Strongly Correlated Growth of Rydberg Aggregates in a Vapor Cell

Exceptional point and hysteresis trajectories in cold Rydberg atomic gases

The interplay between strong long-range interactions and the coherent driving contribute to the formation of complex patterns, symmetry, and novel phases of matter in many-body systems. However, long-range interactions may induce an additional dissipation channel, resulting in non-Hermitian many-body dynamics and the emergence of exceptional points in spectrum. Here, we report experimental observation of interaction-induced exceptional points in cold Rydberg atomic gases, revealing the breaking of charge-conjugation parity symmetry. By measuring the transmission spectrum under increasing and decreasing probe intensity, the interaction-induced hysteresis trajectories are observed, which give rise to non-Hermitian dynamics. We record the area enclosed by hysteresis loops and investigate the dynamics of hysteresis loops. The reported exceptional points and hysteresis trajectories in cold Rydberg atomic gases provide valuable insights into the underlying non-Hermitian physics in many-body systems, allowing us to study the interplay between long-range interactions and non-Hermiticity.

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.

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.

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.

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.

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.

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.

Many-Body Radiative Decay in Strongly Interacting Rydberg Ensembles

When atoms are excited to high-lying Rydberg states they interact strongly with dipolar forces. The resulting state-dependent level shifts allow us to study many-body systems displaying intriguing nonequilibrium phenomena, such as constrained spin systems, and are at the heart of numerous technological applications, e.g., in quantum simulation and computation platforms. Here, we show that these interactions also have a significant impact on dissipative effects caused by the inevitable coupling of Rydberg atoms to the surrounding electromagnetic field. We demonstrate that their presence modifies the frequency of the photons emitted from the Rydberg atoms, making it dependent on the local neighborhood of the emitting atom. Interactions among Rydberg atoms thus turn spontaneous emission into a many-body process which manifests, in a thermodynamically consistent Markovian setting, in the emergence of collective jump operators in the quantum master equation governing the dynamics. We discuss how this collective dissipation-stemming from a mechanism different from the much studied superradiance and subradiance-accelerates decoherence and affects dissipative phase transitions in Rydberg ensembles.

mm-wave Rydberg-Rydberg transitions gauge intermolecular coupling in a molecular ultracold plasma

Out-of-equilibrium, strong correlation in a many-body system can trigger emergent properties that act to constrain the natural dissipation of energy and matter. Signs of such self-organization appear in the avalanche, bifurcation, and quench of a state-selected Rydberg gas of nitric oxide to form an ultracold, strongly correlated ultracold plasma. Work reported here focuses on initial stages of avalanche and quench, and uses the mm-wave spectroscopy of an embedded quantum probe to characterize the intermolecular interaction dynamics associated with the evolution to plasma. Double-resonance excitation prepares a Rydberg gas of nitric oxide composed of a single selected state of principal quantum number, n0. Penning ionization, followed by an avalanche of electron-Rydberg collisions, forms a plasma of NO+ ions and weakly bound electrons, in which a residual population of n0 Rydberg molecules evolves to a state of high orbital angular momentum, l. Predissociation depletes the plasma of low- l molecules. Relaxation ceases and n0l(2) molecules with l {greater than or equal to} 4 persist for very long times. At short times, varying excitation spectra of mm-wave Rydberg-Rydberg transitions mark the rate of electron-collisional l-mixing. Deep depletion resonances that persist for long times signal energy redistribution in the basis of central-field Rydberg states. The widths and asymmetries of Fano lineshapes witness the degree to which coupling in the arrested bath i) broadens the allowed transition and ii) mixes the local network of levels in the ensemble.

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.

