Controlling Excitation Localization in Waveguide QED Systems

TL;DR

We study how excitation localization arises in one-dimensional waveguide QED arrays, identifying geometry-induced subradiance and disorder-induced Anderson-like localization as two distinct mechanisms. The authors use time-domain simulations and spectral analysis of a non-Hermitian effective Hamiltonian to show that transverse emitter geometries, such as single- and double-Gaussian profiles, support long-lived subradiant modes even without disorder, while uniform arrays require disorder to trap population. A crossover between geometry-driven and disorder-driven localization is demonstrated, with a clear signature in double-Gaussian configurations and more gradual changes in single-Gaussian ones; system size studies show improved robustness of geometry-induced localization. The findings offer practical design principles for preserving coherence in scalable photonic networks and are relevant to current platforms including superconducting qubits, cold atoms, and quantum dots. Future work could extend to multi-excitation regimes, temporal disorder, nonlinear interactions, and chiral coupling to realize nonreciprocal localization dynamics.

Abstract

We theoretically investigate excitation dynamics in one-dimensional arrays of quantum emitters coupled to a waveguide, focusing on localization and long-time population trapping. By combining time-domain simulations with spectral analysis of an effective non-Hermitian Hamiltonian, we identify two distinct mechanisms that give rise to localization: geometry-induced subradiance and disorder-induced Anderson-like confinement. Spatially modulated emitter arrangements--such as single- and double-Gaussian transverse profiles--enable long-lived subradiant modes even in the absence of disorder, with decay rates that can be finely controlled via geometric parameters. In contrast, localization in uniform arrays emerges only when disorder breaks spatial symmetry and suppresses collective emission through interference. We track the crossover between geometric and disorder-induced regimes, finding that double-Gaussian profiles exhibit clear spatial signatures of this transition, while single-Gaussian configurations display more gradual changes. These results establish geometry and disorder as complementary tools for engineering long-lived quantum states in waveguide QED systems, with direct relevance for scalable implementations in photonic platforms.

Figures (7)

• Figure 1: Schematic of the system under consideration: a one-dimensional array of quantum emitters symmetrically coupled to a waveguide. Different transverse emitter geometries are realized by introducing position-dependent displacements $y_{\mu}.$ The coupling rate $\gamma_{0}$ is defined with respect to a reference position relative to the waveguide, as illustrated.
• Figure 2: (a) Time evolution of the remaining population in a single-Gaussian configuration for $\xi=0.1\pi,0.15\pi,$ and $0.2\pi.$ (b) Population distribution at time $\gamma_{0}t=10^{4}$ corresponding to (a). (c) Temporal behavior of the remaining population in a double-Gaussian configuration for $\xi=0.15\pi,0.25\pi,$ and $0.35\pi.$ (d) Population distribution at $\gamma_{0}t=10^{4}$ for cases in (c). (e) Eigenmodes contributing to the dynamics at $\gamma_{0}t=10^{4}$ for the single-Gaussian case with $\xi=0.2\pi;$ exactly two long-lived modes are involved. Solid and dashed lines represent the first mode and the second mode, respectively, with real and imaginary parts shown on the left and right axes. (f) Same as (e), but for the double-Gaussian configuration with $\xi=0.35\pi.$
• Figure 3: (a), (b) Decay rate of the dominant eigenmode of the non-Hermitian Hamiltonian $H_{\text{eff}}$ for emitters arranged in a single-Gaussian transverse profile [Eq. (\ref{['eq:single-gaussian']})], with $\xi=0.15\pi.$ In (a), $\sigma=0.2$ is fixed while $\eta$ is varied, showing an exponential suppression of the decay rate as $\eta$ increases. In (b), $\eta=0.05$ is fixed and the decay rate exhibits a minimum around $\sigma=0.1,$ suggesting an optimal configuration for minimizing radiative loss. (c) Colormap of the decay rate as a function of both $\sigma$ and $\eta.$ (d), (e) Decay rate of the dominant eigenmode for emitters arranged in a double-Gaussian transverse profile [Eq. (\ref{['eq:double_gaussian']})], with $\xi=0.25\pi.$ In (d), $\sigma=0.075$ is fixed and $\eta$ is varied, leading to a monotonic reduction in decay rate with increasing $\eta.$ In (e), $\eta=0.05$ is fixed and the decay rate shows a local minimum near $\sigma=0.05.$ A secondary minimum appears around $\sigma=0.35,$ configuration no longer retains the intended double-Gaussian structure. (f) Colormap of the decay rate across the $(\sigma,\eta)$ parameter space, identifying regions that support strongly subradiant dominant modes.
• Figure 4: (a) Time evolution of the total remaining population in a linearly arranged emitter array under increasing disorder. The system comprises $N=101$ uniformly spaced emitters with inter-emitter spacing $\xi=0.15\pi$ and zero transverse displacement. (b) Spatial population distributions at $\gamma_{0}t=10^{4}$ for selected disorder strengths. Parameter values and color coding match those used in (a).
• Figure 5: (a) Time evolution of the total remaining population for emitters arranged in a single-Gaussian transverse profile, with parameters $\eta=0.05,\sigma=0.2,N=101,$ and $\xi=0.15\pi.$ Moderate disorder reduces the effect of geometry-induced localization, while stronger disorder restores trapping via disorder-induced localization. (b) Population distributions at $\gamma_{0}t=10^{4}$ for selected disorder strengths. In the absence of disorder, spatial modulation of the coupling leads to geometry-induced localization near the center of the array. Parameter values and color coding match those used in (a).