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Higher-dimensional HOM effect and quantum state routing with directionally-unbiased linear-optical devices

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

Published Jan 1, 2024• 0 citations
Publisher

Abstract

A four-port beam-splitter only maps between two input and output modes. We introduce a more general four-port scatterer that supports a broader class of state transformations, enabling a higher-dimensional HOM effect and quantum state routing.
DOI
10.1364/cleo_at.2024.jw2a.105

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We expand the two-photon Hong-Ou-Mandel (HOM) effect onto a higher-dimensional set of spatial modes and introduce an effect that allows controllable redistribution of quantum states over these modes using directionally unbiased linear-optical four-ports without post-selection. The original HOM effect only allows photon pairs to exit in two directions in space. But when accompanied by beam splitters and phase shifters, the result is a directionally controllable two-photon HOM effect in four spatial modes, with direction controlled by changing the phases in the system. This controllable quantum amplitude manipulation also allows demonstration of a ``delayed'' HOM effect by exploiting phase shifters in a system of two connected multiport devices. By this means, both spatial and temporal control of the propagation of the two-photon superposition state through a network can be achieved.
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.