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Physical Review A

Reservoir engineering for nonreciprocal photon coupling in three-dimensional helical waveguides

Yuan Liu, Shuyi Wang, Linhan Lin

Published Mar 25, 2025• 4 citations
Publisher

Abstract

A three-dimensional (3D) photonic waveguide array is proposed to simulate the concept of reservoir-engineering-induced nonreciprocal transmission. The reservoir is offered by coupling two optical modes simultaneously to an additional mode with loss, yielding a jump operator, which is a coherent superposition of annihilation operators of these two modes. The waveguides are helically curved, leading to a synthetic gauge field for the propagating photons and consequently an adjustable phase factor for the jump operator. The unidirectional coupling is derived analytically and verified numerically, and an intuitive interpretation is provided. Furthermore, the model is extended to a periodic lattice, where asymmetric hopping arises and unidirectional hopping appears for certain Bloch wave vectors. Our design is based on real-experiment parameters, which can be readily implemented by femtosecond laser direct writing of 3D waveguides in silica.

DOI
10.1103/physreva.111.033528

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A three-dimensional (3D) photonic waveguide array is proposed to simulate the concept of reservoir-engineering-induced nonreciprocal transmission. The reservoir is offered by coupling two optical modes simultaneously to an additional mode with loss, yielding a jump operator, which is a coherent superposition of annihilation operators of these two modes. The waveguides are helically curved, leading to a synthetic gauge field for the propagating photons and consequently an adjustable phase factor for the jump operator. The unidirectional coupling is derived analytically and verified numerically, and an intuitive interpretation is provided. Furthermore, the model is extended to a periodic lattice, where asymmetric hopping arises and unidirectional hopping appears for certain Bloch wave vectors. Our design is based on real-experiment parameters, which can be readily implemented by femtosecond laser direct writing of 3D waveguides in silica.
We present a novel photonic crystal waveguide, engineered to support broadband modes with circular in-plane polarization. We show experimental evidence that for single-photon emitters with circular dipoles these waveguides act as near-lossless unidirectional photonic reservoirs, where the emission direction is given by the helicity of the dipole. This directional coupling has a strong effect on the scattering of single photons transmitted through the system and we discuss how counter-propagating photons acquire a relative phase of π. Combining this effect with photonic structures that can map a phase to a propagation path, we show how one can create nonreciprocal photonic elements.
We show that nonreciprocal unidirectional single-photon quantum transport can be achieved with the photonic Aharonov-Bohm effect. The system consists of a 1D waveguide coupling to two three-level atoms of the V-type. The two atoms, in addition, are each driven by an external coherent field. We show that the phase of the external coherent field provides a gauge potential for the photon states. With a proper choice of the phase difference between the two coherent fields, the transport of a single photon can exhibit unity contrast in its transmissions for the two propagation directions.
Up to now it remains challenging to couple photons from a circularly polarized emitter into a photonic structure to simultaneously realize strong photon-emitter interaction and unidirectional propagation locked by local helicity of the optical mode at the nanoscale. In this paper we propose a unique approach that combines a photonic crystal and metallic nanoparticle structure to create nanocavities with both strong local-field intensity and high helicity. In this system the rate of circularly polarized photons emitting into the photonic crystal waveguide reaches $148{\ensuremath{\gamma}}_{0}$, which is one order of magnitude larger than that without the nanoparticle, and in the ultranarrow band-edge mode the linewidth of Rabi splitting spectra is about one-tenth of that with the nanoparticle only, both with $\ensuremath{\approx}95%$ of photons propagating unidirectionally along the nanoscale waveguide. We suggest that our paper establishes a nanophotonic interface of chiral quantum electrodynamics for on-chip nonreciprocal quantum light sources, quantum circuits, and scalable quantum networks.
