Controlling quantum many-body dynamics in driven Rydberg atom arrays

Quantum Many-Body Scars beyond the PXP Model in Rydberg Simulators

Persistent revivals recently observed in Rydberg atom simulators have challenged our understanding of thermalization and attracted much interest to the concept of quantum many-body scars (QMBSs). QMBSs are non-thermal highly excited eigenstates that coexist with typical eigenstates in the spectrum of many-body Hamiltonians, and have since been reported in multiple theoretical models, including the so-called PXP model, approximately realized by Rydberg simulators. At the same time, questions of how common QMBSs are and in what models they are physically realized remain open. In this Letter, we demonstrate that QMBSs exist in a broader family of models that includes and generalizes PXP to longer-range constraints and states with different periodicity. We show that in each model, multiple QMBS families can be found. Each of them relies on a different approximate su(2) algebra, leading to oscillatory dynamics in all cases. However, in contrast to the PXP model, their observation requires launching dynamics from weakly entangled initial states rather than from a product state. QMBSs reported here may be experimentally probed using Rydberg atom simulator in the regime of longer-range Rydberg blockades.

Anomalous suppression of large-scale density fluctuations in classical and quantum spin liquids

Classical spin liquids (CSLs) are intriguing states of matter that do not exhibit long-range magnetic order and are characterized by an extensive ground-state degeneracy. Adding quantum fluctuations, which induce dynamics between these different classical ground states, can give rise to quantum spin liquids (QSLs). QSLs are highly entangled quantum phases of matter characterized by fascinating emergent properties, such as fractionalized excitations and topological order. One such exotic quantum liquid is the [Formula: see text] QSL, which can be regarded as a resonating valence bond (RVB) state formed from superpositions of dimer coverings of an underlying lattice. In this work, we unveil a hidden large-scale structural property of archetypal CSLs and QSLs known as hyperuniformity, i.e., normalized infinite-wavelength density fluctuations are completely suppressed in these systems. In particular, we first demonstrate that classical ensembles of close-packed dimers and their corresponding quantum RVB states are perfectly hyperuniform in general. Subsequently, we focus on a ruby-lattice spin liquid that was recently realized in a Rydberg-atom quantum simulator, and show that the QSL remains effectively hyperuniform even in the presence of a finite density of spinon and vison excitations, as long as the dimer constraint is still largely preserved. Moreover, we demonstrate that metrics based on the framework of hyperuniformity can be used to distinguish the QSL from other proximate quantum phases. These metrics can help identify potential QSL candidates, which can then be further analyzed using more advanced, computationally intensive quantum numerics to confirm their status as true QSLs.

Probing Dynamics of a Two-Dimensional Dipolar Spin Ensemble Using Single Qubit Sensor

Understanding the thermalization dynamics of quantum many-body systems at the microscopic level is among the central challenges of modern statistical physics. Here we experimentally investigate individual spin dynamics in a two-dimensional ensemble of electron spins on the surface of a diamond crystal. We use a near-surface nitrogen-vacancy center as a nanoscale magnetic sensor to probe correlation dynamics of individual spins in a dipolar interacting surface spin ensemble. We observe that the relaxation rate for each spin is significantly slower than the naïve expectation based on independently estimated dipolar interaction strengths with nearest neighbors and is strongly correlated with the timescale of the local magnetic field fluctuation. We show that this anomalously slow relaxation rate is due to the presence of strong dynamical disorder and present a quantitative explanation based on dynamic resonance counting. Finally, we use resonant spin-lock driving to control the effective strength of the local magnetic fields and reveal the role of the dynamical disorder in different regimes. Our work paves the way towards microscopic study and control of quantum thermalization in strongly interacting disordered spin ensembles.

Bifurcation of time crystals in driven and dissipative Rydberg atomic gas

A time crystal is an exotic phase of matter where time-translational symmetry is broken; this phase differs from the spatial symmetry breaking induced in conventional crystals. Lots of experiments report the transition from a thermal equilibrium phase to a time crystal phase. However, there is no experimental method to probe the bifurcation effect of distinct continuous time crystals in quantum many-body systems. Here, in a driven and dissipative many-body Rydberg atom system, we observe multiple continuous dissipative time crystals and emergence of more complex temporal symmetries beyond the single time crystal phase. Bifurcation of time crystals in strongly interacting Rydberg atoms is observed; the process manifests as a transition from a time crystal of long periodicity to a time crystal of short periodicity, or vice versa. By manipulating the driving field parameters, we observe the time crystal's bistability and a hysteresis loop. These investigations indicate new possibilities for control and manipulation of the temporal symmetries of non-equilibrium systems.

Quantum coarsening and collective dynamics on a programmable simulator

Understanding the collective quantum dynamics of non-equilibrium many-body systems is an outstanding challenge in quantum science. In particular, dynamics driven by quantum fluctuations are important for the formation of exotic quantum phases of matter1, fundamental high-energy processes2, quantum metrology3,4 and quantum algorithms5. Here we use a programmable quantum simulator based on Rydberg atom arrays to experimentally study collective dynamics across a (2+1)-dimensional Ising quantum phase transition. After crossing the quantum critical point, we observe a gradual growth of correlations through coarsening of antiferromagnetically ordered domains6. By deterministically preparing and following the evolution of ordered domains, we show that the coarsening is driven by the curvature of domain boundaries, and find that the dynamics accelerate with proximity to the quantum critical point. We quantitatively explore these phenomena and further observe long-lived oscillations of the order parameter, corresponding to an amplitude ('Higgs') mode7. These observations offer a viewpoint into emergent collective dynamics in strongly correlated quantum systems and non-equilibrium quantum processes.

