Dipole blockade and quantum information processing in mesoscopic atomic ensembles

Rydberg-Atom Manipulation through Strong Interaction with Free Electrons

Optically trapped Rydberg atoms are a suitable platform to explore quantum many-body physics mediated by long-range atom-atom interactions that can be engineered through externally applied light fields. However, this approach is limited to dipole-allowed transitions and a spatial resolution of the order of the optical wavelength. Here, we theoretically investigate the interaction between free electrons and individual Rydberg atoms as an approach to induce nondipolar transitions with subnanometer spatial precision and a substantial degree of control over the final atomic states. We observe unity-order excitation probabilities produced by a single electron for suitably chosen combinations of electron energies and electron-beam distance to the atom. We further discuss free-electron-atom entanglement and atom-atom entanglement in combination with lateral shaping of the electron followed by postselection. Our results support free electrons as powerful tools to manipulate Rydberg atoms in previously inaccessible ways.

Tunable accordion optical lattice for precise control of Rydberg atom interactions in magneto-optical traps (MOTs)

Precise control of Rydberg atom interactions in magneto-optical traps is essential for advanced quantum technologies, yet fine-tuning of strong Rydberg interactions remains challenging. To address this, we present a tunable accordion optical lattice with dynamically adjustable lattice spacings. By stabilizing power and polarization, we improve the power stability of the device by 56.53%, achieving lattice spacings ranging from 46.63 to 2.58 μm and generating stable interference patterns consistent with theoretical predictions. The lattice's versatility and precision enable control of atomic interactions, supporting simulations of quantum phase transitions and many-body physics while advancing quantum simulations and information processing.

Deterministic Photonic Entanglement Arising from Non-Abelian Quantum Holonomy

Realizing deterministic, high-fidelity entangling interactions-of the kind that can be utilized for efficient quantum information processing-between photons remains an elusive goal. Here, we address this long-standing issue by devising a protocol for creating and manipulating highly entangled superpositions of well-controlled states of light by using an on-chip photonic system that has recently been shown to implement three-dimensional, non-Abelian quantum holonomy. Our calculations indicate that a subset of such entangled superpositions are maximally entangled, "volume-law" states, and that the underlying entanglement can be distilled and purified for applications in quantum science. Crucially, we generalize this approach to demonstrate the potentiality of deterministically entangling two arbitrarily high, N-dimensional quantum systems, by formally establishing a deep connection between the matrix representations of the unitary quantum holonomy-within energy-degenerate subspaces in which the total excitation number is conserved-and the (2j+1)-dimensional irreducible representations of the rotation operator, where j=(N-1)/2 and N≥2. Specifically, our protocol deterministically entangles spatially localized modes that are not only distinguishable but are also individually accessible and amenable to state preparation and measurement, and therefore, we envisage that this entangling mechanism could be utilized for deterministic quantum information processing with light.

Dipole Moment of a Superatom

Homodyne detection is used to measure the (collective) atomic dipole moment for an atomic ensemble that is prepared in a superposition of spatially phased Dicke states having at most two excitations (a so-called "superatom"). Homodyne detection allows one to isolate the contributions to the radiated intensity that depend linearly on the average value of the collective atomic dipole moment operator. Depending on whether the atom-reference field interference is constructive or destructive, either super-Poisson or sub-Poisson statistics for the combined field is observed.

Phenomenology of Many-Body Localization in Bond-Disordered Spin Chains

Many-body localization (MBL) hinders the thermalization of quantum many-body systems in the presence of strong disorder. In this Letter, we study the MBL regime in bond-disordered spin-1/2 XXZ spin chain, finding the multimodal distribution of entanglement entropy in eigenstates, sub-Poissonian level statistics, and revealing a relation between operators and initial states required for examining the breakdown of thermalization in the time evolution of the system. We employ a real space renormalization group scheme to identify these phenomenological features of the MBL regime that extend beyond the standard picture of local integrals of motion relevant for systems with disorder coupled to on-site operators. Our results pave the way for experimental probing of MBL in bond-disordered spin chains.

Continuously tunable single-photon level nonlinearity with Rydberg state wave-function engineering

Extending optical nonlinearity into the extremely weak light regime is at the heart of quantum optics, since it enables the efficient generation of photonic entanglement and implementation of photonic quantum logic gate. Here, we demonstrate the capability for continuously tunable single-photon level nonlinearity, enabled by precise control of Rydberg interaction over two orders of magnitude, through the use of microwave-assisted wave-function engineering. To characterize this nonlinearity, light storage and retrieval protocol utilizing Rydberg electromagnetically induced transparency is employed, and the quantum statistics of the retrieved photons are analyzed. As a first application, we demonstrate our protocol can speed up the preparation of single photons in low-lying Rydberg states by a factor of up to∼40. Our work holds the potential to accelerate quantum operations and to improve the circuit depth and connectivity in Rydberg systems, representing a crucial step towards scalable quantum information processing with Rydberg atoms.