Hydrodynamic Stabilization of Self-Organized Criticality in a Driven Rydberg Gas

Signatures of self-organized criticality (SOC) have recently been observed in an ultracold atomic gas under continuous laser excitation to strongly interacting Rydberg states [S. Helmrich et al., Nature, 577, 481-486 (2020)]. This creates unique possibilities to study this intriguing dynamical phenomenon under controlled experimental conditions. Here we theoretically and experimentally examine the self-organizing dynamics of a driven ultracold gas and identify an unanticipated feedback mechanism originating from the interaction of the system with a thermal reservoir. Transport of particles from the flanks of the cloud toward the center compensates avalanche-induced atom loss. This mechanism sustains an extended critical region in the trap center for timescales much longer than the initial self-organization dynamics. The characteristic flattop density profile provides an additional experimental signature for SOC while simultaneously enabling studies of SOC under almost homogeneous conditions. We present a hydrodynamic description for the reorganization of the atom density, which very accurately describes the experimentally observed features on intermediate and long timescales, and which is applicable to both collisional hydrodynamic and chaotic ballistic regimes.

Epidemic growth and Griffiths effects on an emergent network of excited atoms

Whether it be physical, biological or social processes, complex systems exhibit dynamics that are exceedingly difficult to understand or predict from underlying principles. Here we report a striking correspondence between the excitation dynamics of a laser driven gas of Rydberg atoms and the spreading of diseases, which in turn opens up a controllable platform for studying non-equilibrium dynamics on complex networks. The competition between facilitated excitation and spontaneous decay results in sub-exponential growth of the excitation number, which is empirically observed in real epidemics. Based on this we develop a quantitative microscopic susceptible-infected-susceptible model which links the growth and final excitation density to the dynamics of an emergent heterogeneous network and rare active region effects associated to an extended Griffiths phase. This provides physical insights into the nature of non-equilibrium criticality in driven many-body systems and the mechanisms leading to non-universal power-laws in the dynamics of complex systems.

The emergent excitation dynamics of an ultracold gas of Rydberg atoms exhibits features analogous to epidemic spreading on networks. Wintermantel et al. propose a controllable experimental system for studying network dynamics at the interface of mathematical models and real-world complex systems.

Self-Induced Transparency in Warm and Strongly Interacting Rydberg Gases

We study dispersive optical nonlinearities of short pulses propagating in high number density, warm atomic vapors where the laser resonantly excites atoms to Rydberg P states via a single-photon transition. Three different regimes of the light-atom interaction, dominated by either Doppler broadening, Rydberg atom interactions, or decay due to thermal collisions between ground state and Rydberg atoms, are found. We show that using fast Rabi flopping and strong Rydberg atom interactions, both in the order of gigahertz, can overcome the Doppler effect as well as collisional decay, leading to a sizable dispersive optical nonlinearity on nanosecond timescales. In this regime, self-induced transparency (SIT) emerges when areas of the nanosecond pulse are determined primarily by the Rydberg atom interaction, rather than the area theorem of interaction-free SIT. We identify, both numerically and analytically, the condition to realize Rydberg SIT. Our study contributes to efforts in achieving quantum information processing using glass cell technologies.

Dynamics and large deviation transitions of the XOR-Fredrickson-Andersen kinetically constrained model

We study a one-dimensional classical stochastic kinetically constrained model (KCM) inspired by Rydberg atoms in their "facilitated" regime, where sites can flip only if a single of their nearest neighbors is excited. We call this model "XOR-FA" to distinguish it from the standard Fredrickson-Andersen (FA) model. We describe the dynamics of the XOR-FA model, including its relation to simple exclusion processes in its domain wall representation. The interesting relaxation dynamics of the XOR-FA is related to the prominence of large dynamical fluctuations that lead to phase transitions between active and inactive dynamical phases as in other KCMs. By means of numerical tensor network methods we study in detail such transitions in the dynamical large deviation regime.

