Synchronized Aharonov-Bohm Motifs via Engineered Dissipation

Abstract

The interplay between external gauge fields and lattice geometry can induce extreme localization dynamics through complete destructive interference. We show that combining this flux-induced localization with engineered dissipation leads to robust spin synchronization in rotationally symmetric spin geometries, referred to as Aharonov-Bohm motifs, with cyclic symmetries of any order. The synchronized dynamics is independent of initial conditions and features entanglement among spins within each motif. We further demonstrate that multiple motifs can fully synchronize when coupled, which is achieved by applying additional collective dissipation acting on all intra-motif spins. These results reveal a direct connection between flux-induced localization, dissipative engineering, and collective quantum synchronization.

Figures (4)

• Figure 1: Synchronized dynamics in spin motifs of different cyclic order $\mathscr C_n$ arising from the cooperative interplay between AB interference and locally applied dissipation. (a) Motif of order $n =2$ with $N=5$ spins, (b) motif of order $n=4$ with $N=9$ spins, and (c) motif of order $n=6$ with $N=13$ spins. Each motif consists of $n$ plaquettes corresponding to the cyclic order $\mathscr C_n$. When a gauge flux $\phi = \pi$ threads each plaquette and dissipation acts on the outer (pink) spins (indicated by the red discs), the local magnetization $\braket{\sigma_{\alpha}^\mathrm{z}(t)}$ of the inner (brown) spins becomes synchronized with each other and anti-synchronized with the central (blue) spin. The gray background lines show the corresponding dynamics in the absence of dissipation, starting from the same random initial conditions. Parameters: $h = 1.0$, $g = 0.3$, $\phi=\pi$, $\gamma = 0.1$ .
• Figure 2: Concurrence as a measure of entanglement during the dissipative dynamics. Panels (a) and (b) show results for the $\mathscr C_3$-symmetric motif with $N=7$ spins, and panels (c) and (d) for the $\mathscr C_6$-symmetric motif with $N=13$ spins. The top panels display the concurrence between the central spin and an inner spin $\mathcal{C}(\varrho_{ci})$, which is identical for all inner spins due to rotational symmetry. The bottom panels show the concurrence between two inner spins $\mathcal{C}(\varrho_{ij})$, also identical for all inner-spin pairs. Solid lines correspond to the analytical expressions in Eqs. (\ref{['eq:concurrenceC']})–(\ref{['eq:concurrence']}), including a numerically determined constant shift, while dashed lines show the full numerical results obtained from solving the Lindblad equation and include damped dynamics. The concurrence exhibits oscillations in time, reflecting the underlying synchronized spin dynamics. Parameters: $h = 1.0$, $g = 0.5$, $\phi =\pi$, $\gamma = 0.2$.
• Figure 3: (a) Schematic representation of three coupled $\mathscr C_3$-symmetric motifs. In addition to the intra-motif couplings, each spin in the middle motif is coupled to the corresponding spins in the top and bottom motifs (dashed lines). Collective dissipation, $L_\nu =\sqrt{\kappa} \sum_{\alpha\in \mathcal{A}} \sigma_{\alpha\nu}^\mathrm{z}$ indicated by the red outline, acts on all spins within a motif labeld by $\nu$. Panels (b)–(d) show the magnetization dynamics of the motifs shown on the left of each panel. After a short transient, the spins subject to strictly local dissipation (red discs) relax to stationary values (pink lines). The central (blue) spins become fully synchronized, both in amplitude and phase, across all three motifs. The inner (brown) spins also synchronize across motifs, with an oscillation amplitude equal to one third of that of the central spins, and evolve in anti-phase with them. Parameters: $h = 1.0$, $g = 0.3$, $\tilde{g}=0.9g$, $\kappa = \gamma = 0.2$.
• Figure 4: (a) Schematic representation of three coupled $\mathscr C_3$-symmetric motifs, which do not synchronize in the absence of collective dissipation (compared to Fig. \ref{['fig:SyncedMotifs']}a in the main text). Panels (b)–(d) show the corresponding local magnetization dynamics for the motifs depicted to the left of each panel, now without the collective intra-motif dissipation. Although local dissipation is present, the long-term dynamics exhibits no synchronization, neither across motifs nor within each motif individually. Colors match those used in Fig. \ref{['fig:SyncedMotifs']}(b–d) and the spin coloring in panel (a). Parameters: $h = 1.0$, $g = 0.3$, $\tilde{g}=0.9g$, $\kappa = 2\gamma = 0.4$.