Non-Hermitian Topological Sensors

We introduce and study a novel class of sensors whose sensitivity grows exponentially with the size of the device. Remarkably, this drastic enhancement does not rely on any fine-tuning, but is found to be a stable phenomenon immune to local perturbations. Specifically, the physical mechanism behind this striking phenomenon is intimately connected to the anomalous sensitivity to boundary conditions observed in non-Hermitian topological systems. We outline concrete platforms for the practical implementation of these non-Hermitian topological sensors ranging from classical metamaterials to synthetic quantum materials.

Figure 1

Left: Illustration of the non-Hermitian topological sensor (NTOS) setup consisting of a one-dimensional chain with $2N-1$ sites in open ring geometry, described by an effective NH Hamiltonian. The measurand interferes with the coupling $\mathrm{\Gamma }$ between the ends of the open ring (sites 1 and $2N-1$). The simplest measurement signal is the energy shift $\mathrm{\Delta }E$ of the lowest eigenmode. Right: exponential scaling of $|\mathrm{\Delta }E|$ with system size $N$ of the NTOS based on the NH topological insulator model Eq. (5) for different values of $\mathrm{\Gamma }$. Dots are exact numerical energies which are in striking agreement with the analytical perturbative expression Eq. (4) (solid lines). Parameters are $t_1=t_2=2\gamma =1$. In a wide parameter regime, the quotient of $|\mathrm{\Delta }E/\mathrm{\Gamma }|$ gives a good estimate for the sensitivity $\mathcal{S}$ of the NTOS.

Figure 2

Scaling of the boundary-condition induced energy shift $|\mathrm{\Delta }E|$ with system size $2N-1$ in the presence of complex disorder, for various values of $\mathrm{\Gamma }$ and system sizes up to 119 sites. Data for a single disorder realization (solid dots) are compared to a disorder average (circles) over $M={10}^4$ disorder realizations at every $N$ [49]. The disorder strength is $w=0.3$ in both plots. Solid lines indicate the perturbative result [see Eq. (4)] in the absence of disorder.