Non-Hermitian (NH) systems can display exceptional topological defects without Hermitian counterparts, exemplified by exceptional rings in NH two-dimensional systems. However, exceptional topological features associated with higher-dimensional topological defects have only recently come into attention. We here investigate the topology of the singularities in an NH three-dimensional system. We find that the third-order singularities in the parameter space form an exceptional surface (ES), on which all three eigenstates and eigenenergies coalesce. Such an ES corresponds to a two-dimensional extension of a point-like synthetic tensor monopole. We quantify its topology with the Dixmier-Douady invariant, which measures the quantized flux associated with the synthetic tensor field. We further propose an experimentally feasible scheme for engineering such an NH model. Our results pave the way for investigations of exceptional topology associated with topological defects with more than one dimension.

Synthetic monopoles, which correspond to degeneracies of Hamiltonians, play a central role in understanding exotic topological phenomena. Dissipation-induced non-Hermiticity (NH), extending the eigenspectra of Hamiltonians from the real to complex domain, largely enriches the topological physics associated with synthetic monopoles. We here investigate exceptional points (EPs) in a four-dimensional NH system, finding a hypersphere-like non-Abelian Yang monopole in a five-dimensional parameter space, formed by exceptional point of order 2 (EP2) pairs. Such an exotic structure enables the NH Yang monopole to exhibit a unique topological transition, which is inaccessible with the point-like counterpart. We characterize such a topological phenomenon with the second Chern number.

Dissipatively stabilized cat qubits are promising for fault-tolerant quantum information processing, yet their non-Hermitian (NH) spectral topology remains largely unexplored. We uncover rich Liouvillian exceptional structures in a cat-qubit mode stabilized by two-photon drive (TPD) and engineered two-photon loss, in the presence of single-photon drive (SPD) and single-photon loss. In the parameter space spanned by SPD strength and detuning, we identify both second- and third-order Liouvillian exceptional points (LEP2s and LEP3s). Remarkably, we show that the phase θ of TPD provides coherent control over these exceptional points: the LEP3 diverges and vanishes at θ=π/2, while remaining stable and tunable elsewhere. We introduce a topological invariant based on the winding number of a resultant vector, which robustly identifies LEP3s with unit topological charge. Full master-equation simulations confirm that the system dynamics remains confined to the logical subspace with near-unity fidelity. Our results bridge dissipative stabilization, phase-coherent control, and NH topology, demonstrating controllable higher-order LEPs in open quantum systems.

Exceptional points in non-Hermitian quantum systems give rise to novel genuine quantum phenomena. Recent explorations of exceptional-point-induced quantum phase transitions have extended from discrete-variable to continuous-variable-encoded quantum systems. However, quantum phase transitions driven by Liouvillian exceptional points (LEPs) in continuous-variable platforms remain largely unexplored. Here, we construct and investigate a Liouvillian exceptional structure based on a driven-dissipative Kerr-cat qubit. Through numerical simulations, we reveal a quantum phase transition occurring at the LEP characterized by a sudden change in dynamical behavior from underdamped oscillations to overdamped relaxations as visualized via Wigner functions and Bloch sphere trajectories. Notably the negativity of the Wigner function serves as a direct signature of genuine quantum coherence unattainable in conventional single-qubit non-Hermitian systems. Furthermore, we introduce the phase difference between the off-diagonal elements of the Liouvillian eigenmatrices as a novel parameter to quantify the transition. Our results establish the Kerr-cat qubit as a novel continuous-variable setting for exploring dissipative quantum criticality and intrinsic non-Hermitian physics.

Non-Hermitian (NH) systems, due to the existence of exceptional point (or ring, surface), exhibit exotic topological features which are inaccessible with the Hermition ones. Current studies on NH topology mainly focus on pure states at zero temperature, while those on mixed states remain largely unexplored. In this work, we investigate the topological properties of mixed states in two-dimentional NH systems, by use of the Uhlmann phase and the thermal Uhlmann-Chern number which are structured via the Uhlmann connection at specific temperatures, revealing distinct topological features compared to their pure state counterparts. We further extend our study to the mixed states in the three-dimensional Abelian and four-dimentional non-Abelian NH systems and verify the high-order mixed-state topology. Our study provides a conceptual and practical pathway for exploring topological properties in the mixed-state regime of NH physics.

