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arXiv:2209.14837 · Physical Review Research

Enhanced Hong-Ou-Mandel manifolds and figures of merit for linear chains of identical microring resonators

Peter L. Kaulfuss, Paul M. Alsing, A. Matthew Smith, Joseph A. Monteleone, Edwin E. Hach

Published May 12, 2023• 2 citations
arXivHTMLPDF

Abstract

We present an exact analytic expression for the Hong-Ou-Mandel manifold (HOMM) for any number of identical microring resonators (MRRs) in a linear chain. The HOMM is the higher-dimensional manifold of solutions for which the HOM effect is obtained; for the types of MRR systems investigated in this work, it is a one-dimensional curve. We investigate the extreme stability of this HOMM, showing that the HOM effect in linear arrays of MRRs is highly robust. We further use this expression to derive three figures of merit for the HOMM of linear chains of MRRs: the minimum MRR coupling value ${\ensuremath{\tau}}_{c}$, the curvature of the one-dimensional HOMM ${\overline{\ensuremath{\xi}}}_{N}$, and the 5% tolerance in the probability for complete destructive interference to occur on the HOMM $\ensuremath{\delta}{\ensuremath{\tau}}_{N}$. We promote these metrics to characterize the pros and cons of various linear chains of MRRs and inform design and fabrication.

DOI
10.1103/physrevresearch.5.023097

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We present an exact analytic expression for the Hong-Ou-Mandel manifold (HOMM) for any number of identical microring resonators (MRRs) in a linear chain. The HOMM is the higher-dimensional manifold of solutions for which the HOM effect is obtained; for the types of MRR systems investigated in this work, it is a one-dimensional curve. We investigate the extreme stability of this HOMM, showing that the HOM effect in linear arrays of MRRs is highly robust. We further use this expression to derive three figures of merit for the HOMM of linear chains of MRRs: the minimum MRR coupling value \ensuremathτc{\ensuremath{\tau}}_{c}\ensuremathτc​, the curvature of the one-dimensional HOMM \ensuremathξ‾N{\overline{\ensuremath{\xi}}}_{N}\ensuremathξ​N​, and the 5% tolerance in the probability for complete destructive interference to occur on the HOMM \ensuremathδ\ensuremathτN\ensuremath{\delta}{\ensuremath{\tau}}_{N}\ensuremathδ\ensuremathτN​. We promote these metrics to characterize the pros and cons of various linear chains of MRRs and inform design and fabrication.
We investigate the effect of backscattering on the Hong-Ou-Mandel manifold (HOMM) that manifests in double-bus micro-ring resonators (MRRs). The HOMM represents higher-dimensional parameter solutions for the complete destructive interference of coincident detection in the HOM effect. To model the backscattering, we introduce a set of internal ‘beam splitters’ inside the ring that allow photons to ‘reflect’ into new counterpropagating modes inside the MRR. We find that the one-dimensional HOMM in MRRs investigated here is extremely robust against deterioration due to backscattering, even in a linear chain of identical MRRs. Further we find that a small amount of backscattering introduced into a chain of non-identical MRRs connected in parallel could be desirable, causing them to behave more like chain of identical MRRs.
Micro-Ring Resonators (MRRs) allow us to access the Hong-Ou-Mandel (HOM) effect at a variety of tunable parameter combinations along exact analytic solutions. This higher-dimensional space of parameters for which the HOM effect occurs constitutes what is known as a Hong-Ou-Mandel manifold (HOMM). Using a parallel series of non-identical MRRs and changing relative round-trip phase shifts between MRRs allows for the manipulation of the wavelength locations of the HOM effect. Through clever design and fabrication, we can mold the HOMM to place multiple HOM effects, or lack thereof, precisely at desired locations in wavelength. In this paper we discuss how to adjust non-identical MRR parameters to change the resulting HOMM. We also promote example designs that exhibit advantageous HOMM structures, and highlight some of the diverse possibilities that can be accessed with different circuit design. Our main examples are: 1) a wavelength division multiplexer example that matches the HOM effect locations with the already established channels to integrate with a classical communication network and 2) a HOM-based entanglement switch that allows for the rapid switching between 2-photon NOON state outputs and completely separable single photon outputs.
Quantum information processing, from cryptography to computation, based upon linear quantum-optical circuit elements relies heavily on the ability offered by the Hong-Ou-Mandel (HOM) effect to ``route'' photons from separate input modes into one of two common output modes. Specifically, the HOM effect accomplishes the path entanglement of two photons at a time such that no coincidences are observed in the output modes of a system exhibiting the effect. In this paper, we prove, in principle, that by operating a specific nanophotonic device properly, one can conditionally ``bunch'' coincident input photons in a way that is more configurable than with an ordinary 50:50 beam splitter, while maintaining the inherent scalability of such an on-chip device.
Quantum information science aims to revolutionize existing methods for manipulating data by utilizing the unique features of nonclassical physical phenomena. This control is realized over several platforms, one particular being photonics which employs state of the art fabrication techniques that achieve integrated nanocircuit components. The Hong-Ou-Mandel effect underlies the basic entangling mechanism of linear optical quantum computing, and is a critical feature in the design of nanophotonic circuits used for quantum information processing. We will present some results from an on-chip Hong-Ou-Mandel (HOM) experiment that replaces the conventional beam splitter with a more compact and highly versatile ring resonator allowing greater functionality with an expanded parameter space dubbed Hong-Ou-Mandel Manifold (HOMM). The overarching goal of this work is to demonstrate on-chip, scalable, dynamically configurable quantum-optical interconnects for integration into photonic quantum information processing devices.
The Hong-Ou-Mandel (HOM) effect, an effective two-photon interference phenomenon, is a cornerstone of quantum optics and a key tool for linear optical quantum information processing. While the HOM effect has been extensively studied both theoretically and experimentally for various photonic quantum states, particularly in the spectral domain, detailed overviews of its behaviour for structured photons - those with complex spatial profiles - under arbitrary spatial mode measurement schemes are still lacking. This tutorial aims to fill this gap by providing a comprehensive theoretical analysis of the HOM effect for structured photons, including an arbitrary mode projection on quantum interference outcomes. The tutorial also provides analytical, closed-form expressions of the HOM visibility under different measurement conditions.