Multi-qubit gates and Schrödinger cat states in an optical clock

Many-particle entanglement is a key resource for achieving the fundamental precision limits of a quantum sensor1. Optical atomic clocks2, the current state of the art in frequency precision, are a rapidly emerging area of focus for entanglement-enhanced metrology3-6. Augmenting tweezer-based clocks featuring microscopic control and detection7-10 with the high-fidelity entangling gates developed for atom-array information processing11,12 offers a promising route towards making use of highly entangled quantum states for improved optical clocks. Here we develop and use a family of multi-qubit Rydberg gates to generate Schrödinger cat states of the Greenberger-Horne-Zeilinger (GHZ) type with up to nine optical clock qubits in a programmable atom array. In an atom-laser comparison at sufficiently short dark times, we demonstrate a fractional frequency instability below the standard quantum limit (SQL) using GHZ states of up to four qubits. However, because of their reduced dynamic range, GHZ states of a single size fail to improve the achievable clock precision at the optimal dark time compared with unentangled atoms13. Towards overcoming this hurdle, we simultaneously prepare a cascade of varying-size GHZ states to perform unambiguous phase estimation over an extended interval14-17. These results demonstrate key building blocks for approaching Heisenberg-limited scaling of optical atomic clock precision.

Long-range dipole-dipole exchange-induced atomic grating

We propose a theoretical scheme for dipole exchange-induced grating (DEIG) based on a hybrid coherent atomic system. The system consists of an ultra-cold rubidium (87Rb) atomic ensemble and movable Rydberg spin atoms. The optical response of the grating appears as a superposition of three- and four-level configurations, which is similar to the cooperative optical nonlinearity caused by the dipole blockade effect. The far-field diffraction properties of the cooperative optical nonlinear grating are tuned by the probe field (intensity and photon statistics). However, our Rydberg atomic grating uniquely responds to the spatial positions of spin atoms, which offers a novel approach to dynamically control electromagnetically induced gratings (EIG).

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.

Universal Control of Symmetric States Using Spin Squeezing

The manipulation of quantum many-body systems is a crucial goal in quantum science. Entangled quantum states that are symmetric under qubits permutation are of growing interest. Yet, the creation and control of symmetric states has remained a challenge. Here, we introduce a method to universally control symmetric states, proposing a scheme that relies solely on coherent rotations and spin squeezing. We present protocols for the creation of different symmetric states including Schrödinger's cat and Gottesman-Kitaev-Preskill states. The obtained symmetric states can be transferred to traveling photonic states via spontaneous emission, providing a powerful approach for engineering desired quantum photonic states.

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.

Engineering Artificial Atomic Systems of Giant Electric Dipole Moment

The electric dipole moment (EDM) plays a crucial role in determining the interaction strength of an atom with electric fields, making it paramount to quantum technologies based on coherent atomic control. We propose a scheme for engineering the potential in a Paul trap to realize a two-level quantum system with a giant EDM formed by the motional states of a trapped electron. We show that, under realistic experimental conditions, our system exhibits enhanced EDMs compared to those attainable with Rydberg atoms, serving as a complementary counterpart in the megahertz (MHz) resonance-frequency range. Furthermore, we show that such artificial atomic dipoles can be efficiently initialized, read out, and coherently controlled, thereby providing a potential platform for quantum technologies such as ultrahigh-sensitivity electric-field sensing.

Nonlinear Rydberg exciton-polaritons in Cu2O microcavities

Rydberg excitons (analogues of Rydberg atoms in condensed matter systems) are highly excited bound electron-hole states with large Bohr radii. The interaction between them as well as exciton coupling to light may lead to strong optical nonlinearity, with applications in sensing and quantum information processing. Here, we achieve strong effective photon-photon interactions (Kerr-like optical nonlinearity) via the Rydberg blockade phenomenon and the hybridisation of excitons and photons forming polaritons in a Cu2O-filled microresonator. Under pulsed resonant excitation polariton resonance frequencies are renormalised due to the reduction of the photon-exciton coupling with increasing exciton density. Theoretical analysis shows that the Rydberg blockade plays a major role in the experimentally observed scaling of the polariton nonlinearity coefficient as ∝ n4.4±1.8 for principal quantum numbers up to n = 7. Such high principal quantum numbers studied in a polariton system for the first time are essential for realisation of high Rydberg optical nonlinearities, which paves the way towards quantum optical applications and fundamental studies of strongly correlated photonic (polaritonic) states in a solid state system.

Strongly Nonlinear Interaction between Nonclassical Light and a Blockaded Rydberg Atomic Ensemble

We investigate the interaction between nonclassical light with a tunable multiphoton component and a highly nonlinear medium based on cold Rydberg atoms. The nonclassical field emitted by a DLCZ quantum memory is stored using Rydberg electromagnetically induced transparency, experiencing strong nonlinear response due to the dipole blockade. We show that the storage efficiency in the Rydberg ensemble decreases as a function of the multiphoton strength of the input field, as a result of the nonlinearity. We also show that the autocorrelation function g^{(2)}(0) of the retrieved field after storage in the Rydberg state is considerably reduced, leading to the first demonstration of single photon filtering with nonclassical input light. Finally, we develop a simple simulation that allows us to model the effect of our medium on the input state. This work is a step towards matter-mediated photon-photon interactions with nonclassical light.

