Synchronization-induced flat bands in driven-dissipative dimer-waveguide chains

Abstract

Flat bands in driven-dissipative systems offer a route to engineer strongly localized, long-lived excitations, yet their selective population via incoherent pumping remains an open challenge. We study a one-dimensional chain of coupled lasing dimers arranged in a cross-stitch geometry and show that the synchronization regime of the individual dimers, controllable through pump intensity or inter-resonator distance, determines the character of the flat band hosted by the chain. In the in-phase (ferromagnetic) regime, the flat band appears as a subdominant, damped mode in the linear excitation spectrum. In the antiphase (antiferromagnetic) regime, by contrast, the dimers decouple and the flat band becomes the dominant, neutrally stable mode: it corresponds to an infinite family of Goldstone modes arising from the independent phase rotations of non-interacting dimers, and its compact localized states are directly observable in the noise response spectrum. Switching between these two regimes via pump control constitutes a pump-induced phase transition of the lasing lattice. Our results establish synchronization engineering as a practical mechanism for selective flat-band population in driven-dissipative optical systems, and open new avenues for studying flat-band physics, including nonlinear effects, Fano resonances, and excitation coherence in experimentally accessible laser and polariton platforms.

Figures (4)

• Figure 1: (a) Schematic illustration of a single laser dimer consisting of two lasing resonators described by order parameters $\psi_{B}$ and $\psi_{C}$, coupled to a waveguide $A$. A standing wave inside the waveguide has a node at the center, corresponding to the antisymmetric configuration $\psi_C = -\psi_B$. (b) Schematic illustration of a chain of laser dimers coupled to a common horizontal waveguide $W$. Real (c) and imaginary (d) parts of the linear excitation spectrum derived from Eq. \ref{['chain equation']} with respect to the trivial solution, computed for the following parameters: $J=-0.1$, $P=2$, $g=1$, $\alpha = 1$, $\kappa = -1$, $|\zeta| = 0.02$, $\chi = -0.5$.
• Figure 2: Synchronization regimes in a single laser dimer. (a) The Stokes parameter $S_1 = 2\operatorname{Re}[\psi_B\psi_C^*]$ from Eq. \ref{['condensate equation']} as a function of the inter-spot distance $L$ at fixed pump intensity $P=2$ (black solid curve). The values $S_1 = \pm1$ correspond to in-phase ($\Delta\phi=0$) and anti-phase ($\Delta\phi=\pi$) synchronization, respectively. Red solid curve represents the effective coupling parameter $J_\textrm{eff}$ derived from Eq. \ref{['Kuramoto approximation']}. (b) $S_1$ and $J_\textrm{eff}$ as functions of the pump intensity $P$ for a fixed inter-spot distance $L\approx 2.2$. Other parameters of the model are listed in Sim_parameters.
• Figure 3: Linear excitation spectra of the chain described by Eq. \ref{['chain equation']}. Real (a,b) and imaginary (c,d) parts of the modes as functions of the wave number $k$ for different pump intensities: weak lasing $P = 0.9$ (dashed lines), moderate pump $P = 2$ (solid lines), and stronger pump $P = 5$ (clubs). Panels (a) and (c) show the spectra for $J = -0.1$, corresponding to the dimers in the antisymmetric configuration ($\Delta\phi=\pi$). Panels (b) and (d) are for $J = 0.1$, corresponding to the dimers in the symmetric state ($\Delta\phi=0$). (e) Noise response spectrum for the chain of noninteracting antisymmetric dimers with equal phases. (f) Noise response spectrum for the chain of interacting phase-locked ferromagnetic dimers. We used $g=1$, $\alpha = 1$, $\kappa = -1$, $\zeta = 0.02$, $\chi = -0.5$.
• Figure 4: Dynamics of the five-dimer chain under time-varying pump intensity. (a) Waveguide field intensity $|W|^2$ as a function of distance $y$ and time $t$. White dashed lines indicate the positions of the lasing dimers along the waveguide. (b) Total density $I(t) = |\psi_B(t)|^2 + |\psi_C(t)|^2$ of the central dimer as a function of time (the other dimers exhibit similar behavior). The color of the curve reflects the value of the Stokes parameter $S_1$: blue corresponds to $S_1 = -1$ (antiphase dimer configuration), while red corresponds to $S_1 = 1$ (in-phase dimer configuration). Black dashed line shows the time-dependent pump intensity, which changes abruptly at $t = [0, 1, 4, 5, 8, 11, 12, 13] \times 10^3$. The pumps $P = 4$, $P = 10$, and $P < 4$ correspond to $J_{\text{eff}} < 0$, whereas $P = 7$ corresponds to $J_{\text{eff}} > 0$. The parameters of the model are listed in Sim_parameters.