An integrated photonic engine for programmable atomic control

Solutions for scalable, high-performance optical control are important for the development of scaled atom-based quantum technologies. Modulation of many individual optical beams is central to applying arbitrary gate and control sequences on arrays of atoms or atom-like systems. At telecom wavelengths, miniaturization of optical components via photonic integration has pushed the scale and performance of classical and quantum optics far beyond the limitations of bulk devices. However, material platforms for high-speed telecom integrated photonics lack transparency at the short wavelengths required by leading atomic systems. Here, we propose and implement a scalable and reconfigurable photonic control architecture using integrated, visible-light modulators based on thin-film lithium niobate. We combine this system with techniques in free-space optics and holography to demonstrate multi-channel, gigahertz-rate visible beamshaping. When applied to silicon-vacancy artificial atoms, our system enables the spatial and spectral addressing of a dynamically-selectable set of these stochastically-positioned point emitters.

Detecting a Long-Lived False Vacuum with Quantum Quenches

Distinguishing whether a system supports alternate low-energy (locally stable) states-stable (true vacuum) versus metastable (false vacuum)-by direct observation can be difficult when the lifetime of the state is very long but otherwise unknown. Here we demonstrate, in a tractable model system, that there are physical phenomena on much shorter timescales that can diagnose the difference. Specifically, we study the time evolution of the magnetization following a quench in the tilted quantum Ising model, and show that its magnitude spectrum is an effective diagnostic. Small transition bubbles are more common than large ones, and we see characteristic differences in the size dependence of bubble lifetimes even well below the critical size for false vacuum decay. We expect this sort of behavior to be generic in systems of this kind. We show such signatures persist in a continuum field theory. This also opens the possibility of similar signatures of the potential metastable false vacuum of our universe well before the beginning of a decay process to the true vacuum.

Early Warning Signals of the Tipping Point in Strongly Interacting Rydberg Atoms

The identification of tipping points is essential for the prediction of collapses or other sudden changes in complex systems. Applications include studies of ecology, thermodynamics, climatology, and epidemiology. However, detecting early signs of proximity to a tipping is made challenging by complexity and nonlinearity. Strongly interacting Rydberg atom gases offer model systems that offer both complexity and nonlinearity, including phase transition and critical slowing down. Here, via an external probe we observe prior warning of the proximity of a phase transition of Rydberg thermal gases. This warning signal is manifested as a deviation from linear growth of the variance with increasing probe intensity. We also observed the dynamics of the critical slowing down behavior versus different timescales and atomic densities, thus providing insights into the study of a Rydberg atom system's critical behavior. Our experiment suggests that the full critical slowing down dynamics of strongly interacting Rydberg atoms can be probed systematically, thus providing a benchmark with which to identify critical phenomena in quantum many-body systems.

Enhanced Many-Body Quantum Scars from the Non-Hermitian Fock Skin Effect

In contrast with extended Bloch waves, a single particle can become spatially localized due to the so-called skin effect originating from non-Hermitian pumping. Here we show that in kinetically constrained many-body systems, the skin effect can instead manifest as dynamical amplification within the Fock space, beyond the intuitively expected and previously studied particle localization and clustering. We exemplify this non-Hermitian Fock skin effect in an asymmetric version of the PXP model and show that it gives rise to ergodicity-breaking eigenstates-the non-Hermitian analogs of quantum many-body scars. A distinguishing feature of these non-Hermitian scars is their enhanced robustness against external disorders. We propose an experimental realization of the non-Hermitian scar enhancement in a tilted Bose-Hubbard optical lattice with laser-induced loss. Additionally, we implement digital simulations of such scar enhancement on the IBM quantum processor. Our results show that the Fock skin effect provides a powerful tool for creating robust nonergodic states in generic open quantum systems.

Higher-order and fractional discrete time crystals in Floquet-driven Rydberg atoms

Higher-order and fractional discrete time crystals (DTCs) are exotic phases of matter where the discrete time translation symmetry is broken into higher-order and non-integer category. Generation of these unique DTCs has been widely studied theoretically in different systems. However, no current experimental methods can probe these higher-order and fractional DTCs in any quantum many-body systems. We demonstrate an experimental approach to observe higher-order and fractional DTCs in Floquet-driven Rydberg atomic gases. We have discovered multiple n-DTCs with integer values of n = 2, 3, and 4, and others ranging up to 14, along with fractional n-DTCs with n values beyond the integers. The system response can transition between adjacent integer DTCs, during which the fractional DTCs are investigated. Study of higher-order and fractional DTCs expands fundamental knowledge of non-equilibrium dynamics and is promising for discovery of more complex temporal symmetries beyond the single discrete time translation symmetry.

Unraveling PXP Many-Body Scars through Floquet Dynamics

Quantum scars are special eigenstates of many-body systems that evade thermalization. They were first discovered in the PXP model, a well-known effective description of Rydberg atom arrays. Despite significant theoretical efforts, the fundamental origin of PXP scars remains elusive. By investigating the discretized dynamics of the PXP model as a function of the Trotter step τ, we uncover a remarkable correspondence between the zero- and two-particle eigenstates of the integrable Floquet-PXP cellular automaton at τ=π/2 and the PXP many-body scars of the time-continuous limit. Specifically, we demonstrate that PXP scars are adiabatically connected to the eigenstates of the τ=π/2 Floquet operator. Building on this result, we propose a protocol for achieving high-fidelity preparation of PXP scars in Rydberg atom experiments.

Creating and controlling global Greenberger-Horne-Zeilinger entanglement on quantum processors

Greenberger-Horne-Zeilinger (GHZ) states, also known as two-component Schrödinger cats, play vital roles in the foundation of quantum physics and the potential quantum applications. Enlargement in size and coherent control of GHZ states are both crucial for harnessing entanglement in advanced computational tasks with practical advantages, which unfortunately pose tremendous challenges as GHZ states are vulnerable to noise. Here we propose a general strategy for creating, preserving, and manipulating large-scale GHZ entanglement, and demonstrate a series of experiments underlined by high-fidelity digital quantum circuits. For initialization, we employ a scalable protocol to create genuinely entangled GHZ states with up to 60 qubits, almost doubling the previous size record. For protection, we take a different perspective on discrete time crystals (DTCs), originally for exploring exotic nonequilibrium quantum matters, and embed a GHZ state into the eigenstates of a tailor-made cat scar DTC to extend its lifetime. For manipulation, we switch the DTC eigenstates with in-situ quantum gates to modify the effectiveness of the GHZ protection. Our findings establish a viable path towards coherent operations on large-scale entanglement, and further highlight superconducting processors as a promising platform to explore nonequilibrium quantum matters and emerging applications.

