Dissipation-induced Nonlinear Topological Gear Switching

Abstract

Nonlinear interaction enables topological phenomena impossible in linear systems. A paradigm is nonlinear Thouless pump, where the transport of solitons can be topologically quantized even when band occupation is nonuniform. Such nonlinear quantization traditionally requires a time-periodic Hamiltonian with static nonlinearity and, much as in the linear case, is inherently independent of pumping speed. Instead, we demonstrate a dissipation-induced topological gear switching, where quantized soliton transport can be switched on and off via the adiabatic pumping speed itself. This phenomenon has no counterpart in prior conservative nonlinear pumps, nor in linear non-Hermitian pumps. Crucially, quantization here no longer requires a time-periodic nonlinear Hamiltonian; it stems from a genuinely non-equilibrium mechanism captured by an effective conservative model whose \textit{nonlinearity varies aperiodically in time}. Remarkably, a quantized nonlinear transport can be induced even when this nonlinear aperiodic driving is such that the system is pumped from the linear to nonlinear regimes. Our results open a route toward nonequilibrium nonlinear topological matter, where topological effect is dynamically reconfigurable via time-varying nonlinearities, with experimental implications for photonic, atomic, or superconducting platforms and beyond.

Figures (4)

• Figure 1: Dissipatively induced topological gear switching. Propagation of same input in (a)-(c) the conservative ($\delta=\beta=\epsilon=0$) and (d)-(f) weakly dissipative regimes ($\delta = 9 \times 10^{-4}$, $\beta = 10^{-5}$, $\epsilon = -10^{-5}$), for slow pump speeds $\nu=0.001,0.01,0.1$. Numerical results are obtained by solving Eq. (\ref{['CGLE']}) with $g = 1$ and $V_s = V_l = 25$. The initial soliton is taken as the instantaneous nonlinear eigenstate of $H_\textrm{NL}(0)$ with power $P(0) = 15.2$.
• Figure 2: Phase diagrams in (a) conservative vs. (b) weakly dissipative regimes. Solitonic displacement after first cycle is scanned as a function of $P(0)$ and pump speed $\nu$; the displacement equals one unit (zero) in the pumped (trapped) phase. Results are obtained from Eq. (\ref{['CGLE']}) with $g=1$, $V_{s,l}=25$, for $\beta$, $\delta$ and $\epsilon$ in Fig. \ref{['Fig1']}. The initial wavefunction is a nonlinear eigenstate of $H_\textrm{NL}(0)$Supple.
• Figure 3: Mechanism of topological gear switching. (a) The three lowest linear energy bands and their Chern numbers in the linear, conservative regime. (b) Time-varying effective nonlinearity $g_{\text{eff}}(\tilde{z}) P(0)$ in Eq. (\ref{['effective']}). (c) Energy $E_{\text{eff}}(z)$ and (d) center-of-mass position $\langle \tau \rangle_{\mathrm{eff}}$ of the effective instantaneous nonlinear eigenstate $\varphi_{\mathrm{eff}}(z)$. In (c), black curve denotes the dissipation-free counterpart as the reference. Other parameters are same as Figs. \ref{['Fig1']}(d))-(f).
• Figure 4: Quantized nonlinear pumping despite strongly aperiodic nonlinearity. (a1)-(a2) Quantization despite significantly deformed solitons after a cycle. Starting from a soliton ($P(0) = 12.42$), the system evolves under parameters $\delta = 10^{-3}$, $\beta = 5 \times 10^{-5}$, $\epsilon = -5 \times 10^{-5}$ and $\nu = 0.001$. (a1) $g_{\mathrm{eff}}(z) P(0)$ (blue) and $E_{\mathrm{eff}}(z)$ (red). Dashed line indicates dissipation-free counterpart. (a2) Although the soliton profile is significantly deformed after a full cycle (inset), its center of mass (black points, from Eq. (\ref{['CGLE']})) adiabatically follows the effective instantaneous soliton $\varphi_{\mathrm{eff}}(\tilde{z})$ (yellow) and exhibits quantized displacement. (b1)-(b3) Quantization despite transformation from nonsolitary to solitary solutions. For a weak bare nonlinearity $P(0) = 0.5$, the system initializes in a linear pump regime. In the conservative case, (b2) the initial wave packet disperses, whereas (b3) a soliton is dynamically formed in weakly dissipative regime. (b1) Center-of-mass displacement is not quantized in conservative regime, but quantized in weakly dissipative regimes despite fundamental changes in the excitations. Parameters: $\delta = 1.2 \times 10^{-3}$, $\beta = 6.5 \times 10^{-5}$, $\epsilon = -6.5 \times 10^{-5}$. In (b1), dotted curves denote results from Eq. (\ref{['CGLE']}); yellow curve denotes center-of-mass position of $\varphi_{\mathrm{eff}}(\tilde{z})$. All panels: $V_s = V_l = 25$.