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Revista Mexicana de Física

Imaging Mueller matrix determination of transparent, unpolarizing samples using a classically entangled polarization state

Jacqueline Muro, Rafael Espinosa-Luna

Published Jun 28, 2018• 0 citations
Publisher

Abstract

Inspired in a recent theoretical work for the determination of the Mueller matrix, using as incidence a single classically entangled polarization state (F. Töppel et al., New J. Phys. 16 (2014) 073019), an experimental setup is proposed and tested. The open space and two wave plate retarders are used as the transparent, nondepolarizing samples under study. Results show some experimental improvements are necessary in order to implement accurately the theoretical proposal in which this work is based.

DOI
10.31349/revmexfis.64.407

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Inspired in a recent theoretical work for the determination of the Mueller matrix, using as incidence a single classically entangled polarization state (F. Töppel et al., New J. Phys. 16 (2014) 073019), an experimental setup is proposed and tested. The open space and two wave plate retarders are used as the transparent, nondepolarizing samples under study. Results show some experimental improvements are necessary in order to implement accurately the theoretical proposal in which this work is based.
We present a method to determine the Mueller matrix of a sample using polarization-entangled photon pairs. One of the photons of a pair goes through a sample and is then subject to a polarization projection measurement. The other photon, which does not go through the sample, is also subject to a polarization projection. The measured quantum correlations are equivalent to polarimetry measurements, where the initial state of the photon going through the sample is determined by the polarization projection on the entangled partner that does not go through the sample. The correspondence with the classical system is acausal because quantum measurements apply to distinct Hilbert spaces. We tested this method with standard optical elements finding excellent agreement with the expectations. Thus it can be used as an alternative to classical Mueller polarimetry for conditions that would be challenging to do otherwise.
Quantum correlations are non-classical features of quantum systems that can be harnessed in new technologies. Nonlocality, a unique byproduct of the entanglement of more than one particle, can alter the causal sequence that is present in a classical measurement. In this work, we investigate a nonlocal form of Mueller polarimetry. In the classical method, light prepared in an initial state passes through a sample whose polarization properties are unknown, and the light's modified polarization state is subsequently measured. From a series of measurements, the Mueller matrix is obtained, which contains the polarization properties of the sample. In the nonclassical version of the technique presented here, the initial and final parts of this measurement were split into polarization projections on two polarization-entangled photons, but linked through quantum correlations in the post-selection process. We found the results with samples of known and unknown Mueller matrix using this approach to be equivalent to the classical ones. The nonlocal feature of the measurement can invert the causal order of preparation and measurement in the classical method. We present a study of its limitations when the entangled state of the photons is not the ideal one. From this work, we conclude that the technique is very resilient to imperfections in the quantum state of the photons, making it a feasible alternative to the classical method.
We show that the method of maximum-likelihood estimation, recently introduced in the context of quantum process tomography, can be applied to the determination of Mueller matrices characterizing the polarization properties of classical optical systems. Contrary to linear reconstruction algorithms, the proposed method yields physically acceptable Mueller matrices even in the presence of uncontrolled experimental errors. We illustrate our method with the case of an unphysical measured Mueller matrix taken from the literature.
Quantum approaches relying on entangled photons have been recently proposed to increase the efficiency of optical measurements. We demonstrate here that, surprisingly, the use of classical light with entangled degrees of freedom can also bring outstanding advantages over conventional measurements in polarization metrology. Specifically, we show that radially polarized beams of light allow to perform real-time single-shot Mueller matrix polarimetry. Our results also indicate that quantum optical procedures requiring entanglement without nonlocality can be actually achieved in the classical optics regime.
It takes some convincing to realize that light has a polarization degree of freedom, as our eyes are usually ignorant of light's polarization. Since overcoming this hurdle of intuition, polarization has become a fantastic resource that can be easily manipulated both physically and mathematically, opening the door to a wide variety of applications. We have only recently begun to appreciate how many more doors are opened by the quantum mechanical degrees of freedom inherent to optical polarization. One use of optical polarization is for polarimetry: measuring the changes in light's polarization after it interacts with a material is an excellent procedure for nondestructively probing the characteristics and composition of the intervening material. More sensitive measurements require brighter probe light; however, sufficiently intense light will begin to destroy the sample being probed. In this thesis, we seek to provide more sensitive polarimetry without resorting to bright beams of light. Tailoring the quantum properties of various states of light has been shown to increase their usefulness for other estimation protocols and we show how to extend this paradigm to quantum enhancements in polarimetry. We begin by finding the quantum states underlying classical polarization. Each particular set of classical polarization properties corresponds to a large variety of quantum states. Next, we establish quantum descriptions of classical polarization transformations corresponding to arbitrary Jones and Mueller matrices, including quantum mechanical insights into the distinction between processes that can and cannot be described by Jones matrices. We propose candidates for the most likely quantum states underlying classical decompositions into polarized and unpolarized fractions, carefully inspecting how these quantum states behave under polarization transformations. This language allows us to inspect quantum-enhanced sensing in the multiparameter context of polarimetry. We show the dramatic possibilities for quantum enhancements in any metrological scenario that is mathematically equivalent to a rotation, of which polarization rotations are a primary example; in contrast, we also show most attenuating and depolarizing polarization transformations to forbid such dramatic enhancements. Finally, we discuss polarization and its generalizations in the context of generating quantum entanglement via linear optics. These applications serve as mere examples of the usefulness promised by light’s quantum polarization degrees of freedom.
Liquid crystal displays (LCDs) are devices capable of manipulating properties of an incident light beam, such as amplitude, phase, and polarization, based on the voltage applied to their molecules. In this work, we will experimentally characterize the effect of an LCD on light polarization, aiming at its use as a programmable spatial light modulator (SLM) in optics and quantum information experiments. In the first part, we will determine the Mueller matrix of the device and, from it, its polarimetric properties. We will show that the LCD acts only approximately as an ideal retarder plate since it introduces depolarization to the incident light. In the second part, we investigate the behavior of the LCD through the formalism of quantum operations, treating its action as an operation on polarization qubit states. Through process tomography, we determine the matrix characterizing the device's operation and show that it is non-unitary. Next, we derive a general expression for the process matrix of an SLM, given by the combination of the LCD with wave plates. This expression will allow us to implement programmable operations on the polarization states of light based on the configuration of the wave plates and the voltage on the LCD. As an application, we will quantify the fidelity of the actual operation implemented by the SLM with an ideal unitary operation of interest in quantum information protocols.