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arXiv:2209.09414 · Physical Review A

Interferometry and higher-dimensional phase measurements using directionally unbiased linear optics

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

Published Sep 15, 2022• 11 citations
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Abstract

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.

DOI
10.1103/physreva.106.033706

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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.
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.
Summary form only given. The main features of quantum mechanics reside into interference deriving from the superposition of different quantum objects. The Hong-Ou-Mandel effect is a purely quantum phenomenon deriving from the interference of two photons. It is a consequence of the bosonic nature of light and can be observed when two identical photons impinge simultaneously on a two-port balanced beam splitter and, as a result, both are forced to exit from the same port. While current quantum optical technology enables two-photon interference both in bulk and integrated systems, simultaneous interference of more than two particles, leading to richer quantum phenomena, is still a challenging task.The emergence of integrated quantum photonics have opened exciting perspectives for the realization of scalable, miniaturized and intrinsically stable optical setups. In particular, the ultrafast laser-writing technique has proved to be a powerful tool for demonstrating new quantum integrated-optics devices, able to perform quantum logic operations as well as two-photon quantum walks. Here we report the experimental observation of threephoton interference in an integrated three-port directional coupler realized by ultrafast laser-writing. By exploiting the capability of this technique to produce three-dimensional structures, we realized and tested in the quantum regime a three-photon beam splitter, namely a tritter, which allowed us to observe bosonic coalescence of three photons [1]. Such a system can be exploited as a building block to implement a generalized class of multi-arm interferometers. We introduce the concept of 3D multi-photon interferometry [2], and we discuss their application in the context of quantum interferometry and quantum phase estimation. We propose novel geometries for integrated multi-arm interferometers based on three-port (tritter) and four-port (quarter) devices, and we discuss possible measurement protocols, based on the injection of multi-photon Fock states in this kind of multi-port devices, demonstrating relevant metrological advantages in phase-estimation tasks. Furthermore, we provide a first insight on the application of this technology in the still unexplored field of multiparameter estimation.Several other contexts may benefit from the adoption of 3-dimensional integrated interferometers realized by femtosecond laser-writing. For instance, they can be adopted for the realization of “proof-of-principle” quantum simulators [3], and, combined in a modular structure, they can be used to realize full-scale quantum simulators for large size quantum systems. The adoption of multiphoton-multimode platforms may indeed disclose the “hardto-simulate” scenario by adopting linear optics to implement a computational power beyond the one of a classical computer.
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.
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.