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Spontaneous parametric down-conversion (SPDC) is the most widely used process for generating photon pairs entangled in various degrees of freedom such as polarization, time-energy, position-transverse momentum, and angle-orbital angular momentum (OAM). In SPDC, a pump photon interacts with a non-linear optical crystal and splits into two entangled photons called the signal and the idler photons. The SPDC process has been studied extensively in the last few decades for various pump and crystal configurations, and the entangled photon pairs produced by SPDC have been used in numerous experimental studies on quantum entanglement and entanglement-based real-world quantum-information applications. In this tutorial article, we present a thorough study of phase matching in BBO crystals for spontaneous parametric down-conversion and thereby also investigate the generation of entangled photons in such crystals. First, we present a theoretical derivation of two-photon wavefunction produced by SPDC in the frequency and transverse momentum bases. We then discuss in detail the effects due to various crystal and pump parameters including the length of the crystal, the angle between the optic axis and the pump propagation direction, the pump incidence angle on the crystal surface, the refraction at the crystal surfaces, and the pump propagation direction inside the crystal. These effects are extremely relevant in experimental situations. We then present our numerical and experimental results in order to illustrate how various experimental parameters affect the phase matching and thus the generation of entangled photons. Finally, using the

Learning effective visuomotor policies for robots purely from data is challenging, but also appealing since a learning-based system should not require manual tuning or calibration. In the case of a robot operating in a real environment the training process can be costly, time-consuming, and even dangerous since failures are common at the start of training. For this reason, it is desirable to be able to leverage simulation and off-policy data to the extent possible to train the robot. In this work, we introduce a robust framework that plans in simulation and transfers well to the real environment. Our model incorporates a gradient-descent based planning module, which, given the initial image and goal image, encodes the images to a lower dimensional latent state and plans a trajectory to reach the goal. The model, consisting of the encoder and planner modules, is trained through a meta-learning strategy in simulation first. We subsequently perform adversarial domain transfer on the encoder by using a bank of unlabelled but random images from the simulation and real environments to enable the encoder to map images from the real and simulated environments to a similarly distributed latent representation. By fine tuning the entire model (encoder + planner) with far fewer real world expert demonstrations, we show successful planning performances in different navigation tasks.