Superconducting Quantum Simulation for Many-Body Physics beyond Equilibrium

Quantum computing is an exciting field that uses quantum principles, such as quantum superposition and entanglement, to tackle complex computational problems. Superconducting quantum circuits, based on Josephson junctions, is one of the most promising physical realizations to achieve the long-term goal of building fault-tolerant quantum computers. The past decade has witnessed the rapid development of this field, where many intermediate-scale multi-qubit experiments emerged to simulate nonequilibrium quantum many-body dynamics that are challenging for classical computers. Here, we review the basic concepts of superconducting quantum simulation and their recent experimental progress in exploring exotic nonequilibrium quantum phenomena emerging in strongly interacting many-body systems, e.g., many-body localization, quantum many-body scars, and discrete time crystals. We further discuss the prospects of quantum simulation experiments to truly solve open problems in nonequilibrium many-body systems.

Realization of higher-order topological lattices on a quantum computer

Programmable quantum simulators may one day outperform classical computers at certain tasks. But at present, the range of viable applications with noisy intermediate-scale quantum (NISQ) devices remains limited by gate errors and the number of high-quality qubits. Here, we develop an approach that places digital NISQ hardware as a versatile platform for simulating multi-dimensional condensed matter systems. Our method encodes a high-dimensional lattice in terms of many-body interactions on a reduced-dimension model, thereby taking full advantage of the exponentially large Hilbert space of the host quantum system. With circuit optimization and error mitigation techniques, we measured on IBM superconducting quantum processors the topological state dynamics and protected mid-gap spectra of higher-order topological lattices, in up to four dimensions, with high accuracy. Our projected resource requirements scale favorably with system size and lattice dimensionality compared to classical computation, suggesting a possible route to useful quantum advantage in the longer term.

Quantum Slush State in Rydberg Atom Arrays

In this Letter, we propose an exotic quantum state that does not order at zero temperature in a Rydberg atom array with antiblockade mechanism. By performing an unbiased large-scale quantum Monte Carlo simulation, we investigate a minimal model with facilitated excitation in a disorder-free system. At zero temperature, this model exhibits a heterogeneous structure of liquid and glass mixture. This state, dubbed quantum slush state, features a quasi-long-range order with an algebraic decay for its correlation function, and is different from most well-established quantum phases of matter.

Microwave analogy of Förster resonance energy transfer and effect of finite antenna length

The near-field interaction between quantum emitters, governed by Förster resonance energy transfer (FRET), plays a pivotal role in nanoscale energy transfer mechanisms. However, FRET measurements in the optical regime are challenging as they require nanoscale control of the position and orientation of the emitters. To overcome these challenges, microwave measurements were proposed for enhanced spatial resolution and precise orientation control. However, unlike in optical systems for which the dipole can be taken to be infinitesimal in size, the finite size of microwave antennas can affect energy transfer measurements, especially at short distances. This highlights the necessity to consider the finite antenna length to obtain accurate results. In this study, we advance the understanding of dipole-dipole energy transfer in the microwave regime by developing an analytical model that explicitly considers finite antennas. Unlike previous works, our model calculates the mutual impedance of finite-length thin-wire dipole antennas without assuming a uniform current distribution. We validate our analytical model through experiments investigating energy transfer between antennas placed adjacent to a perfect electric conductor mirror. This allows us to provide clear guidelines for designing microwave experiments, distinguishing conditions where finite-size effects can be neglected and where they must be taken into account. Our study not only contributes to the fundamental physics of energy transfer but also opens avenues for microwave antenna impedance-based measurements to complement optical FRET experiments and quantitatively explore dipole-dipole energy transfer in a wider range of conditions.

Embedding Quantum Many-Body Scars into Decoherence-Free Subspaces

Quantum many-body scars are nonthermal excited eigenstates of nonintegrable Hamiltonians, which could support coherent revival dynamics from special initial states when scars form an equally spaced tower in the energy spectrum. For open quantum systems, engineering many-body scarred dynamics by a controlled coupling to the environment remains largely unexplored. Here, we provide a general framework to exactly embed quantum many-body scars into the decoherence-free subspaces of Lindblad master equations. The dissipative scarred dynamics manifest persistent periodic oscillations for generic initial states, and can be practically utilized to prepare scar states with potential quantum metrology applications. We construct the Liouvillian dissipators with the local projectors that annihilate the whole scar towers, and utilize the Hamiltonian part to rotate the undesired states out of the null space of dissipators. We demonstrate our protocol through several typical models hosting many-body scar towers and propose an experimental scheme to observe the dissipative scarred dynamics based on digital quantum simulations and resetting ancilla qubits.

Exact Quench Dynamics of the Floquet Quantum East Model at the Deterministic Point

We study the nonequilibrium dynamics of the Floquet quantum East model (a Trotterized version of the kinetically constrained quantum East spin chain) at its "deterministic point," where evolution is defined in terms of CNOT permutation gates. We solve exactly the thermalization dynamics for a broad class of initial product states by means of "space evolution." We prove: (i) the entanglement of a block of spins grows at most at one-half the maximal speed allowed by locality (i.e., half the speed of dual-unitary circuits); (ii) if the block of spins is initially prepared in a classical configuration, speed of entanglement is a quarter of the maximum; (iii) thermalization to the infinite temperature state is reached exactly in a time that scales with the size of the block.

