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arXiv:quant-ph/0511053 · Journal of Modern Optics

An optimal photon counting polarimeter

Alexander Ling, Kee Pang Soh, Antı́a Lamas-Linares, Christian Kurtsiefer

Published Jun 2, 2006• 17 citations
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Abstract

We present the experimental results for a method used to perform polarimetry on ensembles of single photons. Our setup is based on a measurement method known to be optimal for estimating the state of two-level systems. The setup has no moving parts and is sensitive to weak sources (emitting single photons) of light as it relies on photon counting, and has potential applications in both classical polarization measurements and quantum communication scenarios. In our implementation, we are able to reconstruct the Stokes parameters of pure polarization states with an average fidelity of 99.9%.

DOI
10.1080/09500340600674242

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We present the experimental results for a method used to perform polarimetry on ensembles of single photons. Our setup is based on a measurement method known to be optimal for estimating the state of two-level systems. The setup has no moving parts and is sensitive to weak sources (emitting single photons) of light as it relies on photon counting, and has potential applications in both classical polarization measurements and quantum communication scenarios. In our implementation, we are able to reconstruct the Stokes parameters of pure polarization states with an average fidelity of 99.9%.
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We report on the experimental implementation of a polarimeter based on a scheme known to be optimal for obtaining the polarization vector of ensembles of spin-12\frac{1}{2}21​ quantum systems and the alignment procedure for this polarimeter. We also show how to use this polarimeter to estimate the polarization state for identically prepared ensembles of single photons and photon pairs and extend the method to obtain the density matrix for generic multiphoton states. State reconstruction and performance of the polarimeter is illustrated by actual measurements on identically prepared ensembles of single photons and polarization entangled photon pairs.
A universal and optimal method for the polarimetry of light with arbitrary photon statistics is presented. The method is based on the continuous maximum-likelihood positive operator-valued measure (ML-POVM) for pure polarization states over the surface of the Bloch sphere. The success probability and the mean fidelity are used as the figures of merit to show its performance. The POVM is found to attain the collective bound of polarization estimation with respect to the mean fidelity. As demonstrations, explicit results for the NNN photon Fock state, the phase-randomized coherent state (Poisson distribution), and the thermal light are obtained. It is found that the estimation performances for the Fock state and the Poisson distribution are almost identical, while that for the thermal light is much worse. This suggests that thermal light leaks less information to an eavesdropper and hence could potentially provide more security in polarization-encoded quantum communication protocols than a single-mode laser beam as customarily considered. Finally, comparisons against an optimal adaptive measurement with classical communications are made to show the better and more stable performance of the continuous ML-POVM.
A continuous positive operator-valued measurement (POVM) is described for the polarization state of a single photon propagating in a known spatiotemporal mode. This POVM is shown to be the maximum-likelihood quantum measurement for estimating that polarization state. Moreover, the maximum-likelihood polarization estimate derived from this POVM enables uniformly optimal measure-and-prepare state transmission via classical communication---at the F‾=2/3\overline{F}=2/3F=2/3 classical limit on average teleportation fidelity---for any pure state of polarization. When two continuous-POVM polarimeters are used to detect the singlet state of a pair photons that are in distinct spatial modes, the conditional probability density for one polarimeter's output given the other's encompasses the quantum interference patterns seen in standard singlet-state polarization analysis. For single-photon illumination, a 1:M1:M1:M optical splitter followed by a collection of MMM projective polarization measurements, whose bases are uniformly distributed over the Poincar\'e sphere, yields observation statistics that converge in distribution to those of the continuous-POVM polarimeter as $M\ensuremath{\rightarrow}\ensuremath{\infty}$.
We perform experimental quantum polarimetry using a heralded single photon to analyze the optical activity of linearly polarized light traversing a chiral medium. Three kinds of estimators are considered to estimate the concentrations of sucrose solutions from measuring the rotation angle of the linear polarization of the output photons. Through repetition of independent and identical measurements performed for each individual scheme and different concentration sucrose solutions, we compare the estimation uncertainty among the three schemes. The results are also compared to classical benchmarks for which a coherent state of light is taken into account. The quantum enhancement in the estimation uncertainty is evaluated and the impact of experimental and technical imperfections is discussed. In this work, we lay out a route for future applications relying on quantum polarimetry.
We propose an improved scheme to measure the Stokes polarization parameters by making the to-be-measured state evolve unitarily. An optical setup able to implement the scheme is presented theoretically and experimentally. Theoretical results indicate that at least two unitary operators should be employed to determine the Stokes parameters of light with arbitrary degrees of polarization. Compared with the results acquired by a commercial polarimeter, the proposed scheme is used to obtain the Stokes parameters of 13 representative states with degrees of polarization r = 1 and r = 0.5 , experimentally. The fidelity between the two states gained by the above methods is in the range of 0.9802 ± 0.0046 to 1.0000 ± 0.0000 .