Vibrational Dressing in Kinetically Constrained Rydberg Spin Systems

Quantum spin systems with kinetic constraints have become paradigmatic for exploring collective dynamical behavior in many-body systems. Here we discuss a facilitated spin system which is inspired by recent progress in the realization of Rydberg quantum simulators. This platform allows to control and investigate the interplay between facilitation dynamics and the coupling of spin degrees of freedom to lattice vibrations. Developing a minimal model, we show that this leads to the formation of polaronic quasiparticle excitations which are formed by many-body spin states dressed by phonons. We investigate in detail the properties of these quasiparticles, such as their dispersion relation, effective mass, and the quasiparticle weight. Rydberg lattice quantum simulators are particularly suited for studying this phonon-dressed kinetically constrained dynamics as their exaggerated length scales permit the site-resolved monitoring of spin and phonon degrees of freedom.

Signatures of self-organized criticality in an ultracold atomic gas

Self-organized criticality is an elegant explanation of how complex structures emerge and persist throughout nature¹, and why such structures often exhibit similar scale-invariant properties^2-9. Although self-organized criticality is sometimes captured by simple models that feature a critical point as an attractor for the dynamics^10-15, the connection to real-world systems is exceptionally hard to test quantitatively^16-21. Here we observe three key signatures of self-organized criticality in the dynamics of a driven-dissipative gas of ultracold potassium atoms: self-organization to a stationary state that is largely independent of the initial conditions; scale-invariance of the final density characterized by a unique scaling function; and large fluctuations of the number of excited atoms (avalanches) obeying a characteristic power-law distribution. This work establishes a well-controlled platform for investigating self-organization phenomena and non-equilibrium criticality, with experimental access to the underlying microscopic details of the system.

Using Matrix Product States to Study the Dynamical Large Deviations of Kinetically Constrained Models

Here we demonstrate that tensor network techniques-originally devised for the analysis of quantum many-body problems-are well suited for the detailed study of rare event statistics in kinetically constrained models (KCMs). As concrete examples, we consider the Fredrickson-Andersen and East models, two paradigmatic KCMs relevant to the modeling of glasses. We show how variational matrix product states allow us to numerically approximate-systematically and with high accuracy-the leading eigenstates of the tilted dynamical generators, which encode the large deviation statistics of the dynamics. Via this approach, we can study system sizes beyond what is possible with other methods, allowing us to characterize in detail the finite size scaling of the trajectory-space phase transition of these models, the behavior of spectral gaps, and the spatial structure and "entanglement" properties of dynamical phases. We discuss the broader implications of our results.

Physical swap dynamics, shortcuts to relaxation, and entropy production in dissipative Rydberg gases

Dense Rydberg gases are out-of-equilibrium systems where strong density-density interactions give rise to effective kinetic constraints. They cause dynamic arrest associated with highly constrained many-body configurations, leading to slow relaxation and glassy behavior. Multicomponent Rydberg gases feature additional long-range interactions such as excitation exchange. These are analogous to particle swaps used to artificially accelerate relaxation in simulations of atomistic models of classical glass formers. In Rydberg gases, however, swaps are real physical processes, which provide dynamical shortcuts to relaxation. They permit the accelerated approach to stationarity in experiment and at the same time have an impact on the nonequilibrium stationary state. In particular, their interplay with radiative decay processes amplifies irreversibility of the dynamics, an effect which we quantify via the entropy production at stationarity. Our work highlights an intriguing analogy between real dynamical processes in Rydberg gases and artificial dynamics underlying advanced Monte Carlo methods. Moreover, it delivers a quantitative characterization of the dramatic effect swaps have on the structure and dynamics of their stationary state.

Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton

We study the statistical properties of the long-time dynamics of the rule 54 reversible cellular automaton (CA), driven stochastically at its boundaries. This CA can be considered as a discrete-time and deterministic version of the Fredrickson-Andersen kinetically constrained model (KCM). By means of a matrix product ansatz, we compute the exact large deviation cumulant generating functions for a wide range of time-extensive observables of the dynamics, together with their associated rate functions and conditioned long-time distributions over configurations. We show that for all instances of boundary driving the CA dynamics occurs at the point of phase coexistence between competing active and inactive dynamical phases, similar to what happens in more standard KCMs. We also find the exact finite size scaling behavior of these trajectory transitions, and provide the explicit "Doob-transformed" dynamics that optimally realizes rare dynamical events.