Molecular and Supramolecular Materials: From Light-Harvesting to Quantum Information Science and Technology

The past two decades have witnessed immense advances in quantum information technology (QIT), benefited by advances in physics, chemistry, biology, and materials science and engineering. It is intriguing to consider whether these diverse molecular and supramolecular structures and materials, partially inspired by quantum effects as observed in sophisticated biological systems such as light-harvesting complexes in photosynthesis and the magnetic compass of migratory birds, might play a role in future QIT. If so, how? Herein, we review materials and specify the relationship between structures and quantum properties, and we identify the challenges and limitations that have restricted the intersection of QIT and chemical materials. Examples are broken down into two categories: materials for quantum sensing where nonclassical function is observed on the molecular scale and systems where nonclassical phenomena are present due to intermolecular interactions. We discuss challenges for materials chemistry and make comparisons to related systems found in nature. We conclude that if chemical materials become relevant for QIT, they will enable quite new kinds of properties and functions.

Prethermal Stability of Eigenstates under High Frequency Floquet Driving

Systems subject to high-frequency driving exhibit Floquet prethermalization, that is, they heat exponentially slowly on a timescale that is large in the drive frequency, τ_{h}∼exp(ω). Nonetheless, local observables can decay much faster via energy conserving processes, which are expected to cause a rapid decay in the fidelity of an initial state. Here we show instead that the fidelities of eigenstates of the time-averaged Hamiltonian, H_{0}, display an exponentially long lifetime over a wide range of frequencies-even as generic initial states decay rapidly. When H_{0} has quantum scars, or highly excited eigenstates of low entanglement, this leads to long-lived nonthermal behavior of local observables in certain initial states. We present a two-channel theory describing the fidelity decay time τ_{f}: the interzone channel causes fidelity decay through energy absorption, i.e., coupling across Floquet zones, and ties τ_{f} to the slow heating timescale, while the intrazone channel causes hybridization between states in the same Floquet zone. Our work informs the robustness of experimental approaches for using Floquet engineering to generate interesting many-body Hamiltonians, with and without scars.

Ergodicity breaking from Rydberg clusters in a driven-dissipative many-body system

It is challenging to probe ergodicity breaking trends of a quantum many-body system when dissipation inevitably damages quantum coherence originated from coherent coupling and dispersive two-body interactions. Rydberg atoms provide a test bed to detect emergent exotic many-body phases and nonergodic dynamics where the strong Rydberg atom interaction competes with and overtakes dissipative effects even at room temperature. Here, we report experimental evidence of a transition from ergodic toward ergodic breaking dynamics in driven-dissipative Rydberg atomic gases. The broken ergodicity is featured by the long-time phase oscillation, which is attributed to the formation of Rydberg excitation clusters in limit cycle phases. The broken symmetry in the limit cycle is a direct manifestation of many-body collective effects, which is verified experimentally by tuning atomic densities. The reported result reveals that Rydberg many-body systems are a promising candidate to probe ergodicity breaking dynamics, such as limit cycles, and enable the benchmark of nonequilibrium phase transition.

Planar hyperbolic polaritons in 2D van der Waals materials

Anisotropic planar polaritons - hybrid electromagnetic modes mediated by phonons, plasmons, or excitons - in biaxial two-dimensional (2D) van der Waals crystals have attracted significant attention due to their fundamental physics and potential nanophotonic applications. In this Perspective, we review the properties of planar hyperbolic polaritons and the variety of methods that can be used to experimentally tune them. We argue that such natural, planar hyperbolic media should be fairly common in biaxial and uniaxial 2D and 1D van der Waals crystals, and identify the untapped opportunities they could enable for functional (i.e. ferromagnetic, ferroelectric, and piezoelectric) polaritons. Lastly, we provide our perspectives on the technological applications of such planar hyperbolic polaritons.

Disorder-tunable entanglement at infinite temperature

Emerging quantum technologies hold the promise of unravelling difficult problems ranging from condensed matter to high-energy physics while, at the same time, motivating the search for unprecedented phenomena in their setting. Here, we use a custom-built superconducting qubit ladder to realize non-thermalizing states with rich entanglement structures in the middle of the energy spectrum. Despite effectively forming an "infinite" temperature ensemble, these states robustly encode quantum information far from equilibrium, as we demonstrate by measuring the fidelity and entanglement entropy in the quench dynamics of the ladder. Our approach harnesses the recently proposed type of non-ergodic behavior known as "rainbow scar," which allows us to obtain analytically exact eigenfunctions whose ergodicity-breaking properties can be conveniently controlled by randomizing the couplings of the model without affecting their energy. The on-demand tunability of quantum correlations via disorder allows for in situ control over ergodicity breaking, and it provides a knob for designing exotic many-body states that defy thermalization.

Robust Higher-Order Hamiltonian Engineering for Quantum Sensing with Strongly Interacting Systems

Dynamical decoupling techniques constitute an integral part of many quantum sensing platforms, often leading to orders-of-magnitude improvements in coherence time and sensitivity. Most ac sensing sequences involve a periodic echolike structure, in which the target signal is synchronized with the echo period. We show that for strongly interacting systems, this construction leads to a fundamental sensitivity limit associated with imperfect interaction decoupling. We present a simple physical picture demonstrating the origin of this limitation, and further formalize these considerations in terms of concise higher-order decoupling rules. We then show how these limitations can be surpassed by identifying a novel sequence building block, in which the signal period matches twice the echo period. Using these decoupling rules and the resulting sequence building block, we experimentally demonstrate significant improvements in dynamical decoupling timescales and magnetic field sensitivity, opening the door for new applications in quantum sensing and quantum many-body physics.

Floquet-tailored Rydberg interactions

The Rydberg blockade is a key ingredient for entangling atoms in arrays. However, it requires atoms to be spaced well within the blockade radius, which limits the range of local quantum gates. Here we break this constraint using Floquet frequency modulation, with which we demonstrate Rydberg-blockade entanglement beyond the traditional blockade radius and show how the enlarged entanglement range improves qubit connectivity in a neutral atom array. Further, we find that the coherence of entangled states can be extended under Floquet frequency modulation. Finally, we realize Rydberg anti-blockade states for two sodium Rydberg atoms within the blockade radius. Such Rydberg anti-blockade states for atoms at close range enables the robust preparation of strongly-interacting, long-lived Rydberg states, yet their steady-state population cannot be achieved with only the conventional static drive. Our work transforms between the paradigmatic regimes of Rydberg blockade versus anti-blockade and paves the way for realizing more connected, coherent, and tunable neutral atom quantum processors with a single approach.

