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arXiv:2610.17834

Broadening the reflection band of atomic mirrors by engineering the emitter-waveguide coupling

C. -Y. Lee, G. -D. Lin, H. H. Jen, K. -T. Lin

quant-phSubmitted Oct 13, 2026• Announced Oct 14, 2026• 0 citations
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Abstract

We theoretically investigate single-photon coherent transport through a finite waveguide quantum electrodynamics (QED) array with spatially modulated emitter-waveguide couplings. By combining exact scattering calculations with spectral factorization and a semiclassical WKB analysis, we identify how the coupling profile controls the reflection bandwidth and its finite-size dependence. A Gaussian transverse displacement produces an exponential-of-Gaussian decay-rate profile that broadens the high-reflectivity window and suppresses the boundary-induced Fabry-Perot oscillations compared with a uniform array. The transmission zeros remain exactly degenerate at the atomic resonance for arbitrary positive coupling profiles at non-Bragg spacings. In contrast, the collective poles reorganize under the spatial modulation, redistributing their radiative widths and preventing individual subradiant resonances from terminating the reflection window. We further derive an algebraic 1/N scaling law for the contraction of the bandwidth toward its bulk value. The bulk bandwidth is determined by the largest local decay rate, whereas the finite-size correction increases as the profile becomes sharper, leading to an optimal profile width. These results establish spatial coupling engineering as a practical tool for designing broadband atomic mirrors in atom-nanofiber and circuit-QED platforms.