Active Suppression of Quantum Dephasing in Resonantly Driven Ensembles

We have used quantum control to suppress the impact of random atom positions on coherent population transfer within atom pairs, enabling the observation of dipole-dipole driven Rabi oscillations in a Rydberg gas with hundreds of atoms. The method exploits the reduced coupling-strength sensitivity of the off-resonant Rabi frequency, and coherently amplifies the achievable population transfer in analogy to quasi-phase-matching in nonlinear optics. Simulations reproduce the experimental results and demonstrate the potential benefits of the technique to other many-body quantum control applications.

Classical route to ergodicity and scarring in collective quantum systems

Ergodicity, a fundamental concept in statistical mechanics, is not yet a fully understood phenomena for closed quantum systems, particularly its connection with the underlying chaos. In this review, we consider a few examples of collective quantum systems to unveil the intricate relationship of ergodicity as well as its deviation due to quantum scarring phenomena with their classical counterpart. A comprehensive overview of classical and quantum chaos is provided, along with the tools essential for their detection. Furthermore, we survey recent theoretical and experimental advancements in the domain of ergodicity and its violations. This review aims to illuminate the classical perspective of quantum scarring phenomena in interacting quantum systems.

Universal Quantum Computation in Globally Driven Rydberg Atom Arrays

We develop a model for quantum computation with Rydberg atom arrays, which only relies on global driving, without the need of local addressing of the qubits: any circuit is executed by a sequence of global, resonant laser pulses on a static atomic arrangement. We present two constructions: for the first, the circuit is imprinted in the trap positions of the atoms and executed by the pulses; for the second, the atom arrangement is circuit-independent, and the algorithm is entirely encoded in the global driving sequence. Our results show in particular that a quadratic overhead in atom number is sufficient to eliminate the need for local control to realize a universal quantum processor. We give explicit protocols for all steps of an arbitrary quantum computation, and discuss strategies for error suppression specific to our model. Our scheme is based on dual-species processors with atoms subjected to Rydberg blockade constraints, but it might be transposed to other setups as well.

Rydberg-Rydberg interaction strengths and dipole blockade radii in the presence of Förster resonances

Achieving a substantial blockade radius is crucial for developing scalable and efficient quantum communication and computation. In this theoretical study, we present the enhancement of the Rydberg blockade radius by utilizing Förster resonance. This phenomenon occurs when the energy difference between two initial Rydberg states closely matches that between the corresponding final Rydberg states, giving rise to a resonant energy transfer process. We employ quantum defect theory to numerically calculate the 87Rb-87Rb Rydberg atomic pair, enabling us to accurately estimate the van der Waals interaction. Our investigation reveals that when the principal quantum numbers of two Rydberg states differ only slightly, the Förster transition is rarely able to achieve a large blockade radius. However, in cases where the principal quantum numbers differ significantly, we substantially improve the Rydberg blockade radius. Most notably, we identify transition channels exhibiting an extensive blockade radius, surpassing 50 μm. This significant increase in the blockade radius enables larger-scale quantum operations and advances quantum technologies, with broad implications for achieving long-range quantum entanglement and robust quantum processes.

Interferometry-Integrated Noise-Immune Quantum Memory

A quantum memory with the performances of low noise, high efficiency, and high bandwidth is of crucial importance for developing practical quantum information technologies. However, the excess noises generated during the highly efficient processing of quantum information inevitably destroy quantum state. Here, we present a quantum memory with built-in excess-noise eraser by integrating a photon-correlated quantum interferometry in quantum memory, where the memory efficiency can be enhanced and the excess noises can be suppressed to the vacuum level via destructive interference. This quantum memory is demonstrated in a rubidium vapor cell with a 10-ns-long photonics signal. We observe ∼80% noise suppression, the write-in efficiency enhancement from 87% to 96.2% without and with interferometry, and the corresponding memory efficiency excluding the noises from 70% to 77%. The fidelity is 93.7% at the single-photon level, significantly exceeding the no-cloning limit. Such interferometry-integrated quantum memory, the first expansion of quantum interference techniques to quantum information processing, simultaneously enables low noise, high bandwidth, high efficiency, and easy operation.

Erasure conversion in a high-fidelity Rydberg quantum simulator

Minimizing and understanding errors is critical for quantum science, both in noisy intermediate scale quantum (NISQ) devices1 and for the quest towards fault-tolerant quantum computation2,3. Rydberg arrays have emerged as a prominent platform in this context4 with impressive system sizes5,6 and proposals suggesting how error-correction thresholds could be significantly improved by detecting leakage errors with single-atom resolution7,8, a form of erasure error conversion9-12. However, two-qubit entanglement fidelities in Rydberg atom arrays13,14 have lagged behind competitors15,16 and this type of erasure conversion is yet to be realized for matter-based qubits in general. Here we demonstrate both erasure conversion and high-fidelity Bell state generation using a Rydberg quantum simulator5,6,17,18. When excising data with erasure errors observed via fast imaging of alkaline-earth atoms19-22, we achieve a Bell state fidelity of [Formula: see text], which improves to [Formula: see text] when correcting for remaining state-preparation errors. We further apply erasure conversion in a quantum simulation experiment for quasi-adiabatic preparation of long-range order across a quantum phase transition, and reveal the otherwise hidden impact of these errors on the simulation outcome. Our work demonstrates the capability for Rydberg-based entanglement to reach fidelities in the 0.999 regime, with higher fidelities a question of technical improvements, and shows how erasure conversion can be utilized in NISQ devices. These techniques could be translated directly to quantum-error-correction codes with the addition of long-lived qubits7,22-24.