Robust Coherent Transport of Light in Multilevel Hot Atomic Vapors

Using a model system, we demonstrate both experimentally and theoretically that coherent scattering of light can be robust in hot atomic vapors despite a significant Doppler effect. By operating in a linear regime of far-detuned light scattering, we also unveil the emergence of interference triggered by inelastic Stokes and anti-Stokes transitions involving the atomic hyperfine structure.

Delocalized excitons and interaction effects in extremely dilute thermal ensembles

Long-range interparticle interactions are revealed in extremely dilute thermal atomic ensembles using highly sensitive nonlinear femtosecond spectroscopy. Delocalized excitons are detected in the atomic systems at particle densities where the mean interatomic distance (>10 μm) is much greater than the laser wavelength and multi-particle coherences should destructively interfere over the ensemble average. With a combined experimental and theoretical analysis, we identify an effective interaction mechanism, presumably of dipolar nature, as the origin of the excitonic signals. Our study implies that even in highly-dilute thermal atom ensembles, significant transition dipole-dipole interaction networks may form that require advanced modeling beyond the nearest neighbor approximation to quantitatively capture the details of their many-body properties.

Experimental realization of a Rydberg optical Feshbach resonance in a quantum many-body system

Feshbach resonances are a powerful tool to tune the interaction in an ultracold atomic gas. The commonly used magnetic Feshbach resonances are specific for each species and are restricted with respect to their temporal and spatial modulation. Optical Feshbach resonances are an alternative which can overcome this limitation. Here, we show that ultra-long-range Rydberg molecules can be used to implement an optical Feshbach resonance. Tuning the on-site interaction of a degenerate Bose gas in a 3D optical lattice, we demonstrate a similar performance compared to recent realizations of optical Feshbach resonances using intercombination transitions. Our results open up a class of optical Feshbach resonances with a plenitude of available lines for many atomic species and the possibility to further increase the performance by carefully selecting the underlying Rydberg state.

Ultrafast Coherent Control of Condensed Matter with Attosecond Precision

Coherent control is a technique to manipulate wave functions of matter with light. Coherent control of isolated atoms and molecules in the gas phase is well-understood and developed since the 1990s, whereas its application to condensed matter is more difficult because its coherence lifetime is shorter. We have recently applied this technique to condensed matter samples, one of which is solid para-hydrogen ( p-H₂). Intramolecular vibrational excitation of solid p-H₂ gives an excited vibrational wave function called a "vibron", which is delocalized over many hydrogen molecules in a manner similar to a Frenkel exciton. It has a long coherence lifetime, so we have chosen solid p-H₂ as our first target in the condensed phase. We shine a time-delayed pair of femtosecond laser pulses on p-H₂ to generate vibrons. Their interference results in modulation of the amplitude of their superposition. Scanning the interpulse delay on the attosecond time scale gives a high interferometric contrast, which demonstrates the possibility of using solid p-H₂ as a carrier of information encoded in the vibrons. In the second example, we have controlled the terahertz collective phonon motion, called a "coherent phonon", of a single crystal of bismuth. We employ an intensity-modulated laser pulse, whose temporal envelope is modulated with terahertz frequency by overlap of two positively chirped laser pulses with their adjustable time delay. This modulated laser pulse is shined on the bismuth crystal to excite its two orthogonal phonon modes. Their relative amplitudes are controlled by tuning the delay between the two chirped pulses on the attosecond time scale. Two-dimensional atomic motion in the crystal is thus controlled arbitrarily. The method is based on the simple, robust, and universal concept that in any physical system, two-dimensional particle motion is decomposed into two orthogonal one-dimensional motions, and thus, it is applicable to a variety of condensed matter systems. In the third example, the double-pulse interferometry used for solid p-H₂ has been applied to many-body electronic wave functions of an ensemble of ultracold rubidium Rydberg atoms, hereafter called a "strongly correlated ultracold Rydberg gas". This has allowed the observation and control of many-body electron dynamics of more than 40 Rydberg atoms interacting with each other. This new combination of ultrafast coherent control and ultracold atoms offers a versatile platform to precisely observe and manipulate nonequilibrium dynamics of quantum many-body systems on the ultrashort time scale. These three examples are digested in this Account.

