Exceptional-point-like Sensing near Hermitian Critical Points

Abstract

A non-Hermitian system at an exceptional point (EP), a specific critical point (CP) associated with the parity-time symmetric phase transition, exhibits a sublinear response to perturbation and promise unprecedented sensitivity beyond the linear-response Hermitian sensors, so far operating at the diabolic points (DP). Despite great advancements, its sensitivity enhancement is fundamentally limited by the divergent Petermann factor, intrinsically rooted in the non-Hermitian eigenvector degeneracy, and practically by the system complexity. Here, we report the CP-resulting square-root response to the refractive index change and enhanced sensitivity in a simple chiral Hermitian cavity without phase transitions. Because of the inherent eigenvector orthogonality, this CP-based Hermitian sensor exhibits an EP-like response and enhanced sensitivity, breaking the Petermann-factor limit of sensitivity in non-Hermitian counterparts. This work paves the way towards exploring the Hermitian CPs for ultrasensitive sensing outperforming both the EP- and DP-based sensors.

Figures (10)

• Figure 1: Conceptual illustrations comparing sublinear response enhanced sensing in Hermitian and non-Hermitian systems.a-d, Comparison of dynamic response $R$ (solid blue curves) and PF (dashed red curves) for the non-Hermitian EP-based sensor (a), the Hermitian DP-based sensor (b), the non-Hermitian TPD-based sensor (c) and our Hermitian CP-based sensor (d). The observable is the eigenfrequency splitting in the EP- and DP-based sensors, whereas it is the spectral-extremum splitting in the TPD- and CP-based sensors. Insets in a and b show the real parts of the system eigenvalues of the non-Hermitian and Hermitian sensors in the $\eta-\delta$ parameter space, respectively. Insets in c and d depict the spectral extremum values with respect to their average value in the $\eta-\delta$ parameter space as a and b. The black vertical dashed lines indicate the position of the EP, TPD, and CP, respectively. e, Diagram comparing non-Hermitian EP-based and Hermitian CP-based sensors. Left, EP-based sensor with a panel illustrating nonorthogonal eigenvectors. The eigenmode transmission spectra are presented. Right, CP-based sensor with a panel illustrating orthogonal eigenvectors. The overall transmission spectra are presented.
• Figure 2: Experimental setup and characterization.a Schematic of the experimental setup for the CP-enhanced Hermitian sensor. TGG, terbium gallium garnet. b, CP position ($B_\text{CP}$) of the simulated VP (orange), AP (blue), and HP (green) transmission spectra as a function of the incident polarization angle $\theta$. The purple dashed line indicates the linearly polarized light incident at $\theta = 45°$, as marked by the orange, blue and green asterisks, respectively. c-e, Experimental transmission spectra for the VP (c), the AP (d), and the HP detection (e) under different magnetic fields.
• Figure 3: Experimental observation and theoretical fitting of the CP-enhanced response to a refraction perturbation.a, Eigenfrequency and spectral-extremum splittings versus the magnetic field. The insert shows the same data in a double-logarithmic fashion. b-d, Response enhancement, $G_\text{R}$, of the CP sensor relative to the DP sensor without additional noise (b), with added laser intensity noise (c), and with background noise (d). The discrete data points and curves represent the experimental and fitting results, respectively.
• Figure 4: Comparison of noise and sensitivity. Noise amplification (a-c), sensitivity enhancement (d-f) and sensitivity (g-i) of the CP-based sensors compared to the conventional DP-based sensor in the absence of artificial noise (left panel), with added laser intensity noise (middle panel), and with background noise (right panel). Red, blue, and green data points correspond to the VP, AP, and HP measurements, respectively. Experimental data for the sensitivity, sensitivity enhancement and the noise amplification without artificial noise are fitted (see Methods for details).
• Figure 5: Experimental setups of DP- and CP-based sensors. Schematics of experimental setups for (a) the DP-based sensor measuring the eigenmode transmission spectra and (b) the CP-based sensor measuring the transmission spectra in the AP, HP, and VP spaces. FC, fiber coupler; SMF, single mode fiber; QWP, quarter-wave plate; HWP, half-wave plate; PBS, polarization beam splitter; BS, beam splitter; PD, photoelectric detector; TGG, terbium gallium garnet. The acousto-optic modulator (AOM) is used to add artificial intensity noise to the probe laser field.