Any quantum system inevitably interacts with its natural environment, which can be modeled as a Markovian reservoir consisting of a continuum of electromagnetic field modes. The quantum coherence of qubits in a zero-temperature natural reservoir decays asymptotically, whereas the quantum entanglement of two qubits coupled to such reservoirs may disappear in a finite time. This phenomenon, referred to as entanglement sudden death (ESD), has been simulated with artificially engineered dissipative channels, but ESD induced by natural dissipative channels has not been confirmed. We here present the first demonstration of natural-dissipation-induced ESD for two photonic qubits, each stored in a leaky resonator of a superconducting circuit. The disentanglement dynamics of the two photonic qubits is monitored with two ancilla superconducting qubits, which can be controllably coupled to the corresponding leaky resonators. The techniques developed in our experiment pave the way for experimental exploration of entanglement dynamics in natural environments.

When the photonic mode in the Jaynes-Cummings model is driven by an external classical field, the system can undergo the photon-blockade breakdown phase transition at a critical point. Such a phase transition has been detailedly investigated, but the critical properties of the eigenstates remain largely unexplored so far. We here study the geometric criticality associated with these eigenstates. The amplitude and phase of the drive serve as the control parameter of the governing Hamiltonian. We find the quantum metric and Berry curvature tensors for each eigenstate display divergent behaviors in the critical region. More importantly, the divergence associated with bright eigenstates is much more pronounced than that for the unique dark state. Our theoretical results can be experimentally confirmed in circuit quantum electrodynamics systems, where the driven Jaynes-Cummings model has been realized.

Critical phenomena of quantum systems offer a promising strategy to improve measurement precision. So far, many criticality-enhanced quantum metrological schemes have been proposed by using the adiabatically evolved photonic states of composite systems involving a qubit and a field interacting with each other. These schemes focus on the measurement of the system's inherent frequencies. We here propose a criticality-enhanced quantum sensing protocol, aiming to estimate the amplitude of an external signal field with the interacting qubit-photon system. The signal field is coupled to the photonic mode, so that the composite system has a unique dark state, where the photonic mode follows a squeezed vacuum state. The information about the signal field amplitude is encoded in one quadrature of the quantized photonic mode, which exhibits a divergent behavior near the critical point. The measurement precision can approach the Heisenberg limit with respect to the time to encode the signal and the photon number of the field mode.

The intriguing physical phenomena associated with exceptional points have established non-Hermitian physics as a frontier of modern research. Recent investigations have extended non-Hermitian physics into the fully quantum domain. However, existing studies predominantly concentrate on discrete-variable quantum systems, while non-Hermitian quantum effects in continuous-variable encoded systems remain largely unexplored. In this work, we investigate the exceptional structure for a driven-dissipative Kerr-cat qubit, realized with a Kerr nonlinear resonator. We find that the dissipation leads to a bidirectional jump between the two basis states of the cat qubit, which is in distinct contrast with the unidirectional jump associated with normal two-level systems. The competition between this jump and a single-photon drive gives rise to the emergence of third-order Liouvillian exceptional points (LEP3s), each of which corresponds to a crossing point of two lines of LEP2s. Crucially, the single-photon drive is essential for generating the observed nontrivial Liouvillian topology, which reduces to a trivial case when the drive is turned off. We further show that the LEP3 can exhibit the topological character of the Hamiltonian EP3s, which cannot be realized with a single qubit. Our work opens the possibility of realizing non-Hermitian phenomena with continuous-variable quantum systems.

The fragility of quantum metrological advantages under loss remains a major barrier to practical quantum sensing. For a two-photon-driven (TPD) Kerr resonator (TPD-Kerr model) subject to unavoidable single-photon loss (SPL), both the quantum Fisher information gain and squeezing level exhibit hard-to-track long-lived damped oscillations, restricting useful sensing and squeezing to extremely short time windows. We show that adding engineered two-photon loss (ETPL)—forming a TPD-Kerr-ETPL hybrid model—significantly mitigates these oscillations and converts the decay into a smooth, monotonic drop. This extends the high-sensitivity windows by over an order of magnitude. Moreover, we reveal a temporal hierarchy of quantum resources: the initial boost in metrological sensitivity arises from Gaussian squeezing, while sustained high-precision sensing stems from dissipatively stabilized non-Gaussian even-parity cat states. Crucially, only in models that include ETPL—such as the TPD-Kerr-ETPL and TPD-ETPL systems—does the dynamics actively mitigate SPL’s detrimental effects, transforming damped oscillation into a smooth, easily trackable trajectory and enabling a prolonged, usable metrological window. Our approach transcends encoding-based or feedback-controlled schemes, offering a fully autonomous route to high-precision measurement without real-time feedback control. This establishes a general design principle: engineered loss, combined with appropriate driving, can actively preserve metrologically useful non-Gaussian quantum resources even in the presence of SPL—paving the way toward robust, scalable quantum sensors in superconducting circuits, optomechanics, and trapped-ion platforms.

