Enhancement of quantum sensing in a dissipatively coupled two-mode system

TL;DR

The paper addresses how to realize robust, EP-enhanced quantum sensing in a practical two-mode non-Hermitian system. It analyzes a dissipatively coupled, anti-PT symmetric platform using Lindblad dynamics and quantum Langevin equations to derive the effective Hamiltonian and its EPs, identifying a second-order pole at the EP that yields a quadratic scaling of the frequency sensitivity, $\delta\omega \propto \omega^2$. It characterizes the sensitivity across unbroken, broken, and EP regimes via the quantum Cramér-Rao bound, showing linear scaling away from EPs and a pronounced quadratic enhancement at the EP. The authors argue for experimental feasibility across multiple platforms and highlight the approach as a post-selection-free path to high-precision quantum sensing in scalable photonic and superconducting systems.

Abstract

Quantum sensing near exceptional points (EPs) in non-Hermitian systems has shown promising sensitivity enhancements. However, practical applications are often hindered by structural complexity and strict parameter constraints. In this work, we introduce a simplified anti-parity-time (anti-PT) symmetric platform consisting of two independently cavities, which are indirectly coupled to each other by a shared dissipative environment. We demonstrate a significantly enhanced sensing response at the EPs compared to non-EP configurations. This improvement is attributed to the dominant second-order term in the Laurent series expansion of the eigenvalue response to external perturbations- a characteristic feature of higher-order singularities at EPs. This mechanism not only reinforces the foundation for sensitivity enhancement but also offers a structurally compact and robust strategy for quantum sensing. Our results underscore the potential of anti-PT symmetric systems in enabling high-precision sensing technologies and bridging non-Hermitian physics with scalable photonic device platforms.

Figures (6)

• Figure 1: Two separated modes ($a$ and $b$) interact with each other indirectly via the symmetric dissipation channel. Furthermore, each mode exhibits their intrinsic loss ($\gamma_{a}$ and $\gamma_{b}$) and the additive probe channel (Channels $1$ and $2$).
• Figure 2: Eigenvalues $\lambda_{\pm}$. The black solid lines represent the real part of $\lambda_{\pm}$, and the blue dashed lines give the imaginary part of $\lambda_{\pm}$. The points at which the eigenvalues become degenerate are the EPs of the system, i.e., $\delta=\pm2\Gamma$. The region (green area) between two EPs corresponds to the unbroken anti-PT symmetric phase.
• Figure 3: The magnitude of $\omega_{\pm}^2$ in anti-PT symmetric unbroken region. (a) The positive branch of the expression for $\omega_{+}^2$, and the red elliptical line denotes the relationship in Eq. \ref{['eq18']}. (b) The negative branch of $\omega_{-}^2$, and the two red points are $\gamma_0/\Gamma=-1$ and $\delta/\Gamma=\pm 2$.
• Figure 4: QCRB with a perturbation $\epsilon$. The black dashed line represents the system is at the EPs with $\epsilon=0$. The upper part with $\epsilon>0$ indicates the system is in the anti-PT symmetric broken phase. And the down part with $\epsilon<0$ indicates the system is in the anti-PT symmetric unbroken phase.
• Figure 5: QCRB in different situations. The solid line of purple triangle represents the case $\delta=(2+10^{-1})\Gamma$, the dotted line of red square corresponds to condition $\delta=2\Gamma$, and the green circle dotted line shows the result under condition $\delta=(2-10^{-1})\Gamma$.