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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. 

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.