The investigation of multi-photon quantum interference in symmetric multi-port splitters is attracting an increasing interest, both from a fundamental and an applicative perspective. In fact, simple laws have been identified recently that apply to interferometers implementing the Fourier or the Hadamard transform over the modes, predicting the suppression of a large number of possible output states. Such laws generalize the well-known Hong-Ou-Mandel effect to the case of many photons and optical modes, and they could be conveniently exploited, experimentally, to assess the indistinguishability of single-photon sources. Symmetric multi-port interferometers have also been proposed as benchmark devices to validate Boson-Sampling machines. Photonic Boson-Samplers are devices that sample the output distribution of identical photons interfering in a linear optical network, and are believed to be good candidates for a first demonstration of a quantum task hard or impossible to simulate with classical means.
Here, we report on a novel approach to implement symmetric multi-mode interferometers with three-dimensional integrated waveguide circuits. In detail, our interferometers realize the Fourier and Hadamard transforms over the optical modes, exploiting optical implementations of the Fast-Fourier and Fast-Hadamard transform algorithms. The innovative three-dimensional layouts are made possible by the unique capabilities of the femtosecond laser waveguide writing technology.
We fabricate devices with 4 and 8 optical modes and we let two identical photons evolve in the circuit. We characterize the coincidence output distribution and we are able to observe experimentally the known suppression laws for the output states. We further characterize the robustness of this approach to assess the photons' indistinguishability and to rule out alternative non-quantum states of light. These results pave the way to the adoption of symmetric multiport interferometers as powerful tools in the diagnostics and certification of quantum photonic platforms.