Experimental Demonstration of Stationary Dark-State Polaritons Dressed by Dipole-Dipole Interaction

Dark-state polaritons (DSPs) based on the effect of electromagnetically induced transparency are bosonic quasiparticles, representing the superpositions of photons and atomic ground-state coherences. It has been proposed that stationary DSPs are governed by the equation of motion closely similar to the Schrödinger equation and can be employed to achieve Bose-Einstein condensation (BEC) with transition temperature orders of magnitude higher than that of the atomic BEC. The stationary-DSP BEC is a three-dimensional system and has a far longer lifetime than the exciton-polariton BEC. In this Letter, we experimentally demonstrated the stationary DSP dressed by the Rydberg-state dipole-dipole interaction (DDI). The DDI-induced phase shift of the stationary DSP was systematically studied. Notably, the experimental data are consistent with the theoretical predictions. The phase shift can be viewed as a consequence of elastic collisions. In terms of thermalization to achieve BEC, the μm^{2}-size interaction cross section of the DDI can produce a sufficient elastic collision rate for the stationary DSPs. This Letter makes a substantial advancement toward the realization of the stationary-DSP BEC.

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 Blockade Due to the Charge-Dipole Interaction between an Atom and a Polar Molecule

We demonstrate Rydberg blockade due to the charge-dipole interaction between a single Rb atom and a single RbCs molecule confined in optical tweezers. The molecule is formed by magnetoassociation of a Rb+Cs atom pair and subsequently transferred to the rovibrational ground state with an efficiency of 91(1)%. Species-specific tweezers are used to control the separation between the atom and molecule. The charge-dipole interaction causes blockade of the transition to the Rb(52s) Rydberg state, when the atom-molecule separation is set to 310(40) nm. The observed excitation dynamics are in good agreement with simulations using calculated interaction potentials. Our results open up the prospect of a hybrid platform where quantum information is transferred between individually trapped molecules using Rydberg atoms.

Manipulation of single stored-photon with microwave field based on Rydberg polariton

We demonstrate a coherent microwave manipulation of a single optical photon based on a single Rydberg excitation in an atomic ensemble. Due to the strong nonlinearities in a Rydberg blockade region, a single photon can be stored in the formation of Rydberg polariton using electromagnetically induced transparency (EIT). The manipulation of the stored single photon is performed by applying a microwave field that resonantly couples the nS_1/2 and nP_3/2, while the coherent readout is performed by mapping the excitation into a single photon. We achieve a single photon source with g⁽²⁾(0) = 0.29 ± 0.08 at 80S_1/2 without applying microwave fields. By implementing the microwave field during the storage time and retrieval process, we show the Rabi oscillation and modulation of stored photons that can be controlled to retrieve early or late. Rapid modulation frequencies up to 50 MHz can be obtained. Our experimental observations can be well explained via numerical simulations based on an improved superatom model accounting for the dipole-dipole interactions in a Rydberg EIT medium. Our work provides a way to manipulate the stored photons by employing the microwave field, which is significant for developing quantum technologies.

Rydberg Macrodimers: Diatomic Molecules on the Micrometer Scale

Controlling molecular binding at the level of single atoms is one of the holy grails of quantum chemistry. Rydberg macrodimers─bound states between highly excited Rydberg atoms─provide a novel perspective in this direction. Resulting from binding potentials formed by the strong, long-range interactions of Rydberg states, Rydberg macrodimers feature bond lengths in the micrometer regime, exceeding those of conventional molecules by orders of magnitude. Using single-atom control in quantum gas microscopes, the unique properties of these exotic states can be studied with unprecedented control, including the response to magnetic fields or the polarization of light in their photoassociation. The high accuracy achieved in spectroscopic studies of macrodimers makes them an ideal testbed to benchmark Rydberg interactions, with direct relevance to quantum computing and information protocols where these are employed. This review provides a historic overview and summarizes the recent findings in the field of Rydberg macrodimers. Furthermore, it presents new data on interactions between macrodimers, leading to a phenomenon analogous to Rydberg blockade at the level of molecules, opening the path toward studying many-body systems of ultralong-range Rydberg molecules.

