Parameter trajectory engineering for state transfer and quantum sensing in non-Hermitian two-level systems

Abstract

Exceptional points (EPs) in non-Hermitian systems give rise to enhanced sensitivity and chiral state transfer, which are important for quantum technologies. Although parameter trajectories encircling EPs can control symmetric and chiral state transfer, their robustness against practical perturbations and their role in quantum sensing remain largely unexplored. Here, we study three time-modulated parameter loops in a non-Hermitian two-level system to show how trajectory design governs state-transfer symmetry, robustness, and sensing performance. Trajectories avoiding the EP support robust symmetric transfer, while those encircling the EP yield chiral transfer governed by the topological winding number, whose robustness depends on the distance to the EP and the encircling direction. For quantum sensing, trajectory engineering enables tuning of sensitivity amplitude, time window, and parameter selectivity in both eigenvalue-based and eigenstate-based sensors. Notably, eigenstate-based sensing achieves full parameter selectivity that is unattainable with eigenvalue-based methods. Our results establish a quantitative connection between trajectory topology and system dynamics, providing a unified framework for robust state-transfer protocols and high-performance quantum sensors.

Figures (7)

• Figure 1: Time evolution of the fidelities $F_{\pm}(t)$ for the three trajectories under (a)-(c) CCW and (d)-(f) CW encirclement. The initial state is $|\phi_{+}(0)\rangle$, and the trajectories' parameters have been set in Eqs. (\ref{['eq:traj1']})-(\ref{['eq:traj3']}).
• Figure 2: Final fidelity $F_{+}(T)$ after a full period $T=2\pi/\omega$ for the three trajectories under (a)-(c) CCW and (d)-(f) CW encirclement. The white cross marks the starting/ending point and the initial state is $|\phi_{+}(0)\rangle$.
• Figure 3: Winding number $\nu(\Gamma)$ for the three trajectories under (a)-(c) CCW and (d)-(f) CW encirclement. The white cross marks the same starting point as in Fig. \ref{['fig:fidelity_var']}.
• Figure 4: Real and imaginary parts of the energy splitting $\Delta_E(\theta)$ and susceptibility $\chi(\theta)$ as functions of the scaled time $\theta/\pi$ for small perturbations of control parameters. (a) Trajectory 1 with $G_0$ perturbation ($G_0^{\text{I}} = 0.11$); (b) Trajectory 2 with $\Gamma_0$ perturbation ($\Gamma_0^{\text{I}} = 0.2$); (c) Trajectory 3 with $G_0$ perturbation ($G_0^{\text{I}} = 0.15$). Other parameters are given in Eqs. (\ref{['eq:traj1']})-(\ref{['eq:traj3']}).
• Figure 5: Same as Fig. \ref{['fig:E']}, but evaluated at the fixed scaled time $\theta/\pi=1$.