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Abstract The technologies used in the manipulation of light can be used to do analogue simulations of physical systems with wave-like equations of motion. This analogy is maximized by the use of all the degrees of freedom of light. The Helmholtz equation in physical optics and the Schodinger equation in quantum mechanics share the same mathematical form. We use this connection to prepare non-diffracting optical beams representing the spatial and temporal dynamics of a nonlinear physical system: the quantum pendulum. By using the propagation coordinate to represent time in the quantum problem, we are able to analogue-simulate quantum wavepacket dynamics. These manifest themselves in novel optical beams with rich three-dimensional structures, such as rotation and sloshing of the light's intensity as it propagates. Our experimental results agree very well with the predictions from quantum theory, thus demonstrating that our system can be used as a platform to simulate the quantum pendulum dynamics. This three-dimensional light-sculpting capability has the potential to impact fields such as manipulation with light and imaging. 

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. 

We use spatial light modulation to investigate the diffractive effects of gravitational lensing in the laboratory. Using this new platform for laboratory astrophysics, we can overcome the coherence challenges that prevent the observation of diffraction in astronomical imaging. These studies will inform gravitational lensing of gravitational waves when imaging of gravitational waves becomes available. Our previous work involved studying lensing by a single mass, symmetric and elliptical. This work focuses on the patterns produced by a binary-mass system. We observed rich 2-dimensional interference patterns bounded by caustics. Comparison of experimental results with preliminary theoretical calculations is excellent. 

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.