Driven-Dissipative Rydberg Blockade in Optical Lattices

While dissipative Rydberg gases exhibit unique possibilities to tune dissipation and interaction properties, very little is known about the quantum many-body physics of such long-range interacting open quantum systems. We theoretically analyze the steady state of a van der Waals interacting Rydberg gas in an optical lattice based on a variational treatment that also includes long-range correlations necessary to describe the physics of the Rydberg blockade, i.e., the inhibition of neighboring Rydberg excitations by strong interactions. In contrast to the ground state phase diagram, we find that the steady state undergoes a single first order phase transition from a blockaded Rydberg gas to a facilitation phase where the blockade is lifted. The first order line terminates in a critical point when including sufficiently strong dephasing, enabling a highly promising route to study dissipative criticality in these systems. In some regimes, we also find good quantitative agreement of the phase boundaries with previously employed short-range models, however, with the actual steady states exhibiting strikingly different behavior.

Fast Single-Shot Imaging of Individual Ions via Homodyne Detection of Rydberg-Blockade-Induced Absorption

We introduce well-separated ^{87}Rb^{+} ions into an atomic ensemble by microwave ionization of Rydberg excitations and realize single-shot imaging of the individual ions with an exposure time of 1  μs. This imaging sensitivity is reached by using homodyne detection of ion-Rydberg-atom interaction induced absorption. We obtain an ion detection fidelity of (80±5)% from analyzing the absorption spots in acquired single-shot images. These in situ images provide a direct visualization of the ion-Rydberg interaction blockade and reveal clear spatial correlations between Rydberg excitations. The capability of imaging individual ions in a single shot is of interest for investigating collisional dynamics in hybrid ion-atom systems and for exploring ions as a probe for measurements of quantum gases.

Two-qubit atomic gates: spatio-temporal control of Rydberg interaction

By controlling the temporal and spatial features of light, we propose a novel protocol to prepare two-qubit entangling gates on atoms trapped at close distance, which could potentially speed up the operation of the gate from the sub-micro to the nanosecond scale. The protocol is robust to variations in the pulse areas and the position of the atoms, by virtue of the coherent properties of a dark state, which is used to drive the population through Rydberg states. From the time-domain perspective, the protocol generalizes the one proposed by Jaksch and coworkers [Jaksch et al., Phys. Rev. Lett., 2000, 85, 2208], with three pulses that operate symmetrically in time, but with different pulse areas. From the spatial-domain perspective, it uses structured light. We analyze the map of the gate fidelity, which forms rotated and distorted lattices in the solution space. Finally, we study the effect of an additional qubit to the gate performance and propose generalizations that operate with multi-pulse sequences.

Rabi oscillations in a stretching molecule

Rabi oscillation is an elementary laser-driven physical process in atoms and artificial atoms from solid-state systems, while it is rarely demonstrated in molecules. Here, we investigate the bond-length-dependent Rabi oscillations with varying Rabi frequencies in strong-laser-field dissociation of H2+. The coupling of the bond stretching and Rabi oscillations makes the nuclei gain different kinetic energies while the electron is alternatively absorbing and emitting photons. The resulting proton kinetic energy spectra show rich structures beyond the prediction of the Floquet theorem and the well-accepted resonant one-photon dissociation pathway. Our study shows that the laser-driven Rabi oscillations accompanied by nuclear motions are essential to understanding the bond-breaking mechanism and provide a time-resolved perspective to manipulate rich dynamics of the strong-laser-field dissociation of molecules.

Millisecond-Lived Circular Rydberg Atoms in a Room-Temperature Experiment

Circular Rydberg states are excellent tools for quantum technologies, with large mutual interactions and long lifetimes in the tens of milliseconds range, 2 orders of magnitude larger than those of laser-accessible Rydberg states. However, such lifetimes are observed only at zero temperature. At room temperature, blackbody-radiation-induced transfers cancel this essential asset of circular states, which have thus been used mostly so far in specific, complex cryogenic experiments. We demonstrate here, on a laser-cooled atomic sample, a circular state lifetime of more than 1 millisecond at room temperature for a principal quantum number 60. A simple plane-parallel capacitor efficiently inhibits the blackbody-radiation-induced transfers. One of the capacitor electrodes is fully transparent and provides large optical access to the atoms. This result paves the way to a wide range of quantum metrology and quantum simulation room-temperature experiments with long-lived, trapped circular Rydberg atoms in inhibition capacitors with full optical access.

Demonstration of a Quantum Gate Using Electromagnetically Induced Transparency

We demonstrate a native CNOT gate between two individually addressed neutral atoms based on electromagnetically induced transparency. This protocol utilizes the strong long-range interactions of Rydberg states to enable conditional state transfer on the target qubit when operated in the blockade regime. An advantage of this scheme is it enables implementation of multiqubit CNOT^{k} gates using a pulse sequence independent of qubit number, providing a simple gate for efficient implementation of digital quantum algorithms and stabilizer measurements for quantum error correction. We achieve a loss corrected gate fidelity of F_{CNOT}^{cor}=0.82(6), and prepare an entangled Bell state with F_{Bell}^{cor}=0.66(5), limited at present by laser power. We present a number of technical improvements to advance this to a level required for fault-tolerant scaling.

