Observation of non-Hermitian many-body phase transition in a Rydberg-atom array

TL;DR

This work addresses the realization and probing of PT-symmetry breaking in a genuinely many-body, non-Hermitian spin system. It implements a tunable non-Hermitian XY model in a Rydberg-atom array by engineering state-dependent dissipation and long-range dipolar exchange, and probes the transition with the Loschmidt Echo, defined as $F(t)=|\langle 0_N|e^{-iH_{nh}t}|0_N\rangle|^2$. The experiments reveal an interaction-driven PT-symmetry-breaking phase boundary that shifts with system size $N$, and a non-monotonic $F(t)$ together with a non-Hermitian many-body blockade and quantum Zeno-like effects that protect the initial state. The results demonstrate rich many-body dynamics beyond single-particle physics and point toward exploring non-Hermitian topology, chaos, and correlated dissipation in programmable quantum simulators.

Abstract

Non-Hermitian quantum mechanics with parity-time (PT) symmetry offers a powerful framework for exploring the complex interplay of dissipation and coherent interactions in open quantum systems. While PT-symmetry breaking has been studied in various physical systems, its observation on a quantum many-body level remains elusive. Here, we experimentally realize a non-Hermitian XY model in a strongly-interacting Rydberg-atom array. By measuring the Loschmidt Echo of a fully polarized state, we observe distinct dynamical signatures of a PT-symmetry-breaking phase transition. Dipole interactions are found to play a crucial role, not only determining the transition point but also triggering a non-Hermitian many-body blockade effect that protects the Loschmidt Echo from decay with a non-monotonic dependence on the system size. Our results reveal intricate interaction-induced effects on PT-symmetry breaking and open the door for exploring non-Hermitian many-body dynamics beyond single-particle and mean-field paradigms.

Figures (17)

