Exceptional Point-enhanced Rydberg Atomic Electrometers

Abstract

Rydberg atoms, with their large transition dipole moments and extreme sensitivity to electric fields, have attracted widespread attention as promising candidates for next-generation quantum precision electrometry. Meanwhile, exceptional points (EPs) in non-Hermitian systems have opened new avenues for ultrasensitive metrology. Despite increasing interest in non-Hermitian physics, EP-enhanced sensitivity has rarely been explored in Rydberg atomic platforms. Here, we provide a new theoretical understanding of Autler-Townes (AT)-based Rydberg electrometry under non-Hermitian conditions, showing that dissipation fundamentally modifies the spectral response and enables sensitivity enhancement via EP-induced nonlinearity. Experimentally, we realize a second-order EP in a passive thermal Rydberg system without requiring gain media or cryogenics, and demonstrate the first EP-enhanced atomic electrometer. The EP can be tuned in real time by adjusting laser and microwave parameters, forming a flexible and scalable platform. Near the EP, the system exhibits a square-root response, yielding a nearly 20-fold enhancement in responsivity. Using amplitude-based detection, we achieve a sensitivity of $22.68~\mathrm{nV cm^{-1} Hz^{-1/2}}$ under realistic conditions. Our work establishes a practical, tunable platform for EP-enhanced sensing and real-time control, with broad implications for quantum metrology in open systems.

Figures (4)

• Figure 1: System model for observing EPs in Rydberg atomic ensembles. (a) Energy-level diagram of a four-level Rydberg system driven by probe ($\Omega_{\mathrm{p}}$), coupling ($\Omega_{\mathrm{c}}$), and MW ($\Omega_{\mathrm{L}}$) fields. The probe and coupling lasers form a ladder-type EIT via $|1\rangle \leftrightarrow |2\rangle \leftrightarrow |3\rangle$, while the MW field couples Rydberg states $|3\rangle \leftrightarrow |4\rangle$. Detunings $\Delta_{\mathrm{p}}$, $\Delta_{\mathrm{c}}$, $\Delta_{\mathrm{L}}$ and decay rates $\Gamma_{2,3,4}$ correspond to respective states. (b) Probe transmission spectra versus coupling detuning $\Delta_{\mathrm{c}}$ at various MW Rabi frequencies $\Omega_{\mathrm{L}}$. Increasing $\Omega_{\mathrm{L}}$ enhances EIT peak splitting. (c) Peak splitting versus $\Omega_{\mathrm{L}}$: the Hermitian case (blue dashed) shows linear scaling, while the non-Hermitian case (red solid) exhibits nonlinear enhancement near the exceptional point (EP). Regions labeled AR, NL, and AT denote absorption, nonlinear, and Autler-Townes regimes, respectively.
• Figure 2: Experimental demonstration of EPs and enhanced response near EPs. (a) Experimental setup: probe and reference beams (red arrows) propagate parallel through a room-temperature $^{85}$Rb vapor cell. The probe counter-propagates with a coupling beam (blue arrow), redirected by a dichroic mirror (DM) to excite Rydberg states. A MW field from a horn antenna couples adjacent Rydberg levels. Transmission difference between probe and reference is detected by a balanced photodetector (PD). (b) Probe transmission spectra versus coupling detuning $\Delta_\mathrm{c}$ for increasing MW Rabi frequencies $\Omega_\mathrm{L}$ (bottom to top). The red curve tracks central peak positions, showing nonlinear splitting near the EP. The main peak corresponds to $5P_{3/2} \leftrightarrow 75D_{5/2}$; the smaller peak to $5P_{3/2} \leftrightarrow 75D_{3/2}$. (c) Peak splitting versus perturbation strength near EP; inset log-log plot with slope 1/2 confirms square-root EP response. (d) Enhancement factor versus perturbation strength;inset Fisher information versus perturbation strength. Blue dots: experimental data with error bars (5 measurements); red lines: theoretical fits.
• Figure 3: Nonlinear dynamics and signal response near the EP.(a) Complex eigenvalues of the effective non-Hermitian Hamiltonian versus local MW Rabi frequency $\Omega_\mathrm{L}$, showing coalescence of real (orange solid) and imaginary (blue dashed) parts at the EP (red arrow). Blue and orange shaded regions denote the $\mathcal{PT}$-broken and $\mathcal{PT}$-symmetric phases, respectively. Insets show system response under weak signal $\Omega_\mathrm{s}$ (gray line) in three regimes: $\mathcal{PT}$-broken (c1), at EP (c2), and $\mathcal{PT}$-symmetric (c3).(b1,b2) Schematic EIT spectra (blue solid in b1, orange solid in b2) with fitted eigenmodes (gray dashed), illustrating characteristic linewidth and splitting changes of non-Hermitian eigenstates in $\mathcal{PT}$-broken (b1) and $\mathcal{PT}$-symmetric (b2) phases. Weak signal $\Omega_\mathrm{s}$ induces linewidth modulation (b1) or energy-level shifts (b2), causing measurable EIT changes. Locking coupling laser to resonance center makes probe transmission proportional to signal amplitude. (c1-c3) Time evolution of real (top) and imaginary (bottom) parts of eigenvalues under weak signal $\Omega_\mathrm{s}$ in regimes marked in (a). (d1-d3) Fourier spectra of corresponding time-domain responses, with theoretical results (top) and experimental data (bottom). Signal detuning in experiment is $\delta/2\pi=2~\mathrm{kHz}$.
• Figure 4: Performance of EP-enhanced electric field sensing. (a) Signal response amplitude (blue dots) and noise (green triangles) versus local MW field strength $E_\mathrm{L}$ with fixed weak signal $E_\mathrm{s}$. Maximum response (star) occurs slightly off the EP, optimizing signal-to-noise ratio. Blue spheres: experimental data; black line: fitting curve. (b) Power spectral density (PSD) of probe transmission at optimal point in (a), yielding electric field sensitivity of $22.68(3)~\mathrm{nVcm^{-1}Hz^{-1/2}}$. (c) Time-domain probe transmission under phase-modulated $\Omega_s$, showing optical signal phase inversion as MW input phase $\phi_{\mathrm{in}}$ flips from 0 to $180^\circ$ (shaded). (d) Measured output optical phase $\phi_{\mathrm{out}}$ versus input MW phase $\phi_{\mathrm{in}}$, demonstrating accurate, linear phase mapping. Inset: zoom-in highlighting phase resolution.