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 $N^{-3}$ 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 $N^{-2}$ . 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 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 $N^{-3}$ 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 $N^{-2}$. 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.

quant-pharXiv:2604.03954Apr 7, 20260 citations

Many-body Schroedinger equation in the collective variables

A.K. Petrauskas, L.Yu. Sabalyauskas

Oct 1, 19740 citations

Interference‑Protected Subradiance and Bound States in Nested Atomic Arrays

Bella Santosa, Daniel Leykam

Collective subradiant states in waveguide QED are highly sensitive to disorder, limiting their scalability and robustness. We propose a deterministic approach to engineering atom arrays based on a Minkowski sum construction, generating quasi‑disordered structures with built‑in correlations. This leads to mode-selective radiative coupling: interactions between dark modes are parametrically suppressed, while bright modes can hybridize. We study the stability of these subradiant and bound‑state‑like modes against moderate positional disorder. Our work provides a route to robust, analytically controllable subradiance through engineered quasi‑disorder, with direct relevance to atom–waveguide and circuit‑QED experiments.Collective subradiant states in waveguide QED are highly sensitive to disorder, limiting their scalability and robustness. We propose a deterministic approach to engineering atom arrays based on a Minkowski sum construction, generating quasi‑disordered structures with built‑in correlations. This leads to mode-selective radiative coupling: interactions between dark modes are parametrically suppressed, while bright modes can hybridize. We study the stability of these subradiant and bound‑state‑like modes against moderate positional disorder. Our work provides a route to robust, analytically controllable subradiance through engineered quasi‑disorder, with direct relevance to atom–waveguide and circuit‑QED experiments.

Apr 11, 20260 citations

Interference-Protected Subradiance and Bound States in Nested Atomic Arrays

Bella Santosa, Daniel Leykam

Collective subradiant states in waveguide QED are highly sensitive to disorder, limiting their scalability and robustness. We propose a deterministic approach to engineering atom arrays based on a Minkowski sum construction, generating quasi-disordered structures with built-in correlations. This leads to mode-selective radiative coupling: interactions between dark modes are parametrically suppressed, while bright modes can hybridize. We study the stability of these subradiant and bound-state-like modes against moderate positional disorder. Our work provides a route to robust, analytically controllable subradiance through engineered quasi-disorder, with direct relevance to atom-waveguide and circuit QED experiments.Collective subradiant states in waveguide QED are highly sensitive to disorder, limiting their scalability and robustness. We propose a deterministic approach to engineering atom arrays based on a Minkowski sum construction, generating quasi-disordered structures with built-in correlations. This leads to mode-selective radiative coupling: interactions between dark modes are parametrically suppressed, while bright modes can hybridize. We study the stability of these subradiant and bound-state-like modes against moderate positional disorder. Our work provides a route to robust, analytically controllable subradiance through engineered quasi-disorder, with direct relevance to atom-waveguide and circuit QED experiments.

quant-pharXiv:2604.10197Apr 14, 20260 citations

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^{-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.