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We theoretically investigate single-photon coherent transport through a finite waveguide quantum electrodynamics (QED) array with spatially modulated emitter-waveguide couplings. By combining exact scattering calculations with spectral factorization and a semiclassical WKB analysis, we identify how the coupling profile controls the reflection bandwidth and its finite-size dependence. A Gaussian transverse displacement produces an exponential-of-Gaussian decay-rate profile that broadens the high-reflectivity window and suppresses the boundary-induced Fabry-Perot oscillations compared with a uniform array. The transmission zeros remain exactly degenerate at the atomic resonance for arbitrary positive coupling profiles at non-Bragg spacings. In contrast, the collective poles reorganize under the spatial modulation, redistributing their radiative widths and preventing individual subradiant resonances from terminating the reflection window. We further derive an algebraic 1/N scaling law for the contraction of the bandwidth toward its bulk value. The bulk bandwidth is determined by the largest local decay rate, whereas the finite-size correction increases as the profile becomes sharper, leading to an optimal profile width. These results establish spatial coupling engineering as a practical tool for designing broadband atomic mirrors in atom-nanofiber and circuit-QED platforms.
We present a scheme for achieving broadband complete reflection by constructing photonic band gap via collective atom-atom interaction in a one-dimensional (1D) waveguide quantum electrodynamics (QED) system. Moreover, we propose several strategies to further expand the ultrahigh-reflection windows, including increasing the number of atoms with separations near the Bragg distance and inducing gradient frequency modulation among the atoms. The center frequency and bandwidth of the ultrahigh-reflection window are dynamically adjustable by applying external electromagnetic field. The results here can enrich the many-body physics of the waveguide-QED system and offer a pathway for achieving broadened ultrahigh reflection in a controllable way, which can find important applications in the realms of chip-integrated band filter, quantum storage, optical switching, and wavelength-selective devices.
Abstract We explore the scattering and nonreciprocal transmission of single photons in an array of N coherently coupled two-level atoms, with only the two end atoms interacting with a waveguide at distinct spatial points. The chain serves as a giant-atom-like scatterer with internal collective modes. Using the real-space approach, analytical expressions for the scattering amplitudes are obtained. For the ideal case without atomic loss, the transmission is reciprocal and can be modulated by the relative local coupling phase, the accumulated propagation phase, the interatomic hopping strength, and the photon–atom detuning. We further observe that the oscillatory behavior of the transmission spectrum becomes more pronounced as the number of atoms increases. When atomic loss into nonguided modes is included, phase-dependent interference gives rise to dissipation-assisted nonreciprocal transmission. By appropriately tuning the phase factors, the atomic loss rate, and the hopping strength, one can achieve maximal nonreciprocity, corresponding to complete suppression of transmission for one incident direction. These results establish a flexible platform for engineering directional single-photon transport in guided-wave quantum electrodynamics.
We explore the quantum-metrological potential of subwavelength-spaced emitter arrays coupled to a one-dimensional nanophotonic waveguide. In this system, strong dipole--dipole interactions profoundly modify the collective optical response, leading to the emergence of ultranarrow subradiant resonances. Through an eigenmode analysis of the effective non-Hermitian Hamiltonian, we derive the decay rate of the most subradiant state, which, within the present model and geometry, exhibits an N−3N^{-3}N−3 scaling with even--odd oscillatory behavior in the deep-subwavelength regime. This scaling is directly observable in the single-photon scattering spectrum, enabling the detection of minute changes in atomic separation with a figure of merit that scales as $ N^3 $. The quantum Fisher information (QFI) scales as N6N^6N6 and can be closely approached by measuring spectral shifts near the steepest slope of the most subradiant resonance. These enhancements remain robust under realistic positional disorder, confirming that dipole--dipole-engineered subradiance provides a viable resource for quantum metrology. Our work bridges collective waveguide-QED physics and high-precision sensing, opening a route toward scalable quantum sensors on integrated nanophotonic platforms.
Spectrally and spatially varying ensembles of emitters embedded into waveguides are ever-present in both well-established and emerging technologies. If control of collective excitations can be attained, a plethora of coherent quantum dynamics and applications may be realized on-chip in the scalable paradigm of waveguide quantum electrodynamics (WQED). Here, we investigate inhomogeneously broadened ensembles embedded with subwavelength spatial extent into waveguides employed as single effective and coherent emitters. We develop a method permitting the approximate analysis and simulation of such mesoscopic systems featuring many emitters, and show how collective resonances are observable within the waveguide transmission spectrum once their linewidth exceeds the inhomogeneous line. In particular, this allows for near-unity and tailorable non-Lorentzian extinction of waveguide photons overcoming large inhomogeneous broadening present in current state-of-the-art implementations. As a particular illustration possible in such existing experiments, we consider the classic emulation of the cavity QED (CQED) paradigm here using ensembles of rare-earth ions as coherent mirrors and qubits and demonstrate the possibility of strong coupling given existing restrictions on inhomogeneous broadening and ensemble spatial extent. This work introduces coherent ensemble dynamics in the solid state to WQED and extends the realm to spectrally tailorable emitters.
We present an analytical theory for the most subradiant modes in a finite one-dimensional emitter array coupled to either an ideal or a nonideal waveguide. Using an effective non-Hermitian Hamiltonian together with a Bragg-edge open-boundary ansatz, we derive compact expressions for the full complex collective eigenvalues, including both the linewidths and the collective energy shifts. The linewidths of the most subradiant states exhibit the characteristic N−3N^{-3}N−3 scaling in both cases, while in the deep-subwavelength regime they display even--odd oscillations due to boundary interference. In contrast, the collective energy shift approaches a separation-dependent asymptotic value with a leading finite-size correction scaling as N−2N^{-2}N−2. These results highlight the distinct physical origins of the imaginary and real parts of the subradiant eigenvalue: Bragg-edge destructive interference controls the linewidth, whereas near-field dipole--dipole interactions dominate the collective shift. Our theory provides a transparent framework beyond the ideal-waveguide limit and opens potential applications in subradiant spectroscopy and waveguide-QED-based sensing.
We examine quantum interference effects due to absorption and emission from multiple atoms coupled to a waveguide and highlight the modifications they entail with regard to single-photon transport properties. A prominent upshot of these interference phenomena is the resonant suppression of the reflection amplitude, which leads to the observation of multiple Fano minima in the reflection spectrum. Such minima determine the points at which transparency is induced in the system. By taking recourse to the real-space Hamiltonian framework, we calculate analytically the reflectivity and transmissivity for a one-dimensional waveguide that evanescently couples to a chain of equally spaced quantum emitters. The interemitter spacing relative to the wavelength of the propagating photon, leading to a waveguide-mediated ``phase coupling'' between the atoms, is found to fundamentally affect the existence of Fano minima. For a chain of NNN atoms, the number of minima can be at most $N\ensuremath{-}1$. However, suitable choices of the phase can suppress the discernibility of the full range of roots in the reflection spectrum. A principal observation for the case of multiple emitters is the emergence of super-Gaussian characteristics close to zero detuning and, consequently, a plateau-shaped broadband spectrum in the region of high reflectivity. For a large chain size, the plateau gets transformed into a flat-topped quasirectangular profile in the frequency domain.