Sunburst quantum Ising model under interaction quench: Entanglement and role of initial state coherence

We study the nonequilibrium dynamics of an isolated bipartite quantum system, the sunburst quantum Ising model, under interaction quench. The prequench limit of this model is two noninteracting integrable systems, namely a transverse Ising chain and finite number of isolated qubits. As a function of interaction strength, the spectral fluctuation property goes from Poisson to Wigner-Dyson statistics. We chose entanglement entropy as a probe to study the approach to thermalization or lack of it in postquench dynamics. In the near-integrable limit, as expected, the linear entropy displays oscillatory behavior, while in the chaotic limit it saturates. Along with the chaotic nature of the time evolution generator, we show the importance of the role played by the coherence of the initial state in deciding the nature of thermalization. We further show that these findings are general by replacing the Ising ring with a disordered XXZ model with disorder strength putting it in the many-body localized phase.

Complexity of spin configuration dynamics due to unitary evolution and periodic projective measurements

We study the Hamiltonian dynamics of a many-body quantum system subjected to periodic projective measurements, which leads to probabilistic cellular automata dynamics. Given a sequence of measured values, we characterize their dynamics by performing a principal component analysis (PCA). The number of principal components required for an almost complete description of the system, which is a measure of complexity we refer to as PCA complexity, is studied as a function of the Hamiltonian parameters and measurement intervals. We consider different Hamiltonians that describe interacting, noninteracting, integrable, and nonintegrable systems, including random local Hamiltonians and translational invariant random local Hamiltonians. In all these scenarios, we find that the PCA complexity grows rapidly in time before approaching a plateau. The dynamics of the PCA complexity can vary quantitatively and qualitatively as a function of the Hamiltonian parameters and measurement protocol. Importantly, the dynamics of PCA complexity present behavior that is considerably less sensitive to the specific system parameters for models which lack simple local dynamics, as is often the case in nonintegrable models. In particular, we point out a figure of merit that considers the local dynamics and the measurement direction to predict the sensitivity of the PCA complexity dynamics to the system parameters.

Picosecond-Scale Ultrafast Many-Body Dynamics in an Ultracold Rydberg-Excited Atomic Mott Insulator

We report the observation and control of ultrafast many-body dynamics of electrons in ultracold Rydberg-excited atoms, spatially ordered in a three-dimensional Mott insulator (MI) with unity filling in an optical lattice. By mapping out the time-domain Ramsey interferometry in the picosecond timescale, we can deduce entanglement growth indicating the emergence of many-body correlations via dipolar forces. We analyze our observations with different theoretical approaches and find that the semiclassical model breaks down, thus indicating that quantum fluctuations play a decisive role in the observed dynamics. Combining picosecond Rydberg excitation with MI lattice thus provides a platform for simulating nonequilibrium dynamics of strongly correlated systems in synthetic ultracold atomic crystals, such as in a metal-like quantum gas regime.

Benchmarking Quantum Simulators Using Ergodic Quantum Dynamics

We propose and analyze a sample-efficient protocol to estimate the fidelity between an experimentally prepared state and an ideal target state, applicable to a wide class of analog quantum simulators without advanced spatiotemporal control. Our protocol relies on universal fluctuations emerging from generic Hamiltonian dynamics, which we discover in the present work. It does not require fine-tuned control over state preparation, quantum evolution, or readout capability, while achieving near optimal sample complexity: a percent-level precision is obtained with ∼10^{3} measurements, independent of system size. Furthermore, the accuracy of our fidelity estimation improves exponentially with increasing system size. We numerically demonstrate our protocol in a variety of quantum simulator platforms, including quantum gas microscopes, trapped ions, and Rydberg atom arrays. We discuss applications of our method for tasks such as multiparameter estimation of quantum states and processes.

Embedding Semiclassical Periodic Orbits into Chaotic Many-Body Hamiltonians

Protecting coherent quantum dynamics from chaotic environment is key to realizations of fragile many-body phenomena and their applications in quantum technology. We present a general construction that embeds a desired periodic orbit into a family of nonintegrable many-body Hamiltonians, whose dynamics is otherwise chaotic. Our construction is based on time-dependent variational principle that projects quantum dynamics onto a manifold of low-entangled states, and it complements earlier approaches for embedding nonthermal eigenstates, known as quantum many-body scars, into thermalizing spectra. By designing terms that suppress "leakage" of the dynamics outside the variational manifold, we engineer families of Floquet models that host exact scarred dynamics, as we illustrate using a driven Affleck-Kennedy-Lieb-Tasaki model and a recent experimental realization of scars in a dimerized superconducting qubit chain.

Molecular Dynamics in Rydberg Tweezer Arrays: Spin-Phonon Entanglement and Jahn-Teller Effect

Atoms confined in optical tweezer arrays constitute a platform for the implementation of quantum computers and simulators. State-dependent operations are realized by exploiting electrostatic dipolar interactions that emerge, when two atoms are simultaneously excited to high-lying electronic states, so-called Rydberg states. These interactions also lead to state-dependent mechanical forces, which couple the electronic dynamics of the atoms to their vibrational motion. We explore these vibronic couplings within an artificial molecular system in which Rydberg states are excited under so-called facilitation conditions. This system, which is not necessarily self-bound, undergoes a structural transition between an equilateral triangle and an equal-weighted superposition of distorted triangular states (Jahn-Teller regime) exhibiting spin-phonon entanglement on a micrometer distance. This highlights the potential of Rydberg tweezer arrays for the study of molecular phenomena at exaggerated length scales.

