Topological burning glass effect

We reveal a topological burning glass effect, where the local response of a system exhibits a topological quantization that is enhanced by an integer due to its environmental coupling. As a paradigmatic platform for this intriguing phenomenon, we study a central spin that is quasiperiodically driven by two incommensurate frequencies, and statically coupled to $N-1$ surrounding spins. In the strong-coupling regime, the adiabatic dynamics of the total system is readily understood to imprint on the central spin an $N$-fold enhanced topological frequency conversion between the two driving frequencies. We argue that the topological burning glass effect is induced by the nonunitary dynamics of the central spin, which locally involves the collective motion of the surrounding spins. Our results are derived in the framework of adiabatic perturbation theory and fully corroborated by exact numerical simulations.

Figure 1

Quasiperiodically driven central spin model (CSM) as a topological burning glass. A central spin (red sphere) couples in star geometry to $N-1$ surrounding spins (blue spheres). The isotropic interaction is parametrized by the homogeneous coupling constant $A$. The central spin is subjected to a static magnetic field with amplitude $B_s$ and two circularly polarized drives with incommensurate frequencies ${\omega }_1$ and ${\omega }_2$, so as to induce a topological frequency conversion.

Figure 2

Nonequilibrium phase diagram as a function of interaction strength $\mathcal{A}>0$ and frequencies ${\omega }_1=\omega$, ${\omega }_2=\gamma \omega$ for $N=5$. The mass parameter $M=1.2$ is chosen in the nontrivial topological regime (${\nu }_{\text{gr}}=1$). Provided the adiabatic dynamics is confined to the ferromagnetic ground state, the time-averaged pumping rate $P^{12}$ is proportional to the Chern number $C^{\left(0\right)}=N{\nu }_{\text{gr}}$ (red regime). Nonadiabatic excitations can result in transitions to intermediate/featureless quantum phases with pumping rates ${\overline{P}}^{12}=\frac{{\nu }_{\text{gr}}}{2\pi }{\omega }_1{\omega }_2$ (blue regime)/$P^{12}=0$ (white regime).