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Optics Express

Imaging the polarization of a light field

Roshita Ramkhalawon, Thomas G. Brown, Miguel Angel Alonso

Published Feb 11, 2013• 62 citations
Publisher

Abstract

We describe and analyze a method by which an optical polarization state is mapped to an image sensor. When placed in a Bayesian framework, the analysis allows a priori information about the polarization state to be introduced into the measurement. We show that when such a measurement is applied to a single photon, it eliminates exactly one fully polarized state, offering an important insight about the information gained from a single photon polarization measurement.

DOI
10.1364/oe.21.004106

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We describe and analyze a method by which an optical polarization state is mapped to an image sensor. When placed in a Bayesian framework, the analysis allows a priori information about the polarization state to be introduced into the measurement. We show that when such a measurement is applied to a single photon, it eliminates exactly one fully polarized state, offering an important insight about the information gained from a single photon polarization measurement.
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.
We experimentally demonstrate protective measurements by weakly coupling the polarization of a single-photon-level field to a measurement pointer that corresponds to the arrival time of the photon. By using an optical loop, we implement a variable, controlled number (1--9) of protection and measurement stages. We demonstrate the measurement of expectation values of photon polarization by measuring arrival times while simultaneously protecting the polarization state. No knowledge of the initial photon state is required or available in our experiment, demonstrating that protective measurements provide a genuine information gain that cannot simply be reduced to a priori information about the protection procedure.
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 insights offered by quantum mechanics to the field of optical metrology are many-fold, with non-classical states of light themselves used to make sensors that surpass the sensitivity of sensors using classical states of light. Unfortunately, this advantage, referred to often as "super-sensitivity" is notoriously fragile, and even the slightest experimental imperfections may greatly reduce the efficacy of the non-classical sensors, sometimes completely obviating their advantage. In my thesis I have shown that the performance of an otherwise ideal two-photon interferometer, which exploits entanglement between photons to make super-sensitive measurements of phase, is crippled by the slightest introduction of decoherence between modes of the interferometer. I have shown further that such drastic reduction in sensitivity can also appear in classical measurement problems, specifically that the recently developed methods of estimating the separation between a pair of point sources are rendered less effective when the ideal assumption of complete spatial incoherence is relaxed. Towards overcoming these and other issues, I have designed new configurations that use ancillary optical degrees of freedom, a tool-set that has recently garnered much interest in the field of quantum optics. In the context of two-photon interferometry, I have shown that by coupling polarization to the spatial-structure of the two photon state used to probe phase it is possible to obviate the need for a reference phase, even in the context of decoherence and imperfections in the interferometer. In the context of two-point resolution, I have developed an anisotropic imaging system that performs the function of an image-inversion interferometer and is inherently stable, offering an attractive implementation of recently developed methods of sub-Rayleigh imaging. I have further shown both theoretically and experimentally that the same anisotropic image-inversion interferometer is useful in measuring spatially encoded phases, both in the context of classical illumination as well as quantum-aided two-photon super-sensing. In both cases, the ability to perform interferometric measurements of the spatial structure of an electric field without splitting beam paths forms a bridge between conception and implementation of precision-sensing measurement strategies. Finally, I have shown that binary interferometric method based on the common-path anisotropic imaging system that I introduced, are able to measure both phase gradients and transverse beam tilts with a sensitivity beating conventional systems that are used both commercially and in research laboratories.
We experimentally demonstrate a quantum state estimation and tomography for qubits encoded in a single photon's spatial degree of freedom. The experimental setup depicted in Fig. 1 consists of: 1) polarization entangled photon pairs source; 2) spatial encoder allowing to map a polarization state into spatial state; 3) polarization analyzer and 4) spatial state analyzer. The 28 element spatial quantum state measurement set was implemented using imaging optics and a linear array of 28 single photon avalanche diodes (SPAD). The timing information from all the detectors was acquired using custom made FPGA electronics.