Enhanced quantum sensing in time-modulated non-Hermitian systems

TL;DR

This paper addresses enhanced quantum sensing in time-modulated non-Hermitian systems by proposing two schemes that exploit eigenvalue and eigenstate coalescence in a driven two-level NH sensor. It analyzes the full energy spectrum, eigenstate populations, and optimal timing windows, showing up to a 9.21-fold improvement for eigenvalue-based sensing near EPs and up to a 50-fold improvement for eigenstate-based sensing, with divergent susceptibility even away from EP in the latter. The results demonstrate a time-dependent pathway to surpass Hermitian sensors and match or exceed existing time-independent NH sensors, highlighting practical routes for high-sensitivity measurements in open quantum systems. The work also discusses experimental feasibility in photonic and solid-state platforms and outlines potential extensions to multi-mode and Liouvillian-based sensing frameworks.

Abstract

Enhancing the sensitivity of quantum sensing near an exceptional point represents a significant phenomenon in non-Hermitian (NH) systems. However, the application of this property in time-modulated NH systems remains largely unexplored. In this work, we propose two theoretical schemes to achieve enhanced quantum sensing in time-modulated NH systems by leveraging the coalescence of eigenvalues and eigenstates. We conduct a comprehensive analysis of the full energy spectrum, including both real and imaginary components, the population distribution of eigenstates, and various characteristics associated with optimal conditions for sensitivity enhancement. Numerical simulations confirm that eigenvalue-based quantum sensors exhibit a 9.21-fold improvement compared to conventional Hermitian sensors, aligning with the performance of existing time-independent NH sensors. Conversely, for eigenstate-based quantum sensors, the enhancement reaches up to 50 times that of conventional Hermitian sensors, surpassing the results of existing time-independent NH sensors. Moreover, the eigenstate-based sensor exhibits divergent susceptibility even when not close to an exceptional point. Our findings pave the way for advanced sensing in time-sensitive contexts, thereby complementing existing efforts aimed at harnessing the unique properties of open systems.

Figures (10)

• Figure 1: The real and imaginary parts of the energy splitting $\Delta_E(t)$ and the susceptibility $\chi(t)$ as functions of $\lambda/g_{0}$ and $\omega t/\pi$ for the NH sensor. In panels (a) and (b), the interaction strength $g_{0}$ is set to 0.02 and 0.1, respectively. Other parameters are fixed at $\Delta_{0}=0.04$, $\alpha=-1$, and $\Gamma_{0}=0.2$.
• Figure 2: The energy splitting $\Delta_E(\tau)$ and the susceptibility $|\chi_{NH}(\tau)|$ [$|\chi_{H}(\tau)|$] as functions of $\lambda/g_0$ for the NH sensor (solid black line) and its Hermitian counterpart (dotted red line), respectively. The interaction strength $g_0$ and the selected time $\tau$ are chosen as 0.02 and 0.295$\pi/\omega$ in panel (a), while 0.1 and $\pi/\omega$ in panel (b) according to Eq. (\ref{['eq1-10']}). Other parameters are set as follows: $\Delta_0 = 0.04$, $\alpha = -1$, $\Gamma_0 = 0.2$ for the NH sensor, and $\Gamma_0 = 0$ for the Hermitian sensor.
• Figure 3: The sensitivity enhancement $S_{E}$, enabled by non-Hermiticity, as a function of $\lambda/g_{0}$ for the NH sensor. The other parameters remain consistent with those in Fig. \ref{['fig-Evsg']}.
• Figure 4: The time evolution of the normalized population $P_{m}(t)$ for the time-dependent right eigenstate $|\phi_{m}(t)\rangle$$(m=+,-)$. The initial state is chosen as $|\Psi(0)\rangle = |\phi_{-}(0)\rangle$. In panel (a), the parameters are set to $g_{0}=0.01$, $\Delta_{0}=0.04$, $\Gamma_{0}=0.02$, $\omega=\pi$, and $\alpha=-1$, while in panel (b), they are set to $g_{0}=0.02$, $\Delta_{0}=0.01$, $\Gamma_{0}=0.04$, $\omega=\pi$, and $\alpha=-1$. The population of the system experiences a rapid inversion when ${\omega t}/{\pi} \approx j~(j \in \mathbf{Z}^{+})$.
• Figure 5: The normalized population $P_{+}(t,\lambda)$ of the right eigenstate $|\phi_{+}(t,\lambda)\rangle$ and the susceptibility $\chi(t,\lambda)$ of the NH sensor as functions of $\lambda/g_{0}$ at different times. In panel (a), the parameters are set to $g_{0}=0.01$, $\Delta_{0}=0.04$, $\Gamma_{0}=0.02$, $\omega=\pi$, and $\alpha=-1$, while in panel (b), they are set to $g_{0}=0.02$, $\Delta_{0}=0.01$, $\Gamma_{0}=0.04$, $\omega=\pi$, and $\alpha=-1$. The susceptibility $\chi(t,\lambda)$ exhibits extremely sharp peaks near ${\omega t}/{\pi} \approx 2k-1$ where $k \in \mathbf{Z}^{+}$.