Sensing weak anharmonicities with a passive-active anti-PT symmetric system

TL;DR

This work addresses sensing of weak anharmonicities in a cavity-magnon-waveguide setting by employing a passive-active three-mode anti-PT symmetric system. The authors leverage linewidth suppression controlled by optical gain at EP-like points to boost sensitivity to Kerr nonlinearities in both cavity and magnon modes, even with sizable losses, and show further enhancement with detuned driving. The key results include a cubic-response regime near $E_p\to0$ with sensitivities scaling as $|U|^{-5/3}$ and reported enhancements up to 4.64× at linewidth suppression and ~7× with detuning, with robust operation outside bistability. The approach generalizes to diverse platforms with intrinsic anharmonicities and offers a practical route to high-sensitivity nonlinear sensing in dissipative quantum systems.

Abstract

We propose a scheme for enhanced sensing of weak anharmonicities based on a three-mode anti-parity-time (anti-PT) symmetric cavity-magnon-waveguide system. By tuning the optical gain to the active cavity mode, the linewidth suppression point for the anti-PT symmetric Hamiltonian can be flexibly controlled even when the two dissipative magnonic modes experience strong intrinsic decay. This essential characteristic is utilized for detecting weak nonlinearities in both the cavity and magnonic modes, with both demonstrating similar high levels of sensitivity. Moreover, the sensitivity can be greatly improved with a detuned laser drive. Based on the integrated passive-active three-mode anti-PT symmetric system, the sensing scheme can be generalized to various physical systems with anharmonicities.

Figures (5)

• Figure 1: (a) Theoretical model and (b) Schematic of the cavity-magnon-waveguide setup. The microwave cavity running transverse to the waveguide interacts with two YIG spheres via the transmission line. $g_{1}$ and $g_{2}$ are the coherent coupling strengths between the active cavity mode $a$ and the two magnon modes $b_{1}$ and $b_{2}$, respectively. The magnon modes $b_{1}$ and $b_{2}$ also dissipatively couple to the cavity via the waveguides, with the rates $\Gamma$ being identical to the cavity-waveguide coupling. $\gamma_{b_{1}}$ and $\gamma_{b_{2}}$ are the damping rates of $b_{1}$ and $b_{2}$, and $\gamma_{a}=\kappa_{-}-\kappa_{+}$ denotes the effective gain of the cavity mode $a$ (i.e., the net rate defined by the difference between cavity loss and incoherent gain).
• Figure 2: (a) Real parts (eigenfrequencies) and (b), (c) imaginary parts (linewidths) of the eigenvalues for the anti-PT symmetric system (with $g=0$) plotted against $\Delta$. The EPs appear at $\Delta=\pm\sqrt{2}\Gamma$. APT denotes the anti-PT symmetric phase, and APTB represents the anti-PT symmetry broken phase. Panels (b) and (c), show the imaginary parts of the eigenvalues under the conditions of $\gamma=\Gamma$ and $\gamma=\sqrt{2}\Gamma$, respectively. The green dashed line is used to screen out the parameter conditions when the imaginary part of the eigenvalue is zero, which are marked with green crosses.
• Figure 3: (a) The rescaled cavity response $\textrm{log}_{10}x$ plotted against $\Delta$ and $\gamma$ for $U_{a}/2\pi=1\textrm{ nHz}$ and $\Delta_{a}=0$. The blue dashed line delineates the boundary of the unstable region and corresponds to the set of linewidth suppression points. (b) The cavity responses plotted against $\Delta$ with different nonlinearity strengths $U_{a1}/2\pi=0.1\textrm{ nHz}$ and $U_{a2}/2\pi=1\textrm{ nHz}$ and two different drive powers. Here we have set $\gamma=\sqrt{2}\Gamma$, $\Delta_{a}=0$, $P_{1,in}=8$$\mu$W, and $P_{2,in}=8$ mW. At $\Delta=0$, the peak in the cavity response arises from linewidth suppression. For comparison, the green- and blue-dotted curves have been scaled up by 10. (c) The ratio $\eta$ as a function of $\Delta_{a}$, at the drive power of $8\textrm{ mW}$ and $\Delta=0$ with $U_{a1}=0.1\textrm{ $\mu$Hz}$ and $U_{a2}=1\textrm{ $\mu$Hz}$. The monostable regime and bistable regime are denoted by the pink solid line and dotted line, respectively. The horizontal dashed line represents the response enhancement factor of 4.64, corresponding to the sensitivity at the linewidth suppression condition. Other parameters are: $\Gamma/2\pi=1\textrm{ MHz}$, $\kappa_{-}=0.05\Gamma$, $\lambda_{d}=1550\textrm{ nm}$, $\Omega=\sqrt{P_{j,in}\kappa_{-}/\hbar\omega_{d}}$.
• Figure 4: The cavity responses plotted against $\Delta$ in the presence of a coherent coupling $g=0.03\Gamma$ with drive powers (a) $8\textrm{ $\mu$W}$ and (b) $8\textrm{ mW}$. Other parameters are the same as in Fig. \ref{['Response1']}(c).
• Figure 5: (a) The magnon spin-current responses plotted against $\Delta$ for $\gamma=\sqrt{2}\Gamma$ with weak Kerr nonlinearity strengths $U_{b_{1}1}/2\pi=0.1\textrm{ nHz}$ and $U_{b_{1}2}/2\pi=1\textrm{ nHz}$. The green- and blue-dotted curves have been scaled up by 10. The spin-current responses show similar behavior to those in sensing weak cavity nonlinearity. (b) $\eta$ as a function of $\Delta_{a}$, at the drive power of $8\textrm{ mW}$ for two different nonlinearity strengths $U_{b_{1}1}=0.1\textrm{ $\mu$Hz}$ and $U_{b_{1}2}=1\textrm{ $\mu$Hz}$. The monostable regime and bistable regime are denoted by the pink solid line and dotted line, respectively. The horizontal dashed line represents the response enhancement factor of 4.64, corresponding to the sensitivity at the linewidth suppression condition. Other parameters are the same as Fig. \ref{['Response1']}(c).