Deterministic generation of entanglement states between Silicon-Vacancy centers via acoustic modes

We propose a scheme to entangle Silicon-Vacancy (SiV) centers embedded in a diamond acoustic waveguide. These SiV centers interact with acoustic modes of the waveguide via strain-induced coupling. Through Morris-Shore transformation, the Hilbert space of this hybrid quantum system can be factorized into a closed subspace in which we can deterministically realize the symmetrical Dicke states between distant SiV centers with high fidelity. In addition, the generation of entangled Dicke states can be controlled by manipulating the strength and frequency of the driving field applied on SiV centers. This protocol provides a promising way to prepare multipartite entanglement in spin-phonon hybrid systems and could have broad applications for future quantum technologies.

Gauge-Theoretic Origin of Rydberg Quantum Spin Liquids

Recent atomic physics experiments and numerical works have reported complementary signatures of the emergence of a topological quantum spin liquid in models with blockade interactions. However, the specific mechanism stabilizing such a phase remains unclear. Here, we introduce an exact relation between an Ising-Higgs lattice gauge theory on the kagome lattice and blockaded models on Ruby lattices. This relation elucidates the origin of previously observed topological spin liquids by directly linking the latter to a deconfined phase of a solvable gauge theory. By means of exact diagonalization and unbiased quantum Monte Carlo simulations, we show that the deconfined phases extend in a broad region of the parameter space; these states are characterized by a large ground state overlap with resonating valence bond wave functions. These blockaded models include both creation or annihilation and hopping dynamics, and can be experimentally realized with Rydberg-dressed atoms, offering novel and controllable platforms for the engineering and characterization of spin liquid states.

Exploring bifurcations in Bose-Einstein condensates via phase field crystal models

To facilitate the analysis of pattern formation and the related phase transitions in Bose-Einstein condensates, we present an explicit approximate mapping from the nonlocal Gross-Pitaevskii equation with cubic nonlinearity to a phase field crystal (PFC) model. This approximation is valid close to the superfluid-supersolid phase transition boundary. The simplified PFC model permits the exploration of bifurcations and phase transitions via numerical path continuation employing standard software. While revealing the detailed structure of the bifurcations present in the system, we demonstrate the existence of localized states in the PFC approximation. Finally, we discuss how higher-order nonlinearities change the structure of the bifurcation diagram representing the transitions found in the system.

Highly nonlinear dipolar exciton-polaritons in bilayer MoS2

Realizing nonlinear optical response in the low photon density limit in solid-state systems has been a long-standing challenge. Semiconductor microcavities in the strong coupling regime hosting exciton-polaritons have emerged as attractive candidates in this context. However, the weak interaction between these quasiparticles has been a hurdle in this quest. Dipolar excitons provide an attractive strategy to overcome this limitation but are often hindered by their weak oscillator strength. The interlayer dipolar excitons in naturally occurring homobilayer MoS₂ alleviates this issue owing to their formation via hybridization of interlayer charge transfer exciton with intralayer B exciton. Here we demonstrate the formation of dipolar exciton polaritons in bilayer MoS₂ resulting in unprecedented nonlinear interaction strengths. A ten-fold increase in nonlinearity is observed for the interlayer dipolar excitons compared to the conventional A excitons. These highly nonlinear dipolar polaritons will likely be a frontrunner in the quest for solid-state quantum nonlinear devices.

Dipolar excitons enable large nonlinear interaction but are usually hampered by their weak oscillator strength. Here, the authors demonstrate the strong light-matter coupling of interlayer dipolar excitons having unusually large oscillator strength in bilayer MoS₂ resulting in highly nonlinear dipolar polaritons.

Criticality and Phase Classification for Quadratic Open Quantum Many-Body Systems

We study the steady states of translation-invariant open quantum many-body systems governed by Lindblad master equations, where the Hamiltonian is quadratic in the ladder operators, and the Lindblad operators are either linear or quadratic and Hermitian. These systems are called quasifree and quadratic, respectively. We find that steady states of one-dimensional systems with finite-range interactions necessarily have exponentially decaying Green's functions. For the quasifree case without quadratic Lindblad operators, we show that fermionic systems with finite-range interactions are noncritical for any number of spatial dimensions and provide bounds on the correlation lengths. Quasifree bosonic systems can be critical in D>1 dimensions. Last, we address the question of phase transitions in quadratic systems and find that, without symmetry constraints beyond invariance under single-particle basis and particle-hole transformations, all gapped Liouvillians belong to the same phase.

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.

Density-wave-ordered phases of Rydberg atoms on a honeycomb lattice

Rydberg atom arrays have recently emerged to be a promising platform for the exploration of exotic quantum phases of matter and quantum phenomena. In this work, we map out the ground-state phase diagram of Rydberg atoms on a honeycomb lattice as a function of the Rydberg blockade radius and the laser detuning by performing large-scale finite-size density matrix renormalization group simulations. Apart from a featureless disordered phase, we find five other intricate long-range density-wave-ordered phases within a relatively wide parameter space. The properties of these quantum phases are analyzed by calculating their Rydberg excitation profiles and static structure factors. In addition, a continuous quantum phase transition belonging to the (2+1)-dimensional Ising universality class is explored by a standard finite-size scaling analysis. Our work implies some different physics, such as the possible nontrivial quantum phase transitions and a highly degenerate string ordered phase, that a honeycomb geometry could bring to the Rydberg system and serves as a numerical guide for possible real experiments.

