A synthetic gauge field in a two-dimensional time-multiplexed quantum random walk

Time-multiplexed quantum random walk provides an efficient method to realize a quantum random walk via time delays and beam-splitters. Previously, researchers have demonstrated the control of random walk evolution based on photon’s polarization degree of freedom. In this presentation, we propose adding synthetic gauge fields for controlling the evolution of the random walk which is important to simulate a broad class of physical effects. In this platform, varied lengths of optical fibers create the time delays and the gauge fields are implemented through phase modulations. We show how different gauge fields provide the possibility of opening band gaps in the band structure. The presence of these bandgaps leads to the pseudo magnetic confinement of the random walk distribution. We present the theoretical predictions and experimental observations of this confinement. We also demonstrate the possibility of creating edge states by applying different gauge fields to different regions of the synthetic space. The experimental results confirm the confinement of the evolution of the random walk around the boundary.