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Abstract The study of light lensed by cosmic matter has yielded much information about astrophysical questions. Observations are explained using geometrical optics following a ray-based description of light. After deflection the lensed light interferes, but observing this diffractive aspect of gravitational lensing has not been possible due to coherency challenges caused by the finite size of the sources or lack of near-perfect alignment. In this article, we report on the observation of these wave effects of gravitational lensing by recreating the lensing conditions in the laboratory via electro-optic deflection of coherent laser light. The lensed light produces a beam containing regularities, caustics, and chromatic modulations of intensity that depend on the symmetry and structure of the lensing object. We were also able to observe previous and new geometric-optical lensing situations that can be compared to astrophysical observations. This platform could be a useful tool for testing numerical/analytical simulations, and for performing analog simulations of lensing situations when they are difficult to obtain otherwise. We found that laboratory lensed beams constitute a new class of beams, with long-range, low expansion, and self-healing properties, opening new possibilities for non-astrophysical applications. 

This article presents a table-top experiment that acquires the interference pattern from single photons passing through a double-slit. The experiment is carried out using the heralded, single-photon experimental setup now affordable and fairly common in advanced instructional laboratories. By scanning a single-photon detector on a translation stage, this experiment is implemented without the need of an expensive gate-intensified CCD camera. The authors compare the acquired single-slit and double-slit interference patterns to predicted ones and include a quantum eraser measurement. The experiments are dramatic demonstrations of wave-particle quantum effects and are excellent additions to the collection of single-photon experiments that have been developed over the past several years for the advanced instructional laboratory curriculum. 

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. 

The Hong–Ou–Mandel interference experiment is a fundamental demonstration of nonclassical interference and a basis for many investigations of quantum information. This experiment involves the interference of two photons reaching a symmetric beamsplitter. When the photons are made indistinguishable in all possible ways, an interference of quantum amplitudes results in both photons always leaving the same beamsplitter output port. Thus, a scan of distinguishable parameters, such as the arrival time difference of the photons reaching the beamsplitter, produces a dip in the coincidences measured at the outputs of the beamsplitter. The main challenge for its implementation as an undergraduate laboratory is the alignment of the photon paths at the beamsplitter. We overcome this difficulty by using a pre-aligned commercial fiber-coupled beamsplitter. In addition, we use waveplates to vary the distinguishability of the photons by their state of polarization. We present a theoretical description at the introductory quantum mechanics level of the two types of experiments, plus a discussion of the apparatus alignment and list of parts needed. 

Einstein beams are coherent optical beams generated by the conditions of gravitational lensing. In the ray picture, Einstein beams are formed by the intersection of light rays deflected by a lensing mass, similar to nondiffracting Bessel beams, but with the difference that adjacent rays diverge slightly. When accounting for the wave properties of light, they form beam-like diffraction patterns that preserve their shape but expand as the light propagates. The addition of a topological charge to the light, leads to more complex patterns carrying orbital angular momentum. For symmetric lensing conditions, Einstein beams carry modes described by confluent hypergeometric functions, which can be approximated by Bessel functions. A theoretical analysis of this is presented here. In astrophysical observations, many of these features can only be inferred because conditions of coherence and alignment make them difficult to observe. Studies of Einstein beams in the laboratory can be used to inform astrophysical observations and discover new non-astrophysical laboratory applications. 

There is interest in using photon entanglement in biomedical applications. In one application, polarization-entangled photons pass through brain tissue. The effect of the brain tissue on the photon entanglement is measured via the decoherence that is imparted on the entangled state. Our current method to obtain a measure of the decoherence involves quantum state tomography, where a minimum of 16 measurements are used in conjunction with tomographic optimization to obtain the density matrix representing the state of the photons. In this work we report on a method to avoid tomographic optimization on behalf of a direct measurement of the elements of the density matrix. We make preliminary comparisons between the two methods. 

Abstract The rise of quantum information as a viable technology requires appropriate instructional curricula for preparing a future workforce. Key concepts that are the basis of quantum information involve fundamentals of quantum mechanics, such as superposition, entanglement and measurement. To complement modern initiatives to teach quantum physics to the emerging workforce, lab experiences are needed. We have developed a curriculum of quantum optics experiments to teach quantum mechanics fundamentals and quantum algebra. These laboratories provide hands-on experimentation of optical components on a table-top. We have also created curricular materials, manuals, tutorials, parts and price lists for instructors. Automation of the apparatus offers the flexibility of using the apparatus remotely and for giving access to a greater number of students with a single setup. 

The generation, manipulation and quantification of non-classical light, such as quantum-entangled photon pairs, differs significantly from methods with classical light. Thus, quantum measures could be harnessed to give new information about the interaction of light with matter. In this study we investigate if quantum entanglement can be used to diagnose disease. In particular, we test whether brain tissue from subjects suffering from Alzheimer’s disease can be distinguished from healthy tissue. We find that this is indeed the case. Polarization-entangled photons traveling through brain tissue lose their entanglement via a decohering scattering interaction that gradually renders the light in a maximally mixed state. We found that in thin tissue samples (between 120 and 600 micrometers) photons decohere to a distinguishable lesser degree in samples with Alzheimer’s disease than in healthy-control ones. Thus, it seems feasible that quantum measures of entangled photons could be used as a means to identify brain samples with the neurodegenerative disease. 

The similarity between the 2D Helmholtz equation in elliptical coordinates and the Schr¨odinger equation for the simple mechanical pendulum inspires us to use light to mimic this quantum system. When optical beams are prepared in Mathieu modes, their intensity in the Fourier plane is proportional to the quantum mechanical probability for the pendulum. Previous works have produced a two-dimensional pendulum beam that oscillates as a function of time through the superpositions of Mathieu modes with phases proportional to pendulum energies. Here we create a three-dimensional pendulum wavepacket made of a superposition of Helical Mathieu-Gaussian modes, prepared in such a way that the components of the wave-vectors along the propagation direction are proportional to the pendulum energies. The resulting pattern oscillates or rotates as it propagates, in 3D, with the propagation coordinate playing the role of time. We obtained several different propagating beam patterns for the unbound-rotor and the bound-swinging pendulum cases. We measured the beam intensity as a function of the propagation distance. The integrated beam intensity along elliptical angles plays the role of quantum pendulum probabilities. Our measurements are in excellent agreement with numerical simulations. 

The rise of quantum information as a viable technology requires appropriate instructional curricula for preparing a future workforce. Key concepts that are the basis of quantum information involve fundamentals of quantum mechanics, such as superposition, entanglement and measurement. To complement modern initiatives to teach quantum physics to the emerging workforce, lab experiences are needed. We have developed a curriculum of quantum optics experiments to teach quantum mechanics fundamentals and quantum algebra. These laboratories provide hands-on experimentation of optical components on a table-top. We have also created curricular materials, manuals, tutorials, parts and price lists for instructors. Automation of the apparatus offers the fexibility of using the apparatus remotely and for giving access to a greater number of students with a single setup.