Dynamical Preparation of Quantum Spin Liquids in Rydberg Atom Arrays

We theoretically analyze recent experiments [Semeghini et al., Science 374, 1242 (2021)SCIEAS0036-807510.1126/science.abi8794] demonstrating the onset of a topological spin liquid using a programmable quantum simulator based on Rydberg atom arrays. In the experiment, robust signatures of topological order emerge in out-of-equilibrium states that are prepared using a quasiadiabatic state preparation protocol. We show theoretically that the state preparation protocol can be optimized to target the fixed point of the topological phase-the resonating valence bond state of hard dimers-in a time that scales linearly with the number of atoms. Moreover, we provide a two-parameter variational manifold of tensor network states that accurately describe the many-body dynamics of the preparation process. Using this approach we analyze the nature of the nonequilibrium state, establishing the emergence of topological order.

Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays

Executing quantum algorithms on error-corrected logical qubits is a critical step for scalable quantum computing, but the requisite numbers of qubits and physical error rates are demanding for current experimental hardware. Recently, the development of error correcting codes tailored to particular physical noise models has helped relax these requirements. In this work, we propose a qubit encoding and gate protocol for ¹⁷¹Yb neutral atom qubits that converts the dominant physical errors into erasures, that is, errors in known locations. The key idea is to encode qubits in a metastable electronic level, such that gate errors predominantly result in transitions to disjoint subspaces whose populations can be continuously monitored via fluorescence. We estimate that 98% of errors can be converted into erasures. We quantify the benefit of this approach via circuit-level simulations of the surface code, finding a threshold increase from 0.937% to 4.15%. We also observe a larger code distance near the threshold, leading to a faster decrease in the logical error rate for the same number of physical qubits, which is important for near-term implementations. Erasure conversion should benefit any error correcting code, and may also be applied to design new gates and encodings in other qubit platforms.

In quantum computing, realistic error models can allow tailored correction schemes for specific platforms. Here, while considering the case of qubits encoded in metastable electronic levels of atomic arrays, the authors propose a way to convert a large fraction of occurring errors into detectable leakages, or erasure errors, which are vastly easier to correct.

High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source

Compared to other types of qubits, photon is one of a kind due to its unparalleled advantages in long-distance quantum information exchange. Therefore, photon is a natural candidate for building a large-scale, modular optical quantum computer operating at room temperature. However, low-fidelity two-photon quantum logic gates and their probabilistic nature result in a large resource overhead for fault tolerant quantum computation. While the probabilistic problem can, in principle, be solved by employing multiplexing and error correction, the fidelity of linear-optical quantum logic gate is limited by the imperfections of single photons. Here, we report the demonstration of a linear-optical quantum logic gate with truth table fidelity of 99.84(3)% and entangling gate fidelity of 99.69(4)% post-selected upon the detection of photons. The achieved high gate fidelities are made possible by our near-optimal Rydberg single-photon source. Our work paves the way for scalable photonic quantum applications based on near-optimal single-photon qubits and photon-photon gates.

The current main source of errors for photonic quantum logic gates is the imperfections of the single photons. Here, by using high-quality photons from Rydberg atoms, the authors are able to reach 99.7% entangling gate fidelity in a photonic CNOT gate.

Observation of a molecular bond between ions and Rydberg atoms

Atoms with a highly excited electron, called Rydberg atoms, can form unusual types of molecular bonds^1-4. The bonds differ from the well-known ionic and covalent bonds^5,6 not only by their binding mechanisms, but also by their bond lengths ranging up to several micrometres. Here we observe a new type of molecular ion based on the interaction between the ionic charge and a flipping-induced dipole of a Rydberg atom with a bond length of several micrometres. We measure the vibrational spectrum and spatially resolve the bond length and the angular alignment of the molecule using a high-resolution ion microscope⁷. As a consequence of the large bond length, the molecular dynamics is extremely slow. These results pave the way for future studies of spatio-temporal effects in molecular dynamics (for example, beyond Born-Oppenheimer physics).

Autoionization of Ultracold Cesium Rydberg Atom in 37D5/2 State

We present the observation of an autoionization of cesium 37D5/2 Rydberg atoms in ultracold gases and analyze the autoionization mechanism. The autoionization process is investigated by varying the delay time tD and Rydberg atomic density. The dependence of ionization signals on Rydberg density shows that the Rydberg density has an effect on not only the initial ion signals but also the evolution of the Rydberg atoms. The results reveal that the initial ionization of 37D5/2 Rydberg atoms is mostly attributed to the blackbody radiation (BBR)-induced photoionization, and the BBR-induced transitions to the nearby Rydberg states that lead to further ionization. Our work plays a significant role in investigating the collision between Rydberg atoms and many-body physics.

