Enhancement of signal-to-noise ratio at a high-order exceptional point of coherent perfect absorption

Abstract

Exceptional points (EPs) in non-Hermitian systems offer a remarkably strong response to weak perturbations, but the nonorthogonal nature of the corresponding eigenvectors causes noise to diverge, hindering EPs practical application. Here, we report a twelve-fold enhancement of signal-to-noise ratio (SNR) in magnetic field sensing enabled by a third-order EP of coherent perfect absorption (CPA EP3) in a passive cavity magnonic system. This non-Hermitian magnonic platform comprises two identical yttrium iron garnet (YIG) spheres coherently coupled to a cavity mode, in which the CPA EP3 is realized by engineering the three-mode loss to form a pseudo-Hermitian absorption Hamiltonian. By independently tailoring the absorption EP apart from the resonance EP, the system circumvents the noise divergence caused by eigenbasis collapse. Notably, we harness the sensitivity of the minimum output intensity near CPA to perturbations, yielding a seventyfold SNR improvement and a 400-fold increase in responsivity compared with non-CPA system. A comprehensive noise analysis over one hundred repeated measurements confirms the suppression of frequency noise near the CPA EP3. This demonstrates that our scheme not only avoids the noise divergence plaguing conventional higher-order EP sensors but also provides a general strategy to exploit both CPA and EP for SNR enhancement in passive non-Hermitian systems.

Figures (4)

• Figure 1: Sensing via higher-order exceptional point of coherent perfect absorption in a cavity magnonic system.a, Left: schematic of a third-order exceptional point of coherent perfect absorption (CPA EP3) sensing, where two magnon modes (purple), with equal dissipation rates and opposite detunings $\pm\delta$, are coherently coupled to a cavity mode (orange). Two coherent probe signals are injected into the cavity, while frequency perturbations $\Delta_B$ are applied to the magnon modes. Right: Eigenvalues of $H_{\rm abs}$ (circles) and $H_{\rm res}$ (triangles) in the complex plane, where pseudo-Hermiticity enables the coalescence of three CPA solutions. b, Two 0.5 mm-diameter YIG spheres are placed in a 3D cavity, where the step motors allow both displacement and rotation. The magnetic-field distribution of the cavity mode $\text{TE}_{102}$ is shown as a color map. c,d, Real and imaginary parts of the eigenvalues of $H_{\rm abs}$ versus the coupling strength $g/2\pi$ and frequency detuning $\delta/2\pi$, illustrated by the green, orange, and purple surfaces, respectively. The black dashed curves indicate the EP2 lines, and their intersection point corresponds to the EP3 (red star). e, Eigenfrequency response of $\Omega^{\rm res}$ ($F_{\rm res}$, pink dotted) and $\Omega^{\rm abs}$ ($F_{\rm EP3}$, pink solid), Petermann factor (PF, pink dashed), together with the minimum output intensity response at CPA EP3 ($I_{\rm CPA}$, blue solid) and under normal conditions ($I_{\rm nor}$, blue dashed) versus perturbation $\Delta_B$. f, Numerically calculated output spectra versus $\Delta_p=\omega-\omega_c$ for $\Delta_B/\delta=0$ and $10^{-3}$, comparing the system operating at the CPA EP3 (purple and green lines) with the normal configuration (orange and brown dashed lines).
• Figure 2: Output spectra of the system under the third-order exceptional point of coherent perfect absorption and normal conditions.a,b, Eigenvalues $\Omega^{\rm abs}$ on the complex plane under third-order exceptional point of coherent perfect absorption (CPA EP3) (a) and normal (b) conditions, with perturbations $\Delta_B/2\pi$= 0 (circles) and 1.2 MHz (triangles). The cross on the x-axis marks $\omega_{\rm min}$ at each $\Delta_B$. The orange solid and green dashed lines represent the distances $R_{0,\pm}$ from $\Omega_{0,\pm}^{\rm abs}$ to the corresponding $\omega_{\rm min}$ at $\Delta_B/2\pi$= 0 and 1.2 MHz, respectively. c,d, Numerical calculations of $|R_0R_+R_-|^2$ versus $\Delta_B$ under CPA EP3 and normal conditions, shown in normalized linear scale (c) and logarithmic scale (d), respectively.e,f, Total output spectra versus the perturbation $\Delta_B$ under the CPA EP3 (e, $g=g_{\rm EP3}=2\pi \times 3.46$ MHz) and normal conditions (f, $g=0.9g_{\rm EP3}$). The dashed lines indicates the frequency corresponding to the minimum output intensity. g,h, Total output spectra in g and h are extracted from e and f at $\Delta_B/2\pi=0$ and $0.06$ MHz, respectively.
• Figure 3: Measured responses in frequency and minimum output intensity to magnetic-field variations.a,b, Log-log plots of the changes in frequency $\Delta_\omega/2\pi$ (a) and intensity $\Delta|S_{\rm tot}^{({\rm min})}|^2$ (b) of the minimum output spectra versus the perturbation $\Delta_B/2\pi$ under the third-order exceptional point of coherent perfect absorption (CPA EP3) and normal conditions. The slopes 1/3, 1/5, and 1 are obtained by numerical fitting with the system parameters. c,d, Response enhancement factors at the CPA EP3 for frequency (c) and minimum output intensity (d).
• Figure 4: Enhanced signal-to-noise ratio of the third-order exceptional point of coherent perfect absorption sensor.a,b, Noise quantified as the one-standard-deviation uncertainty in frequency $\sigma_\omega$ (a) and in the minimum output intensity $\sigma_{S_{\rm tot}^{\rm min}}, \sigma_{S_{11}^{\rm min}}$ (b) versus the perturbation $\Delta_B$, obtained from one hundred independent repeated measurements. Yellow and blue data correspond to single- and two-port excitations at $g=g_{\rm EP3}$, respectively. c,d, Histograms of the frequency deviations (c) and minimum output intensity deviations (d) at the $\Delta_B$ values indicated by the arrows in a and b, respectively. e,f, Signal-to-noise ratio of the third-order exceptional point of coherent perfect absorption sensor for frequency $\rho_{\omega}$ (e) and minimum output intensity $\rho_{S_{\rm tot}^{\rm min}}$ (f) plotted versus the perturbation $\Delta_B$. The left and right y-axes show the absolute and normalized values, respectively. The inset in f shows the noise reduction factor $N_{\rm CPA}$ calculated from the noise in the minimum output intensity $\sigma_{S_{\rm tot}^{\rm min}}$.