Grover-Sagnac interferometer

We demonstrate a nontraditional design of the Sagnac interferometer by replacing the commonly used beam splitter with a linear-optical Grover multiport. This substitution creates a pole at the origin of the device parameter space, with an associated resonance in the output intensity. The structure of this resonance is dictated only by the nonreciprocal portion of the phase acquired in the Sagnac loop. This property directly results from adopting the more symmetric and higher-dimensional central scattering coin, and it allows for a different approach to registering and detecting the nonreciprocal Sagnac phase. This parameter may be extracted from the width of a peak or dip in the interferogram, instead of tracing small changes in power as in traditional Sagnac interferometry. We discuss how losses affect the system and potential metrological applications.