Two-way enhancement of sensitivity by tailoring higher-order exceptional points

Higher-order exceptional points in non-Hermitian systems have recently been used as a tool to engineer high-sensitivity devices, attracting tremendous attention from multidisciplinary fields. Here, we present a simple yet effective scheme to enhance the device sensitivity by slightly deviating the gain-neutral-loss linear configuration to a triangular one, resulting in an abrupt phase transition from third-order to second-order exceptional points. Our analysis demonstrates that the exceptional points can be tailored by a judicious tuning of the coupling parameters of the system, resulting in enhanced sensitivity to a small perturbation. The tunable coupling also leads to a sharp change in the sensitivity slope, enabling the perturbation to be measured precisely as a function of coupling. This two-way detection of the perturbation opens up a rich landscape toward ultrasensitive measurements, which could be applicable to a wide range of non-Hermitian ternary platforms.

Figure 1

(a) Schematic diagram of three-channel couplers with linear and triangular configurations. Here, $\kappa$ is the coupling between the gain (G) and the loss (L) channels and ${\alpha }_1$ (${\alpha }_2$) is the coupling between the neutral (N) channel and the gain (loss) channel. Different components of $\mathcal{PT}$-symmetric devices: (b) electronic trimer circuit (another possible configuration would be a third-order $\mathcal{PT}$-symmetric telemetry system [38] with an additional coupling capacitor $C_c$), (c) multicore fibers or PCFs, and (d) three closely spaced single-core fibers, where EPs can be tailored by controlling coupling (between gain and loss) for practical applications.

Figure 2

The real (solid curves) and imaginary parts (dashed curves) of the eigenvalues (${\lambda }_n$) as a function of the gain/loss parameter $\mathrm{\Gamma }$ for $\mathcal{PT}$-symmetric (a)–(c) triangular and (d) linear configurations. The EPs [Eq. (3)] are denoted by arrows. (e) An alternative phase-space representation of the eigenvalues and EPs. (f) Manipulation of EPs by controlling the coupling contrast $\kappa /\alpha$. Here, the red circle represents the isolated fixed EP3.

Figure 3

Bifurcation of complex eigenvalues around EPs in the presence of perturbation: (a), (b) for a linear configuration ($\kappa /\alpha =0$); (c), (d) and (e), (f) for triangular configurations with $\kappa /\alpha =0.5$ and $\kappa /\alpha =0.01$, respectively. Here, the solid red dots represent the EPs.

Figure 4

(a) Evolution of real (solid curves) and imaginary (dashed curves) parts of the eigenvalues around the EP as a function of perturbation. Sensitivity in terms of the splitting of eigenvalues $\mathrm{Re}({\lambda }_2-{\lambda }_1)/\alpha =\mathrm{\Delta }\lambda /\alpha$ against perturbations for different coupling contrasts ($\kappa /\alpha$) in (b) linear and (c) logarithmic scales. (d) Precise measurement of the strength of perturbation by locating the slope changing point ($1/2\to 1/3$) [solid red circle in (c)] as a function of $\kappa /\alpha$.