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arXiv:2012.08745 · Physical Review A

Higher-dimensional Hong-Ou-Mandel effect and state redistribution with linear-optical multiports

Shuto Osawa, David S. Simon, Alexander V. Sergienko

Published Dec 15, 2020• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.102.063712

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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.
Two-photon interference effects arise because photons are indistinguishable particles. In the wellknown Hong-Ou-Mandel (HOM) effect, the transmission of two photons at a beam splitter interferes destructively with the reflection of both photons, requiring both photons to "bunch up" by leaving the beam splitter on the same side. Here, we show that the interference between locally propagating photons and photons exchanged by a mode swap can be implemented by post-selecting spatially separated photon outputs of a four-path interferometer. Even though the photons detected at spatially separated locations must have travelled along paths that never met up at the same beam splitter, the Hong-Ou-Mandel effect can be observed in correlations between the output ports that originate from the association of detection events with non-local output modes defined by the two single photon inputs. Local phase shifts can be used to map out non-classical correlations between the photons detected at different output locations, clarifying the role of linear optics in generating entanglement between spatially separated photons. Our work thus establishes a fundamental relation between multiphoton interference and entanglement, opening the door to new possibilities in optical quantum technologies.
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.
The progress in modern quantum information processing (QIP) strongly depends on new algorithms and on the development of novel quantum entanglement processing elements enabling to perform quantum computation and quantum simulation effectively. Several examples of quantum information processing applications based on freshly designed linear-optics devices are presented. A beam splitter (BS) is a central device in linear-optical quantum information processing because it can split the incoming photon amplitudes into spatially distinct modes to establish conditions for quantum superposition. The BS naturally possesses directional-bias in a sense that incoming photons can only propagate in a forward manner. When the execution of certain quantum information tasks would require multiple operations, this directionality condition becomes a serious obstacle by creating significant overhead in the number of needed elements and other supporting devices. We introduce a family of amplitude-controllable fully-reversible linear-optical quantum information processors, called directionally-unbiased linear-optical multiports, in order to achieve significant reduction in the number of required hardware. The theoretical analysis of the device design as well as the experimental realization of three-port unit using bulk linear optics is demonstrated. These devices offer several fresh approaches in quantum-walk-based applications such as quantum simulation of solid-state Hamiltonians, topological protection of polarization qubits against errors, and quantum communication. Topological photonics is an emerging and actively developing field because of its capability to stabilize and protect some quantum states from perturbation errors by ensuring the environment carries a distinct topological signature. Topology-dependent quantum information processing is globally stable due to the entire system being engaged in the information manipulation. We demonstrate suppression of quantum amplitude transfer between two distinct bulk regions of a system. This results in error avoidance for a two-photon polarization-entangled state under specific conditions. The goal of modern quantum communication is a reliable distribution of quantum entanglement between multiple nodes performing quantum operations such as quantum memories and quantum computers. We demonstrated that local quantum information processing using new fully-reversible four-port linear-optical structures could find an immediate application in quantum communication. A quantum information routing device is introduced based on the use of four-dimensional Grover matrices and beam splitters. Several multiport-based units are developed to demonstrate new higher-dimensional Hong-Ou-Mandel (HOM) effect and directionally-controllable entangled state distribution while changing only phases in a waveguided unit. Several such operational elements could be linked to form a reconfigurable network of quantum users without losing control of quantum amplitudes. This allows controllable routing of entangled photons and sharing entanglement between any designated users in the future quantum computational networks.