Proposal for Observing Yang-Lee Criticality in Rydberg Atomic Arrays

Yang-Lee edge singularities (YLES) are the edges of the partition function zeros of an interacting spin model in the space of complex control parameters. They play an important role in understanding non-Hermitian phase transitions in many-body physics, as well as characterizing the corresponding nonunitary criticality. Even though such partition function zeroes have been measured in dynamical experiments where time acts as the imaginary control field, experimentally demonstrating such YLES criticality with a physical imaginary field has remained elusive due to the difficulty of physically realizing non-Hermitian many-body models. We provide a protocol for observing the YLES by detecting kinked dynamical magnetization responses due to broken PT symmetry, thus enabling the physical probing of nonunitary phase transitions in nonequilibrium settings. In particular, scaling analyses based on our nonunitary time evolution circuit with matrix product states accurately recover the exponents uniquely associated with the corresponding nonunitary CFT. We provide an explicit proposal for observing YLES criticality in Floquet quenched Rydberg atomic arrays with laser-induced loss, which paves the way towards a universal platform for simulating non-Hermitian many-body dynamical phenomena.

Extracting Quantum Many-Body Scarred Eigenstates with Matrix Product States

Quantum many-body scarred systems host nonthermal excited eigenstates immersed in a sea of thermal ones. In cases where exact expressions for these special eigenstates are not known, it is computationally demanding to distinguish them from their exponentially many thermal neighbors. We propose a matrix-product-state (MPS) algorithm, dubbed DMRG-S, to extract such states at system sizes far beyond the scope of exact diagonalization. Using this technique, we obtain scarred eigenstates in Rydberg-blockaded chains of up to 80 sites and perform a finite-size scaling study to address the lingering question of the stability for the Néel state revivals in the thermodynamic limit. Our method also provides a systematic way to obtain exact MPS representations for scarred eigenstates near the target energy without a priori knowledge. In particular, we find several new scarred eigenstates with exact MPS representations in kinetically constrained spin and clock models. The combination of numerical and analytical investigations in our work provides a new methodology for future studies of quantum many-body scars.

Observation of Rydberg moiré excitons

Rydberg excitons, the solid-state counterparts of Rydberg atoms, have sparked considerable interest with regard to the harnessing of their quantum application potentials, but realizing their spatial confinement and manipulation poses a major challenge. Lately, the rise of two-dimensional moiré superlattices with highly tunable periodic potentials provides a possible pathway. Here, we experimentally demonstrate this capability through the spectroscopic evidence of Rydberg moiré excitons (X_RM), which are moiré-trapped Rydberg excitons in monolayer semiconductor tungsten diselenide adjacent to twisted bilayer graphene. In the strong coupling regime, the X_RM manifest as multiple energy splittings, pronounced red shift, and narrowed linewidth in the reflectance spectra, highlighting their charge-transfer character wherein electron-hole separation is enforced by strongly asymmetric interlayer Coulomb interactions. Our findings establish the excitonic Rydberg states as candidates for exploitation in quantum technologies.

Genuine Many-Body Quantum Scars along Unstable Modes in Bose-Hubbard Systems

The notion of many-body quantum scars is associated with special eigenstates, usually concentrated in certain parts of Hilbert space, that give rise to robust persistent oscillations in a regime that globally exhibits thermalization. Here we extend these studies to many-body systems possessing a true classical limit characterized by a high-dimensional chaotic phase space, which are not subject to any particular dynamical constraint. We demonstrate genuine quantum scarring of wave functions concentrated in the vicinity of unstable classical periodic mean-field modes in the paradigmatic Bose-Hubbard model. These peculiar quantum many-body states exhibit distinct phase-space localization about those classical modes. Their existence is consistent with Heller's scar criterion and appears to persist in the thermodynamic long-lattice limit. Launching quantum wave packets along such scars leads to observable long-lasting oscillations, featuring periods that scale asymptotically with classical Lyapunov exponents, and displaying intrinsic irregularities that reflect the underlying chaotic dynamics, as opposed to regular tunnel oscillations.

Spatially Tunable Spin Interactions in Neutral Atom Arrays

Analog quantum simulations with Rydberg atoms in optical tweezers routinely address strongly correlated many-body problems due to the hardware-efficient implementation of the Hamiltonian. Yet, their generality is limited, and flexible Hamiltonian-design techniques are needed to widen the scope of these simulators. Here we report on the realization of spatially tunable interactions for XYZ models implemented by two-color near-resonant coupling to Rydberg pair states. Our results demonstrate the unique opportunities of Rydberg dressing for Hamiltonian design in analog quantum simulators.

Emergent Glassy Behavior in a Kagome Rydberg Atom Array

We present large-scale quantum Monte Carlo simulation results on a realistic Hamiltonian of kagome-lattice Rydberg atom arrays. Although the system has no intrinsic disorder, intriguingly, our analyses of static and dynamic properties on large system sizes reveal emergent glassy behavior in a region of parameter space located between two valence bond solid phases. The extent of this glassy region is demarcated using the Edwards-Anderson order parameter, and its phase transitions to the two proximate valence bond solids-as well as the crossover towards a trivial paramagnetic phase-are identified. We demonstrate the intrinsically slow (imaginary) time dynamics deep inside the glassy phase and discuss experimental considerations for detecting such a quantum disordered phase with numerous nearly degenerate local minima. Our proposal paves a new route to the study of real-time glassy phenomena and highlights the potential for quantum simulation of a distinct phase of quantum matter beyond solids and liquids in current-generation Rydberg platforms.

Discrete Time Crystal Enabled by Stark Many-Body Localization

Discrete time crystals (DTCs) have recently attracted increasing attention, but most DTC models and their properties are only revealed after disorder average. In this Letter, we propose a simple disorder-free periodically driven model that exhibits nontrivial DTC order stabilized by Stark many-body localization (MBL). We demonstrate the existence of the DTC phase by analytical analysis from perturbation theory and convincing numerical evidence from observable dynamics. The new DTC model paves a new promising way for further experiments and deepens our understanding of DTCs. Since the DTC order does not require special quantum state preparation and the strong disorder average, it can be naturally realized on the noisy intermediate-scale quantum hardware with much fewer resources and repetitions. Moreover, in addition to the robust subharmonic response, there are other novel robust beating oscillations in the Stark-MBL DTC phase that are absent in random or quasiperiodic MBL DTCs.

