Interferometry with higher-dimensional gauge-symmetric optical multiports

David S. Simon, Christopher R. Schwarze, Alexander V. Sergienko

Grover multiports are higher-dimensional generalizations of beam splitters, in which input to any one of the four ports has equal probability of exiting at any of the same four ports, including the input port. In this paper, we demonstrate that interferometers built from such multiports have novel features. For example, when combined with two-photon input and coincidence measurements, it is shown that such interferometers have capabilities beyond those of standard beam-splitter-based interferometers, such as easily controlled interpolation between Hong-Ou-Mandel (HOM) and anti-HOM behavior. Further, it is shown that the Grover-based analog of the Mach-Zehnder interferometer can make three separate phase measurements simultaneously. By arranging the transmission lines between the two multiports to lie in different planes, the same interferometer acts as a higher-dimensional Sagnac interferometer, allowing rotation rates about three different axes to be measured with a single device.

Juan F. Hodelin

Christopher R. Schwarze, Anthony D. Manni, David S. Simon +2 more

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.

Dirk Bouwmeester

Marek Z-dotukowski, Anton Zeilinger, Michael Horne

Multiport beam splitters are shown to be applicable in feasible optical realizations of higher-dimensional EPR correlations, and of tests of local realism involving measurements of nondichotomic variables. These multiports permit optical realizations of any unitary operator in Hilbert spaces of arbitrary finite dimension. Thus it is shown that one is by no means constrained to entangled spin systems, and to Stern-Gerlach apparatuses. In the analysis the concept of generalized Bell numbers is employed, which is more suitable than the standard set of spin eigenvalues. The results presented here move the discussion on entangled higher-than- spin systems from the realm of gedanken experiments to real experiments.

Gregg S. Jaeger, Alexander V. Sergienko