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Institute of Physics eBooks

The polarization of photons

Muhammad Sabieh Anwar, Faizan-e-Ilahi, Syed Bilal Hyder, Muhammad Waseem

Published Aug 1, 2024• 0 citations
Publisher

Abstract

To obtain meaningful information from quantum systems, we must measure a physical property of that system, bringing it to the confines of our classical world in the process. Each photon is a complete entity carrying all the polarization details relevant to any electromagnetic field, and since polarization is a measurable quantity, we can use it to extract information from photonic systems. In this chapter, we describe two experiments where we explore the use of photon detection statistics to determine the polarization of down-converted single photons.

DOI
10.1088/978-0-7503-6315-0ch5

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To obtain meaningful information from quantum systems, we must measure a physical property of that system, bringing it to the confines of our classical world in the process. Each photon is a complete entity carrying all the polarization details relevant to any electromagnetic field, and since polarization is a measurable quantity, we can use it to extract information from photonic systems. In this chapter, we describe two experiments where we explore the use of photon detection statistics to determine the polarization of down-converted single photons.
The photon statistics of a single spatial mode of the optical field (including the two polarization states) resulting from a single-photon state undergoing unsaturated amplification by a two-level medium are derived. Results are compared with those for an idealized noiseless linear amplifier and a conventional quantum-noise-limited amplifier in the limit of no gain. When the amplified field is divided for detection of different polarization states, distinctive polarization biases and correlations are evident on average when the polarization of the input state is constant. However, the results are insufficient to determine the initial polarization state based on a single measurement. If one must average over two orthogonally polarized input states (e.g., an incoherent mixture of either linearly or circularly polarized initial states) as required in the absence of hidden variable information in an Einstein–Podolsky-Rosen experiment, the distinctions are completely erased.
Understanding the particle nature of light and its consequences requires quantization of light. Quantization is a process of transforming a continuous system to a discrete system. In physical sciences, quantization is carried out for entities and quantities that are inherently discrete in nature. This refers to the graininess in the actual physical state (here, electromagnetic field) whose macroscopic ensemble manifestation (wave nature) is a large-number approximation. The microscopic grainy dynamics gives rise to delicate and tiny perturbations at the level of a single grain that sum up to produce large effects at the macroscopic level (continuous domain). Thus, quantization describes the physical state at the scale of a single grain while the continuous domain describes the average dynamics (macroscopic manifestation), which wipes out the properties of single grains. As an example, quantization of an electromagnetic field yields grainy particles called photons, the existence of which has been verified experimentally. These grains have well-defined quantized quantities such as energy. In this chapter, we discuss the grainy nature of light and its quantized quantities (energy, angular momentum, etc.) associated with the grains (photons) of light.
We report on two quantum polarization experiments. The first one shows that three geometrical rotations can in principle be distinguished with certainty using two photons. The second experiment shows quantum polarization properties of classically unpolarized light. We outline a new treatment of polarization in quantum optics. Our formalism differs from the usual quantum description, which uses the Stokes operators. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
In this chapter we introduce the principle of local discriminability, which stipulates the possibility of discriminating states of composite systems via local measurements on the component systems. The phenomenon of entanglement has relevant consequences on the accessibility of information in composite systems and on the complexity of characterization of transformations: local discriminability brings dramatic simplifications to the structure of the sets of states and transformations, reconciling the holism of entangled states with the reductionist scientific approach. In order to illustrate the structural relevance of the principle, we will briefly review some OPTs that do not satisfy it, contrasting the features of such theories with those of quantum and classical probabilistic theories, where the principle holds. Entanglement and Holism Holism is a widely known feature of quantum theory, related to the existence of entangled states. In quantum theory one has pure entangled states, whose marginal states are completely mixed. This situation corresponds to having maximal knowledge of the whole with minimal knowledge of the parts. The main manifestation of the holism of entanglement is the impossibility of reconciling the statistics of joint measurements on entangled states with local realism . Local realism is the assumption that any measurement on a system is just the reading of a pre-existing quantity encoded on the system. In other words, we cannot explain the statistics of measurements on the parts of a composite system as a manifestation of our ignorance of locally pre-existing values, as in classical OPT. Does entanglement make information about composite systems locally unaccessible? This would pose severe practical issues on the possibility of acquiring information about physical systems. For example, suppose that two distant telescopes observe a source of entangled photons from a stellar emission. Holism would imply that some features of the emission process could never be detected, unless we are able to make the entangled photons interact in a joint measurement. On the other hand, if a reductionist approach is possible, local observations of the two photons at the sites of the two telescopes would be enough to characterize the emitting source. Thanks to the local discriminability principle, this is actually the case with entangled quantum sources. Another consequence of holism is the fact that transformations generally cannot be characterized by local experiments, namely by applying the unknown transformation only to its input system.
In quantum information processing, one of the most common methods to represent a qubit is by means of the polarization degree of freedom of a photon. Efficient methods to determine the photon polarization state are hence the fundamental tools in the studies of qubit systems. In fact, both theoretically optimal and practical polarization measurement schemes have been investigated extensively in the past two decades. These studies nevertheless focus on the situation when a definite number of photons are given and the results demonstrate the polarization estimation performance in terms of the mean fidelity [1, 2].