Emergent Z_{2} Gauge Theories and Topological Excitations in Rydberg Atom Arrays

Strongly interacting arrays of Rydberg atoms provide versatile platforms for exploring exotic many-body phases and dynamics of correlated quantum systems. Motivated by recent experimental advances, we show that the combination of Rydberg interactions and appropriate lattice geometries naturally leads to emergent Z_{2} gauge theories endowed with matter fields. Based on this mapping, we describe how Rydberg platforms could realize two distinct classes of topological Z_{2} quantum spin liquids, which differ in their patterns of translational symmetry fractionalization. We also discuss the natures of the fractionalized excitations of these Z_{2} spin liquid states using both fermionic and bosonic parton theories and illustrate their rich interplay with proximate solid phases.

Exploring the Regime of Fragmentation in Strongly Tilted Fermi-Hubbard Chains

Intriguingly, quantum many-body systems may defy thermalization even without disorder. One example is so-called fragmented models, where the many-body Hilbert space fragments into dynamically disconnected subspaces that are not determined by the global symmetries of the model. In this Letter we demonstrate that the tilted one-dimensional Fermi-Hubbard model naturally realizes distinct effective Hamiltonians that are expected to support nonergodic behavior due to fragmentation, even at resonances between the tilt energy and the Hubbard on site interaction. We find that the effective description captures the observed dynamics in experimentally accessible parameter ranges of moderate tilt values. Specifically, we observe a pronounced dependence of the relaxation dynamics on the initial doublon fraction, which directly reveals the microscopic processes of the fragmented model. Our results pave the way for future studies of nonergodic behavior in higher dimensions.

Down-conversion of a single photon as a probe of many-body localization

Decay of a particle into more particles is a ubiquitous phenomenon to interacting quantum systems, taking place in colliders, nuclear reactors or solids. In a nonlinear medium, even a single photon would decay by down-converting (splitting) into lower-frequency photons with the same total energy¹, at a rate given by Fermi's golden rule. However, the energy-conservation condition cannot be matched precisely if the medium is finite and only supports quantized modes. In this case, the fate of the photon becomes the long-standing question of many-body localization, originally formulated as a gedanken experiment for the lifetime of a single Fermi-liquid quasiparticle confined to a quantum dot². Here we implement such an experiment using a superconducting multimode cavity, the nonlinearity of which was tailored to strongly violate the photon-number conservation. The resulting interaction attempts to convert a single photon excitation into a shower of low-energy photons but fails owing to the many-body localization mechanism, which manifests as a striking spectral fine structure of multiparticle resonances at the standing-wave-mode frequencies of the cavity. Each resonance was identified as a many-body state of radiation composed of photons from a broad frequency range and not obeying Fermi's golden rule theory. Our result introduces a new platform to explore the fundamentals of many-body localization without having to control many atoms or qubits^3-9.

Formation of robust bound states of interacting microwave photons

Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles1. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states2-9. Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-½ XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.

Disorder-assisted assembly of strongly correlated fluids of light

Guiding many-body systems to desired states is a central challenge of modern quantum science, with applications from quantum computation1,2 to many-body physics3 and quantum-enhanced metrology4. Approaches to solving this problem include step-by-step assembly5,6, reservoir engineering to irreversibly pump towards a target state7,8 and adiabatic evolution from a known initial state9,10. Here we construct low-entropy quantum fluids of light in a Bose-Hubbard circuit by combining particle-by-particle assembly and adiabatic preparation. We inject individual photons into a disordered lattice for which the eigenstates are known and localized, then adiabatically remove this disorder, enabling quantum fluctuations to melt the photons into a fluid. Using our platform11, we first benchmark this lattice melting technique by building and characterizing arbitrary single-particle-in-a-box states, then assemble multiparticle strongly correlated fluids. Intersite entanglement measurements performed through single-site tomography indicate that the particles in the fluid delocalize, whereas two-body density correlation measurements demonstrate that they also avoid one another, revealing Friedel oscillations characteristic of a Tonks-Girardeau gas12,13. This work opens new possibilities for the preparation of topological and otherwise exotic phases of synthetic matter3,14,15.

Tuning between Continuous Time Crystals and Many-Body Scars in Long-Range XYZ Spin Chains

Persistent oscillatory dynamics in nonequilibrium many-body systems is a tantalizing manifestation of ergodicity breakdown that continues to attract much attention. Recent works have focused on two classes of such systems: discrete time crystals and quantum many-body scars (QMBS). While both systems host oscillatory dynamics, its origin is expected to be fundamentally different: discrete time crystal is a phase of matter which spontaneously breaks the Z_{2} symmetry of the external periodic drive, while QMBS span a subspace of nonthermalizing eigenstates forming an su(2) algebra representation. Here, we ask a basic question: is there a physical system that allows us to tune between these two dynamical phenomena? In contrast to much previous work, we investigate the possibility of a continuous time crystal (CTC) in undriven, energy-conserving systems exhibiting prethermalization. We introduce a long-range XYZ spin model and show that it encompasses both a CTC phase as well as QMBS. We map out the dynamical phase diagram using numerical simulations based on exact diagonalization and time-dependent variational principle in the thermodynamic limit. We identify a regime where QMBS and CTC order coexist, and we discuss experimental protocols that reveal their similarities as well as key differences.

Discrete Time Crystals Enforced by Floquet-Bloch Scars

We analytically identify a new class of quantum scars protected by spatiotemporal translation symmetries, dubbed Floquet-Bloch scars. They are distinguished from previous (quasi-)static scars by a rigid spectral pairing only possible in Floquet systems, where strong interaction and drivings equalize the quasienergy corrections to all scars and maintain their spectral spacings against generic bilinear perturbations. Scars then enforce the spatial localization and rigid discrete time crystal (DTC) oscillations as verified numerically in a trimerized kagome lattice model relevant to recent cold atom experiments. Our analytical solutions offer a potential scheme to understand the mechanisms for more generic translation-invariant DTCs.