Few generalized entropic relations related to Rydberg atoms

We calculate the analytical and numerical values of the position space Shannon entropy, momentum space Shannon entropy, and total Shannon entropy, [Formula: see text], [Formula: see text], and [Formula: see text], respectively, of free and trapped Rydberg hydrogen-like atoms. The influence of atomic number Z, the principal quantum number n, and energy E on the Shannon entropy of the Rydberg atoms are illustrated. The scaling properties of Shannon entropy with energy of states E and the principal quantum number n have been reported for the first time to the best of our knowledge. Our work explains how Shannon entropy indicates localization-delocalization of the wavefunction. The total Shannon entropy as a measure of the number of nodes in the trapped Rydberg atom's wavefunction is also discussed. We show why an uncertainty relation based on Shannon entropy is superior to Heisenberg uncertainty for Rydberg atoms.

Quantum optimization of maximum independent set using Rydberg atom arrays

Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally investigate quantum algorithms for solving the Maximum Independent Set problem. We use a hardware-efficient encoding associated with Rydberg blockade, realize closed-loop optimization to test several variational algorithms, and subsequently apply them to systematically explore a class of graphs with programmable connectivity. We find the problem hardness is controlled by the solution degeneracy and number of local minima, and experimentally benchmark the quantum algorithm's performance against classical simulated annealing. On the hardest graphs, we observe a superlinear quantum speedup in finding exact solutions in the deep circuit regime and analyze its origins.

Transient Density-Induced Dipolar Interactions in a Thin Vapor Cell

We exploit the effect of light-induced atomic desorption to produce high atomic densities (n≫k^{3}) in a rubidium vapor cell. An intense off-resonant laser is pulsed for roughly one nanosecond on a micrometer-sized sapphire-coated cell, which results in the desorption of atomic clouds from both internal surfaces. We probe the transient atomic density evolution by time-resolved absorption spectroscopy. With a temporal resolution of ≈ 1 ns, we measure the broadening and line shift of the atomic resonances. Both broadening and line shift are attributed to dipole-dipole interactions. This fast switching of the atomic density and dipolar interactions could be the basis for future quantum devices based on the excitation blockade.

Dynamical Collective Excitations and Entanglement of Two Strongly Correlated Rydberg Superatoms

Based on the dipole blockade effect and with the aid of the superatom (SA) model, we propose a scheme to investigate the correlated evolution of two Rydberg sub-superatoms (SSAs), formed by two spatially separated atomic Rydberg sub-ensembles but in the same blockade region. Starting from the pure separable states, we investigate the in-phase or anti-phase correlated dynamics and explore how two Rydberg SSAs entangle with each other mediated by a single Rydberg excitation. Starting from the entangled states, we discuss the robustness of the system against decoherence induced by the dephasing rate. Our results show that both the correlated evolution of two Rydberg SSAs and their collective-state entanglement are usually sensitive to the number of each Rydberg SSA. This allows us to coherently manipulate the Rydberg ensemble over long distances from the single-quantum level to the mesoscopic level by changing the number of atoms. Furthermore, the method for dividing an SA into two SSAs and obtaining their spin operators without any approximation can be readily generalized to the case of many SSAs. It may have potential promising applications in quantum information processing and provide an attractive platform to study the quantum-classical correspondence, many-body physics and so on.

Collective Resonance of D States in Rubidium Atoms Probed by Optical Two-Dimensional Coherent Spectroscopy

Collective resonance of interacting particles has important implications in many-body quantum systems and their applications. Strong interactions can lead to a blockade that prohibits the excitation of a collective resonance of two or more nearby atoms. However, a collective resonance can be excited with the presence of weak interaction and has been observed for atoms in the first excited state (P state). Here, we report the observation of collective resonance of rubidium atoms in a higher excited state (D state) in addition to the first excited state. The collective resonance is excited by a double-quantum four-pulse excitation sequence. The resulting double-quantum two-dimensional (2D) spectrum displays well-isolated peaks that can be attributed to collective resonances of atoms in P and D states. The experimental one-quantum and double-quantum 2D spectra can be reproduced by a simulation based on the perturbative solutions to the optical Bloch equations, confirming collective resonances as the origin of the measured spectra. The experimental technique provides a new approach for preparing and probing collective resonances of atoms in highly excited states.

Lifetime Measurement of Cesium Atoms Using a Cold Rydberg Gas

The lifetimes of nS1/2 and nD5/2 (n = 60–83) cesium Rydberg states are measured accurately in a magneto-optical trap using the field ionization technique and analyzed with the existing theoretical model. The room temperature blackbody radiation (BBR) and interaction between Rydberg atoms can enhance the decay rate and reduce the spontaneous lifetime of the given Rydberg atom. The measured lifetime shows a good agreement with the calculation accounting a room temperature BBR at low enough Rydberg atomic density. The dependence of measured lifetime on atomic density shows that the collision and interaction between Rydberg atoms have a large effect on the lifetime at higher Rydberg atomic density. The scaling laws of n2.55±0.02 for nD5/2 state and n2.30±0.01 for nS1/2 state within n = 60–83 range are obtained and agreement with the model calculation with a relative deviation less than 3%.