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.
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.
Analysis of fundamentally open systems which exhibit both spatial reflection (parity) and time-reversal symmetry, called PT-symmetric [1] systems, has played an important role in understanding the dynamics of a broad class of non-Hermitian systems. Such systems support distinct regimes of stability and instability respectively, and the transition between these plays an important role in the system dynamics. We investigate a variety of non-Hermitian systems which exhibit a PT-symmetry breaking transition in both classical and quantum contexts using an array of theoretical and numerical approaches which are directly amenable to physical experiments. Organizationally, we divide these studies into those done on classical and quantum systems. Specifically for classical systems we analyze several interesting phenomena in the context of optical waveguide arrays. These provide an important testing ground for much of the discrete, PT-symmetric theory. In our case, we analyze PT-symmetric extensions of several interesting lattice models. Firstly, we explore single gain/loss pair, PT-symmetric extensions of the Su-Schreiffer-Heeger (SSH) model [2] and the Aubry-Andre-Harper (AAH) model [3,4]. In both cases, we find a veiled symmetry which is responsible for the PT-symmetry. Secondly we expand upon the Rudner-Levitov (RL) model [5,6], a non-Hermitian extension of the SSH model with multiple gain/loss pairs, and we explore the dependence of topological phenomena on changes in the initial state as well as their robustness in the presence of gain-induced nonlinearity. For quantum systems, we explore the rich PT-symmetric phase diagram resulting from time-periodic, Floquet PT-symmetry [7,8]. This is experimentally implementable in ultracold atomic systems [9], and features a reentrant PT-symmetric phase. Secondly, we examine quantum multi-photon statistics for a simple non-Hermitian model which is transformed and mapped to a system with unitary evolution via a unitary dilation, and is fully realizable on a small-scale quantum simulator [10].
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.
The interplay between strong long-range interactions and the coherent driving contribute to the formation of complex patterns, symmetry, and novel phases of matter in many-body systems. However, long-range interactions may induce an additional dissipation channel, resulting in non-Hermitian many-body dynamics and the emergence of exceptional points in spectrum. Here, we report experimental observation of interaction-induced exceptional points in cold Rydberg atomic gases, revealing the breaking of charge-conjugation parity symmetry. By measuring the transmission spectrum under increasing and decreasing probe intensity, the interaction-induced hysteresis trajectories are observed, which give rise to non-Hermitian dynamics. We record the area enclosed by hysteresis loops and investigate the dynamics of hysteresis loops. The reported exceptional points and hysteresis trajectories in cold Rydberg atomic gases provide valuable insights into the underlying non-Hermitian physics in many-body systems, allowing us to study the interplay between long-range interactions and non-Hermiticity. Long-range interactions in many-body quantum systems may induce dissipation channels described by non-Hermitian dynamics. Here, the authors report the observation of higher-order exceptional points, a hallmark of non-Hermitian physics, in a Rydberg atom gas. This enables design of quantum dynamics around these points, providing insight into phase transitions.
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.
A parity-time (PT) transition is a spectral transition characteristic of non-Hermitian generators; it typically occurs at an exceptional point, where multiple eigenvectors coalesce. The concept of a PT transition has been extended to Markovian open quantum systems, which are described by the GKSL equation. Interestingly, the PT transition in many-body Markovian open quantum systems, the so-called \textit{Lindbladian PT (L-PT) phase transition}, is closely related to two classes of exotic nonequilibrium many-body phenomena: \textit{continuous-time crystals} and \textit{non-reciprocal phase transitions}. In this review, we describe the recent advances in the study of L-PT phase transitions. First, we define PT symmetry in three distinct contexts: non-Hermitian systems, nonlinear dynamical systems, and Markovian open quantum systems, highlighting the interconnections between these frameworks. Second, we develop mean-field theories of L-PT phase transitions for collective-spin systems and for bipartite bosonic systems with particle-number conservation. Within these classes of models, we show that L-PT symmetry can induce a breaking of continuous time-translation symmetry down to a discrete one, leading to persistent periodic dynamics. We further demonstrate that the L-PT phase transition point is typically \textit{a critical exceptional point}, where multiple collective excitation modes with zero excitation spectrum coalesce. These findings establish an explicit connection to continuous-time crystals and non-reciprocal phase transitions. Third, going beyond the mean-field theory, we analyze statistical and quantum properties, such as purity and quantum entanglement indicators of time-independent steady states for several specific models with the L-PT symmetry. Finally, we discuss future research directions for L-PT phase transitions.
Non-Hermitian systems having parity-time (PT) symmetry can undergo a transition, spontaneously breaking the symmetry. Ultracold atomic gases provide an ideal platform to study interaction effects on the transition. We consider a model system of N bosons of two components confined in a tight trap. Radio-frequency and laser fields are coupled to the bosons such that the single-particle Non-Hermitian Hamiltonian ${h}_{\mathcal{P}T}=\ensuremath{-}i\mathrm{\ensuremath{\Gamma}}{\ensuremath{\sigma}}_{z}+J{\ensuremath{\sigma}}_{x}$, which has PT symmetry, can be simulated in a passive way, namely, in the physical system there is only incurred atom loss but no gain. We show that when interatomic interactions are tuned to maintain the symmetry, the PT-symmetry-breaking transition is affected only by the SU(2) variant part of the interatomic interactions. We find that the transition point ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{tr}}$ decreases as the strength of this interaction part or N increases; in the strong strength limit for this interaction part, ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{tr}}$ scales as the strength to the power of $\ensuremath{-}(N\ensuremath{-}1)$. We also give signatures of the PT-symmetric and the symmetry-breaking phases for the interacting bosons in experiment.