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A quarter century of progress in holographic optical trapping has yielded fundamental advances in the science of classical wave-matter interactions. These efforts have drawn attention to the connection between wavefront topology and wave-mediated forces, including the interrelated roles of orbital and spin angular momentum, and the interplay between conservative intensity-gradient forces and non-conservative phase-gradient forces. Holographically structured force landscapes can act as knots, micromachines and even tractor beams and have permeated application areas ranging from biomedical research to quantum computing. Lessons learned from holographic optical trapping recently have been applied to acoustic micromanipulation, with remarkable effect. Beyond an overall leap in the force scales that can be achieved with sound, advances in acoustic trapping are casting new light on the nature of wave-matter interactions, including the role of nonreciprocal wave-mediated interactions in creating novel states of organization. 

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. 

We review highlights of our recent contributions to understanding the propagation dynamics and transverse orbital angular momentum of optical pulses carrying spatiotemporal optical vortices (STOVs). STOVs, which were first observed as an emergent phenomenon in nonlinear self-focusing, were first linearly generated using a 4𝑓 pulse shaper and measured using transient-grating single-shot supercontinuum spectral interferometry (TG-SSSI). That STOV-based transverse orbital angular momentum (OAM) is carried at the single photon level was then confirmed in measurements of OAM conservation in second harmonic generation. Our recent theory for the electromagnetic mode structure and transverse OAM of STOVcarrying pulses in dispersive media predicts half-integer OAM and the existence of a transverse OAM-carrying quasiparticle: the bulk medium STOV polariton. 

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. 

When situations make it diffcult for students to be physically present in the laboratory, there is a need to provide remote instructional offerings. This is a particularly acute problem in upper-level physics laboratories because they involve the use of sophisticated equipment for the investigation of advanced topics. The possibility of automating such experiences presents itself as a possible solution. In this article I present the offering of an automated quantum optics lab for advanced physics students. I do so by automating the laboratory components via actuators and sensors controlled through serial connections. Live images of the laboratory provide visual inspection of the apparatus and sensors. All of these components are connected to a personal computer that students can control by remote access. The experience provides a new paradigm for experimentation, giving students experience on laboratory work with a remote apparatus at fexible times, making the experiment a form of homework assignment. 

We use a spatial light modulator (SLM) to mimic the e ect of gravity and steer the light from a laser to observe Einstein rings with a laboratory camera. The derived programming of the phase of the SLM follows a logarithmic dependence with impact parameter. As expected, we also observe arcs when the source and lensing object are not in line with the observer. Measurements for distinct parameters are consistent with the expectations. The coherent optical beams that are programmed to follow gravitational lensing trajectories have a transverse mode consistent with Bessel functions, yet they do not exhibit the non-di racting properties of Bessel beams: they expand linearly with the propagation distance. The addition of a vortex phase also produces patterns that coincide with Bessel modes of order given by the topological charge of the vortex.