Localization and Melting of Interfaces in the Two-Dimensional Quantum Ising Model

We study the nonequilibrium evolution of coexisting ferromagnetic domains in the two-dimensional quantum Ising model-a setup relevant in several contexts, from quantum nucleation dynamics and false-vacuum decay scenarios to recent experiments with Rydberg-atom arrays. We demonstrate that the quantum-fluctuating interface delimiting a large bubble can be studied as an effective one-dimensional system through a "holographic" mapping. For the considered model, the emergent interface excitations map to an integrable chain of fermionic particles. We discuss how this integrability is broken by geometric features of the bubbles and by corrections in inverse powers of the ferromagnetic coupling, and provide a lower bound to the timescale after which the bubble is ultimately expected to melt. Remarkably, we demonstrate that a symmetry-breaking longitudinal field gives rise to a robust ergodicity breaking in two dimensions, a phenomenon underpinned by Stark many-body localization of the emergent fermionic excitations of the interface.

Practical quantum advantage in quantum simulation

The development of quantum computing across several technologies and platforms has reached the point of having an advantage over classical computers for an artificial problem, a point known as 'quantum advantage'. As a next step along the development of this technology, it is now important to discuss 'practical quantum advantage', the point at which quantum devices will solve problems of practical interest that are not tractable for traditional supercomputers. Many of the most promising short-term applications of quantum computers fall under the umbrella of quantum simulation: modelling the quantum properties of microscopic particles that are directly relevant to modern materials science, high-energy physics and quantum chemistry. This would impact several important real-world applications, such as developing materials for batteries, industrial catalysis or nitrogen fixing. Much as aerodynamics can be studied either through simulations on a digital computer or in a wind tunnel, quantum simulation can be performed not only on future fault-tolerant digital quantum computers but also already today through special-purpose analogue quantum simulators. Here we overview the state of the art and future perspectives for quantum simulation, arguing that a first practical quantum advantage already exists in the case of specialized applications of analogue devices, and that fully digital devices open a full range of applications but require further development of fault-tolerant hardware. Hybrid digital-analogue devices that exist today already promise substantial flexibility in near-term applications.

Quantum many-body scars and Hilbert space fragmentation: a review of exact results

The discovery of quantum many-body scars (QMBS) both in Rydberg atom simulators and in the Affleck-Kennedy-Lieb-Tasaki spin-1 chain model, have shown that a weak violation of ergodicity can still lead to rich experimental and theoretical physics. In this review, we provide a pedagogical introduction to and an overview of the exact results on weak ergodicity breaking via QMBS in isolated quantum systems with the help of simple examples such as the fermionic Hubbard model. We also discuss various mechanisms and unifying formalisms that have been proposed to encompass the plethora of systems exhibiting QMBS. We cover examples of equally-spaced towers that lead to exact revivals for particular initial states, as well as isolated examples of QMBS. Finally, we review Hilbert space fragmentation, a related phenomenon where systems exhibit a richer variety of ergodic and non-ergodic behaviors, and discuss its connections to QMBS.

Experimental verification of generalized eigenstate thermalization hypothesis in an integrable system

Identifying the general mechanics behind the equilibration of a complex isolated quantum system towards a state described by only a few parameters has been the focus of attention in non-equilibrium thermodynamics. And several experimentally unproven conjectures are proposed for the statistical description of quantum (non-)integrable models. The plausible eigenstate thermalization hypothesis (ETH), which suggests that each energy eigenstate itself is thermal, plays a crucial role in understanding the quantum thermalization in non-integrable systems; it is commonly believed that it does not exist in integrable systems. Nevertheless, integrable systems can still relax to the generalized Gibbs ensemble. From a microscopic perspective, understanding the origin of this generalized thermalization that occurs in an isolated integrable system is a fundamental open question lacking experimental investigations. Herein, we experimentally investigated the spin subsystem relaxation in an isolated spin-orbit coupling quantum system. By applying the quantum state engineering technique, we initialized the system with various distribution widths in the mutual eigenbasis of the conserved quantities. Then, we compared the steady state of the spin subsystem reached in a long-time coherent dynamics to the prediction of a generalized version of ETH and the underlying mechanism of the generalized thermalization is experimentally verified for the first time. Our results facilitate understanding the origin of quantum statistical mechanics.

A quantum processor based on coherent transport of entangled atom arrays

The ability to engineer parallel, programmable operations between desired qubits within a quantum processor is key for building scalable quantum information systems^1,2. In most state-of-the-art approaches, qubits interact locally, constrained by the connectivity associated with their fixed spatial layout. Here we demonstrate a quantum processor with dynamic, non-local connectivity, in which entangled qubits are coherently transported in a highly parallel manner across two spatial dimensions, between layers of single- and two-qubit operations. Our approach makes use of neutral atom arrays trapped and transported by optical tweezers; hyperfine states are used for robust quantum information storage, and excitation into Rydberg states is used for entanglement generation^3–5. We use this architecture to realize programmable generation of entangled graph states, such as cluster states and a seven-qubit Steane code state^6,7. Furthermore, we shuttle entangled ancilla arrays to realize a surface code state with thirteen data and six ancillary qubits⁸ and a toric code state on a torus with sixteen data and eight ancillary qubits⁹. Finally, we use this architecture to realize a hybrid analogue–digital evolution² and use it for measuring entanglement entropy in quantum simulations^10–12, experimentally observing non-monotonic entanglement dynamics associated with quantum many-body scars^13,14. Realizing a long-standing goal, these results provide a route towards scalable quantum processing and enable applications ranging from simulation to metrology.

A quantum processer is realized using arrays of neutral atoms that are transported in a parallel manner by optical tweezers during computations, and used for quantum error correction and simulations.