Non-Hermitian physics in the many-body system of Rydberg atoms

TL;DR

The paper surveys how non-Hermitian physics emerges in many-body Rydberg-atom systems, linking complex spectra, biorthogonal dynamics, and Liouvillian topology to tunable dissipation and long-range interactions. It combines foundational theory—biorthogonality, symmetry classifications, point/line gaps, Lindblad dynamics, and Liouvillian EPs—with a broad array of experiments in hot and cold Rydberg ensembles, synthetic dimensions, and programmable arrays, demonstrating exceptional points, chiral dynamics, and dissipative topological phases. Key contributions include observation of interaction-induced exceptional points, Liouvillian chiral state transfer, non-Hermitian spectral topology in dissipative Rydberg gases, and topological dissipative SSH structures, as well as practical sensing enhancements leveraging EPs in Rydberg electrometers. The work establishes Rydberg platforms as versatile testbeds for open quantum systems, with implications for quantum simulation, precision sensing, and robust topological quantum states in driven-dissipative many-body settings.

Abstract

Non-Hermitian physics exhibits unique physical properties beyond those of traditional Hermitian systems, such as symmetry breaking, the emergence of exceptional points, topological phase transitions, and more. These phenomena have been extensively studied across various platforms, including quantum optics, cold atom systems, superconducting circuits, and condensed matter physics. Rydberg atoms, with their long-range interactions and flexible controllability, provide a promising platform for the experimental realization of non-Hermitian physics. This review primarily summarizes the key experimental and theoretical achievements in the field of non-Hermitian physics within Rydberg atomic systems in recent years. It outlines the fundamental construction of non-Hermitian Hamiltonians, reveals the effective dissipation mechanisms induced by Rydberg atomic interactions, and discusses their impact on spectral properties and symmetry breaking. These studies not only deepen the understanding of quantum phase transitions in non-Hermitian many-body systems but also highlight the unique value of Rydberg atomic platforms in realizing and controlling topological states.

Figures (11)

• Figure 1: (a) On the complex spectral plane, non-trivially encircle nonzero areas and form the so-called point gaps, or may eigenbands (red) may be separated by line gaps, thereby leading to much richer symmetry-protected topological states (Figure adapted from Ref. meng2024exceptional). (b) a universal photonic non-Hermitian system consists of coupled gain and loss materials, such as a ring resonator (inset in Figure A). Under certain critical coupling values and gain/loss coefficients, exceptional points may occur in the frequency spectrum of such systems.The topological properties of a second-order exceptional point are best understood by two Riemann surfaces (shown in blue and brown colours) connected at the square root branch point. Starting on the upper surface, one ends up on the lower surface after one round and vice versa (the states move smoothly from one surface to the other). Encircling twice brings one back to the initial point, but the modes acquire a $\pi$-Berry phase; after 4 cycles, the modes return to their starting phases (Figure adapted from Ref. midya2018non). (c) All eigenstates are localized at the system boundary in an exponentially decaying manner, which is the non-Hermitian skin effect.
• Figure 2: Schematic of many-body interaction induced hysteresis loops in Rydberg atoms. (a) Rydberg atomic energy level diagrams. Probe $\rm{\Omega_{p}}$ and coupling $\rm{\Omega_{c}}$ fields excite atoms with detunings ${\rm{\Delta_{p}}}$ and ${\rm{\Delta_{c}}}$. $\gamma_{1}$ and $\gamma_2$ are decay rates of states $\ket{e}$ and $\ket{r}$, and $\gamma_{\text{eff}}$ is the decay rate caused by Rydberg many-body interactions. (b) Measured transmission by positively (Up, pink) and negatively (Down, blue) scanning $(\rm{\Omega_{p}}/2\pi)^{2}$ in ($\rm{b}_1$), the trajectories connected by data points exhibit hysteresis loop in ($\rm{b}_2$) (Figure adapted from Ref. zhang2025exceptional). (c) The atomic system in ($\rm{c}_1$) and hysteresis trajectory in ($\rm{c}_2$) after adding microwaves field (Figure adapted from Ref. wang2026quantum).
• Figure 3: Measured phase diagram and theoretical phase diagram (Figure adapted from Ref. zhang2025exceptional). (a) The measured phase diagram versus the probe intensity $(\rm{\Omega_{p}}/2\pi)^{2}$ and detuning $\rm{\Delta_p}$. ($\rm{a_1}$)-($\rm{a_4}$) The measured electromagnetically induced transparency spectrum varies with the intensity of the probe field. (b) Theoretical spectrum Im$[\rho_{eg}]$ versus the interaction strength $V$ and detuning $\rm{\Delta_p}$. With further increase in interaction strength, the system transits an exceptional point (marked by the black arrow in the up panel of (b)). As the interaction strength $V$ gradually increases, the spectrum Im$[\rho_{eg}]$ as shown in ($\rm{b_1}$)-($\rm{b_4}$).
• Figure 4: Exceptional structures in a thermal Rydberg gas and the measured chiral mode (Figure adapted from Ref. xie2025chiral). (a) Schematics of the coupling scheme. (b) Experimental setup. (c)-(d) Experimentally measured phase diagrams. The color bar represents the normalized transmission difference, $\delta T$ between the forward and backward scans of ${\rm{\Delta_c}}$. The green lines represent the numerically fitted second-order exceptional lines, and the yellow star is the third order exceptional point. (a1-d1) Chiral mode switching without the microwave field. (a2–d2) The corresponding numerically calculated encircling trajectories on the landscape of the steady-state Rydberg population. (e1-h1) Chiral mode switching with the microwave-field dressing. (e2–h2) The corresponding numerically calculated encircling trajectories on the landscape of the steady-state Rydberg population.
• Figure 5: Rydberg electromagnetically induced transparency as a remote detector of single Rydberg atoms (Figure adapted from Ref. vsumarac2026controlling). (a) Three distinct regimes, corresponding to probabilistic hopping, coherent exchange, and polariton blockade, can be identified. (b) The real (solid) and imaginary (dashed) parts of the eigenvalues as a function of the dipole-dipole interaction strength, $V_\mathrm{PD}$. An exceptional point clearly emerges at the interaction strength corresponding to the blockade radius (gray line). (c) Single-shot histogram for 30 $\mu s$ of readout, showing the difference in detected photons exiting the detector ensemble with (green) and without (purple) a Rydberg atom nearby. The measurement fidelity is 47(5) %. (d) Using repeated preparation and detection (20 repetitions of 10 $\mu s$ detection), we achieve a fidelity of 79(4) %. (e) Detection schematic diagram. (f) Following a global microwave drive, state-selective and remote detection of the Rydberg qubit is performed, showing long-lived coherent microwave Rabi oscillations.