accuracy for both signal and background shot noise limited condition. The results presented are applicable to both active and passive systems where measurements of polarization signatures can improve detection and/or discrimination of targets, or when polarization coding is used to transmit information.
The classically defined minimum uncertainty of the optical phase is known as the standard quantum limit or shot-noise limit (SNL), originating in the uncertainty principle of quantum mechanics. Based on the SNL, the phase sensitivity is inversely proportional to K, where K is the number of interfering photons or statistically measured events. Thus, using a high-power laser is advantageous to enhance sensitivity due to the K gain in the signal-to-noise ratio. In a typical interferometer, however, the resolution remains in the diffraction limit of the K = 1 case unless the interfering photons are resolved as in quantum sensing. Here, a projection measurement method in quantum sensing is adapted for classical sensing to achieve an additional K gain in the resolution. To understand the projection measurements, several types of conventional interferometers based on N-wave interference are coherently analyzed as a classical reference and numerically compared with the proposed method. As a result, the Kth-order intensity product applied to the N-wave spectrometer exceeds the diffraction limit in classical sensing and the Heisenberg limit in quantum sensing, where the classical N-slit system inherently satisfies the Heisenberg limit of π/N in resolution.