Critical systems near quantum phase transitions were predicted to be useful for improvement of metrological precision, thanks to their ultrasensitive response to tiny variations of the control Hamiltonian. However, realizing criticality enhanced quantum metrology is experimentally challenging, mainly owing to decoherence and critical slowing down associated with the corresponding quantum state preparation. We circumvent these problems by making use of the critical behaviors in the Jaynes-Cummings model, to which the signal field is coupled. The information is encoded in the qubit's excitation number, which displays a divergent changing rate at the critical point, and is extremely robust against decoherence and nonadiabatic effects. We demonstrate such a metrological protocol in a superconducting circuit, where an Xmon qubit, interacting with a resonator, is used as a probe for estimating the amplitude of a microwave field. The measured quantum Fisher information exhibits a critical quantum enhancement, confirming the potential for quantum metrology.

The quantum Rabi model (QRM), composed of a qubit interacting with a quantized photonic field, is a cornerstone of quantum optics. The QRM with dominant unitary dynamics has been demonstrated in circuit quantum electrodynamics (QED) systems, but an open QRM with a strong photonic dissipation has not been experimentally explored. We here present the first experimental demonstration of such an open system in circuit QED, featuring a controlled competition between the coherent qubit-field interaction and the photonic dissipation. We map out the photon number distributions of the dissipative resonator for different coupling strengths in the steady state. We further observe the variation of the photon number during the system's evolution toward the steady state with fixed control parameters. The results demonstrate that the system's behavior is significantly modified by photonic dissipation.

Spontaneous symmetry breaking (SSB) is crucial to the occurrence of phase transitions. Once a phase transition occurs, a quantum system presents degenerate eigenstates that lack the symmetry of the Hamiltonian. After crossing the critical point, the system is essentially evolved to a quantum superposition of these eigenstates until decoherence sets in. Despite the fundamental importance and potential applications in quantum technologies, such quantum-mechanical SSB phenomena have not been experimentally explored in many-body systems. We here present an experimental demonstration of the SSB process in the Lipkin-Meshkov-Glick model, governed by the competition between the individual driving and intra-qubit interaction. The model is realized in a circuit quantum electrodynamics system, where 6 Xmon qubits are coupled in an all-to-all manner through virtual photon exchange mediated by a resonator. The observed nonclassical correlations among these qubits in the symmetry-breaking region go beyond the conventional description of SSB, shedding new light on phase transitions for quantum many-body systems.

Non-Hermitian (NH) systems can display exotic topological phenomena without Hermitian counterparts, enabled by exceptional points (EPs). So far, investigations of NH topology have been restricted to EPs of the NH Hamiltonian, which governs the system dynamics conditional upon no quantum jumps occurring. The Liouvillian superoperator, which combines the effects of quantum jumps with NH Hamiltonian dynamics, possesses EPs (LEPs) that are significantly different from those of the corresponding NH Hamiltonian. We here study the topological features of the LEPs in the system consisting of a qubit coupled to a non-Markovian reservoir. We find that two distinct winding numbers can be simultaneously produced by executing a single closed path encircling the twofold LEP2, formed by two coinciding LEP2s, each involving a pair of coalescing eigenvectors of the extended Liouvillian superoperator. We experimentally demonstrate this purely non-Markovian phenomenon with a circuit, where a superconducting qubit is coupled to a decaying resonator which acts as a reservoir with memory effects. The results push the exploration of exceptional topology from the Markovian to non-Markovian regime.

Non-Hermiticity can lead to the emergence of many intriguing phenomena that are absent in Hermitian systems, enabled by exceptional topological defects, among which Weyl exceptional rings (WER) are particularly interesting. The topology of a WER can be characterized by the quantized Berry phase and a nonzero Chern number, both encoded in the eigenvectors of the non-Hermitian Hamiltonian. So far, WERs have been realized with classical wave systems, whose eigenvectors can be well described by classical physics. We here report the first quantum-mechanical implementation of WERs and investigate the related topology transitions. The experiment system consists of a superconducting qubit and a dissipative resonator, coupled to each other. The high flexibility of the system enables us to characterize its eigenvectors on different manifolds of parameter space, each of which corresponds to a quantum-mechanical entangled state. We extract both the quantized Berry phase and Chern number from these eigenvectors, and demonstrate the topological transition triggered by shrinking the size of the manifold.