• Figure 1: Experimental protocol. (A) One-dimensional array of $^{87}$Rb atoms. Atoms are initialized in the Rydberg state $\ket{\uparrow} = \ket{r_2} = \ket{69P_{3/2}, m_J=3/2}$. The state $\ket{\uparrow}$ is coupled to a dressed Rydberg state $\ket{\downarrow} = \tfrac{1}{\sqrt{2}}(\ket{e} + \ket{r_1})$ via a microwave (MW) field with Rabi frequency $\Omega$. The dressed state is a superposition of the Rydberg state $\ket{r_1} = \ket{68D_{5/2}, m_J=5/2}$ and a low-lying state $\ket{e}$. The insets show the electronic (B) and encoded (C) energy levels. By choosing state $\ket{e} = \ket{5P_{3/2}}$ or $\ket{6P_{3/2}}$, the effective decay rate of the dressed state $\ket{\downarrow}$ is $\Gamma = 2\uppi \times 3.0MHz$ or $2\uppi \times 0.7MHz$, respectively. The exchange interaction is controlled by varying the distance between the Rydberg atoms. (D) Timing sequence. LE is measured via a two-step projective protocol: after the evolution, atoms in state $\ket{\downarrow}$ spontaneously decay to state $\ket{g}$ and are subsequently removed by a push-out laser, while those remaining in state $\ket{\uparrow}$ are transferred back to state $\ket{g}$ for fluorescence detection. Successful detection of all atoms confirms that state $\ket{\uppsi_N(t)}$ returns to the initial state $\ket{0_N}$, giving the survival probability of the initial state, i.e., the LE, normalized with respect to the initial state (see Supplementary Materials).
• Figure 2: Non-Hermitian spectra and dynamics of LE. Imaginary (A) and real (B) parts of the eigenvalues $E$. When $V = 0$, the four eigenstates are degenerate, while the non-negligible interaction $V$ lifts some of the degeneracy in Re$(E)$. The initial state $\ket{\uparrow\uparrow}$ does not couple to the anti-symmetric dark state $\propto (\ket{\uparrow\downarrow}-\ket{\downarrow\uparrow})$ (gray dashed line). Im$(E)$ is shifted by $-\Gamma/2$ relative to the $H_\text{pt}$ spectrum due to $H_\text{im}$.The exceptional point (EP, star) shifts to higher $\Omega$ with increasing $V$, as given by the yellow dashed curve obtained from diagonalization of $H_\text{pt}$ (see Supplementary Materials). (C to E) Evolution of the LE $F(t)$ for $V \to 0$ (C), $V = 0.73\Gamma$ (D), and $\Omega = 0.95\Gamma$ (E). The EPs are $\Omega_\text{c} = 0.50\Gamma$, $\Omega_\text{c} = 1.07\Gamma$, and $V_\text{c} = 0.50\Gamma$, respectively. Solid curves are numerical simulations using the experimental parameters, while dashed curves are simulated results at the EPs. (F to H) Scaled LE, $F(t) \text{e}^{\Gamma t}$, corresponding to the data in (C to E). The scaled LE exhibits oscillatory (monotonic) behavior in the PTS (PTSB) phase. The experimental data agree well with numerical simulations (solid). To highlight the distinct dynamics in the PTS and PTSB regimes, linear scales are used for LE values between 0 and 1, and logarithmic scales for values above 1. Error bars represent the binomial standard deviation.
• Figure 3: $\mathcal{PT}$ phase diagram of interacting Rydberg atoms. Measured (A) and simulated (B) PTS--PTSB phase diagram. The color scale represents the rate function $\uplambda$ at the evolution time $\Gamma t_\text{e}=2.3\uppi$. The phase boundary is extracted at $\uplambda \approx 5$. The solid curve shows the phase boundary numerically obtained by analyzing spectra of the Hamiltonian $H_\text{pt}$, while the dotted line corresponds to the analytic approximation $\Omega_\text{c} \approx \Gamma \sqrt{1/4 + V/\Gamma}$.
• Figure 4: Non-Hermitian phase transition and LE of $N$ Rydberg atoms. (A) Many-body PTS--PTSB phase diagram. In PTSB phases, the participation ratio $R$, i.e., the fraction of eigenvalues that are imaginary in the spectra, is nonzero. The ratio varies with the system size $N$. (B) The measured LE value, $F(t_{\text{e}})$, as a function of $N$. The solid and dashed lines show numerical simulations with full-range and nearest-neighbor (NN) interactions, respectively. The full-range model agrees well with the experimental data for all $N$ and interaction strengths, underscoring the essential role of long-range interactions. For the interacting cases ($V/\Gamma = 4.1, 2.0, 1.0$), the corresponding positions in the phase diagram (A) are marked by solid, dashed, and dotted lines, respectively. Data for $V/\Gamma=1.0$ are measured for up to 9 atoms, limited by the field of view of the atom trapping and imaging system. Data points for $V/\Gamma = 0$ are inferred from single-atom measurements. Parameters used in the experiment are: $\Gamma = 2\uppi \times 0.7MHz$, $\Omega/\Gamma = 1.2$, and $t_\text{e} = 1.5\us$. Error bars indicate the binomial standard deviation.
• Figure 5: Non-Hermitian blockade in the $N$-atom chain. (A) Synthesized images of the $N$-atom chain. The color scale indicates the relative intensity of atomic fluorescence, rescaled by the corresponding measured LE in Fig. \ref{['fig:fig4']}B. (B) Energy $U_k$ (orange) and coupling strength $\Omega_k$ of the spin-wave states. Arrow thickness shows the coupling strength $\Omega_k$, with dashed arrows indicating $\Omega_k = 0$. The red arrow marks the resonant case $U_k = 0$. (C) Illustration of the spin-wave function (orange) for $N=7$. The site-dependent coupling $\braket{1_i|k}$ is represented by the vertical projection of the blue arrows. The wave function oscillates with increasing $k$. (D) Non-Hermitian blockade dynamics. Simulated excitation probability versus evolution time $t$ for different system sizes (see Supplementary Materials). The excitation probability is calculated by $1-\tilde{F}(t)$, where $\tilde{F}(t)$ denotes the LE normalized by the total population remaining in the Hilbert space $\left\{\ket{\uparrow},\ket{\downarrow}\right\}^{\otimes N}$ at $t$. Excitation is strongly suppressed for $N>1$ cases. Parameters: $V/\Gamma = 4.1$; other parameters as in Fig. \ref{['fig:fig4']}B. (E) Suppression of multi-excitations. Accumulated population loss, defined as $\Gamma\int_0^t p_m(t') {\rm d}t'$, for the single- ($m=1$; solid lines) and double-excitation ($m=2$; dashed lines) manifolds. Here, $p_m(t')$ represents the instantaneous population in the $m$-excitation manifold at time $t'$. The significantly lower populations in the double-excitation manifold show the quantum Zeno-like mechanism induced by dissipation.