We demonstrate nonreciprocal optical transmission for both intense classical fields and weak quantum signals within a reconfigurable optomechanical platform driven by three-mode parametric interactions. The platform is modular, where each three-mode optomechanical system serves as a fundamental building block. Operating independently, a single block achieves nonreciprocity for classical fields. Specifically, asymmetric radiation pressure from intrinsic optomechanical nonlinearity induces nonreciprocal mechanical displacement, modulating the cavity intensity through optomechanical feedback. This enables full isolation of backward transmission without requiring parameter initialization. Alternatively, for quantum signals, the platform is reconfigured by activating photonic and phononic exchange channels between the two blocks. In this configuration, nonreciprocity arises from quantum interference between direct photon hopping and indirect conversion pathways. Constructive interference enables unidirectional low-loss transmission, while destructive interference completely suppresses the reverse direction. After adiabatically eliminating the auxiliary modes, the optimal nonreciprocal frequency and the trade-off between insertion loss and nonreciprocal bandwidth can be controlled by engineering optomechanically induced mechanical dissipation. Additionally, the three-mode-based device requires less control-field power than two-mode systems under resolved-sideband conditions, demonstrating versatile potential for optical nonreciprocity applications across classical and quantum domains.
We propose and analyze a general scheme to engineer programmable and nonreciprocal interactions in an array of atoms coupled to a photonic waveguide. By subjecting each atom to a local harmonic frequency modulation with a defined phase ${\ensuremath{\theta}}_{i}$, we demonstrate the emergence of effective long-range couplings whose parameters are dynamically controllable. For atoms coupled to a conventional waveguide, the modulation dresses the atomic operators, leading to effective interactions governed by the Bessel function J0{\mathcal{J}}_{0}J0​ whose argument depends on the phase differences $\mathrm{\ensuremath{\Delta}}{\ensuremath{\theta}}_{ij}$. For atoms coupled to a photonic crystal waveguide near its band edge, where the density of states is sharply varying, the modulation can be tuned to selectively activate the J12{\mathcal{J}}_{1}^{2}J12​ term, which simultaneously scales both the coherent and dissipative components of the complex coupling strength ${\mathrm{\ensuremath{\Gamma}}}_{ij}$. Crucially, the spatial profile of the local modulation phases imprints a factor $exp(\mathrm{i}\mathrm{\ensuremath{\Delta}}{\ensuremath{\theta}}_{ij})$ onto the waveguide-mediated coupling strength ${\mathrm{\ensuremath{\Gamma}}}_{ij}$, enabling the synthesis of nonreciprocal quantum interactions. Our approach thus provides a flexible toolbox for simulating a wide range of non-Hermitian Hamiltonians on waveguide-QED platforms.
Electromagnetically induced transparency (EIT) in ΛΛΛ-type atomic systems underpins quantum technologies such as high-fidelity memory and nonlinear optics, but conventional setups face intrinsic limitations. Standard geometries of one-dimensional atomic chains coupled to waveguides allow only a single bright superradiant channel, while subradiant modes remain weakly accessible, limiting control over collective radiative behavior and dark-state pathways. This leads to unwanted inelastic processes, degrading memory fidelity and reducing nonlinear photon generation efficiency. Here, we propose two two-dimensional (2D) atomic lattice geometries coupled to a photonic crystal waveguide, namely Zigzag and Orthogonal structures. In the Zigzag model, engineered collective super- and subradiant modes produce a flattened EIT window, broadening the transmission bandwidth and suppressing unwanted scattering to enhance quantum memory fidelity. In the Orthogonal model, four-wave mixing (FWM) intensity is amplified by up to six orders of magnitude relative to a conventional one-dimensional ΛΛΛ-type EIT chain with identical Γ1DΓ_{1D}Γ1D​, ΩcΩ_cΩc​, and probe intensity, with localized idler photons forming well-defined spectral modes. These results demonstrate a versatile route to engineer structured photonic reservoirs for on-demand photon generation, high-fidelity quantum storage, and enhanced nonlinear optical processes.