One of the most remarkable features that distinguish open systems from closed ones is the presence of exceptional points (EPs), where two or more eigenvectors of a non-Hermitian operator coalesce, accompanying the convergence of the corresponding eigenvalues. So far, EPs have been demonstrated on a number of platforms, ranging from classical optical systems to fully quantum-mechanical spin-boson models. In these demonstrations, the reservoir that induced the non-Hermiticity was treated as a Markovian one, without considering its memory effect. We here present the first experimental demonstration of non-Markovian quantum EPs, engineered by coupling a Josephson-junction-based qubit to a leaky electromagnetic resonator, which acts as a non-Markovian reservoir. We map out the spectrum of the extended Liouvillian superoperator by observing the quantum state evolution of the qubit and the pseudomode, in which the memory of the reservoir is encoded. We identify a twofold second-order EP and a third-order EP in the Liouvillian spectrum, which cannot be realized with a Markovian reservoir. Our results pave the way for experimental exploration of exotic phenomena associated with non-Markovian quantum EPs.

Dissipation usually plays a negative role in quantum metrological technologies, which aim to improve measurement precision by leveraging quantum effects that are vulnerable to environment-induced decoherence. Recently, it has been demonstrated that dissipation can actually be used as a favorable resource for enhancing the susceptibility of signal detection. However, demonstrations of such enhancement for detecting physical quantities in open quantum systems are still lacking. Here we propose and demonstrate a protocol for realizing such non-Hermitian quantum sensors for probing the coupling between a qubit and a resonator subjecting to energy dissipations. The excitation-number conversion associated with the no-jump evolution trajectory enables removal of the noisy outcomes with quantum jumps, implementing the exceptional point (EP), where the Rabi splitting exhibits a divergent behavior in response to a tiny variation of the effective coupling. The sensitivity enhancement near the EP is confirmed by both theoretical calculation and experimental measurement.

We propose a scheme to generate the generalized two-mode Schr & ouml;dinger cat state for two optical fields coupled to a three-level atom. The scheme is based on the competition between the unitary dynamics induced by a classical driving and the field-atom coupling. Under the condition of strong ground-state coupling, the two-mode displaced Schr & ouml;dinger's cat state can be successfully prepared by adjusting the coupling strength between the classical laser and the atom to be much larger than that between the two fields and the atom. Furthermore, by choosing different initial states, it is also possible to prepare a maximally three-dimensional entangled state through strong ground-state coupling. To rigorously assess its feasibility, we have also analyzed the scheme's robustness against dissipation, confirming its practicality under realistic noise and identifying a broad, experimentally accessible parameter "sweet spot." Our proposal provides insights into the area of multimode Schr & ouml;dinger cat states.

The decoherence of superpositions of classically distinguishable states (cat states) is crucial for understanding quantum-to-classical transitions and quantum measurements. So far, decoherence processes of mesoscopic cat states have been demonstrated in several experiments. However, the issue of how the unitary system-reservoir dynamics can lead to irreversible system decoherence remains largely unexplored in experiments. Here we experimentally explore this fundamental issue with a circuit quantum electrodynamics device, where a bus microwave resonator storing a photonic cat state is connected to many nonlinear electronic oscillators. Each of these oscillators that are effectively coupled to the bus resonator serves as one degree of freedom of the reservoir. By gradually increasing the number of the reservoir's degrees of freedom, we find that the revivable quantum coherence progressively decays, owing to the growth in the amount of inerasable information about the system's state encoded in the reservoir. Our results illustrate that irreversible decoherence of a quantum system is an emergent phenomenon, arising from the unitary dynamics involving the system and many of the reservoir's degrees of freedom, which is crucial for the reconciliation of quantum mechanics and classical physics.

Investigation of the nonlocality evolution of entangled mesoscopic fields under decoherence not only is important for understanding the quantum-classical transition, but also has relevance to quantum communication and quantum computation protocols based on continuous variables. According to previous formulations of Bell inequalities, the system loses nonlocal features far before the disappearance of entanglement. We here construct a new version of Bell signal based on rotated and displaced on-off correlations, with which the Bell inequality is violated as long as there remains entanglement and the field state components keep quasiorthogonal. Consequently, the nonlocal character revealed by our formulation decays much slower compared with those based on previous ones. More importantly, there exists a wide regime where the Bell inequality is restored with previous formulations but remains to be violated based on our correlation operators.