Rydberg interaction induced enhanced excitation in thermal atomic vapor

We present the experimental demonstration of interaction induced enhancement in Rydberg excitation or Rydberg anti-blockade in thermal atomic vapor. We have used optical heterodyne detection technique to measure Rydberg population due to two-photon excitation to the Rydberg state. The anti-blockade peak which doesn’t satisfy the two-photon resonant condition is observed along with the usual two-photon resonant peak which can’t be explained using the model with non-interacting three-level atomic system. A model involving two interacting atoms is formulated for thermal atomic vapor using the dressed states of three-level atomic system to explain the experimental observations. A non-linear dependence of vapor density is observed for the anti-blockade peak which also increases with increase in principal quantum number of the Rydberg state. A good agreement is found between the experimental observations and the proposed interacting model. Our result implies possible applications towards quantum logic gates using Rydberg anti-blockade in thermal atomic vapor.

Spontaneous avalanche dephasing in large Rydberg ensembles

Strong dipole-exchange interactions due to spontaneously produced contaminant states can trigger rapid dephasing in many-body Rydberg ensembles [E. Goldschmidt et al., PRL 116, 113001 (2016)]. Such broadening has serious implications for many proposals to coherently use Rydberg interactions, particularly Rydberg dressing proposals. The dephasing arises as a runaway process where the production of the first contaminant atoms facilitates the creation of more contaminant atoms. Here we study the time dependence of this process with stroboscopic approaches. Using a pump-probe technique, we create an excess "pump" Rydberg population and probe its effect with a different "probe" Rydberg transition. We observe a reduced resonant pumping rate and an enhancement of the excitation on both sides of the transition as atoms are added to the pump state. We also observe a timescale for population growth significantly shorter than predicted by homogeneous mean-field models, as expected from a clustered growth mechanism where high-order correlations dominate the dynamics. These results support earlier works and confirm that the time scale for the onset of dephasing is reduced by a factor which scales as the inverse of the atom number. In addition, we discuss several approaches to minimize these effects of spontaneous broadening, including stroboscopic techniques and operating at cryogenic temperatures. It is challenging to avoid the unwanted broadening effects, but under some conditions they can be mitigated.

Epidemic Dynamics in Open Quantum Spin Systems

We explore the nonequilibrium evolution and stationary states of an open many-body system that displays epidemic spreading dynamics in a classical and a quantum regime. Our study is motivated by recent experiments conducted in strongly interacting gases of highly excited Rydberg atoms where the facilitated excitation of Rydberg states competes with radiative decay. These systems approximately implement open quantum versions of models for population dynamics or disease spreading where species can be in a healthy, infected or immune state. We show that in a two-dimensional lattice, depending on the dominance of either classical or quantum effects, the system may display a different kind of nonequilibrium phase transition. We moreover discuss the observability of our findings in laser driven Rydberg gases with particular focus on the role of long-range interactions.

Effect of stray fields on Rydberg states in hollow-core PCF probed by higher-order modes

The spectroscopy of atomic gases confined in hollow-core photonic crystal fiber (HC-PCF) provides optimal atom-light coupling beyond the diffraction limit, which is desirable for various applications such as sensing, referencing, and nonlinear optics. Recently, coherent spectroscopy was carried out on highly excited Rydberg states at room temperature in a gas-filled HC-PCF. The large polarizability of the Rydberg states made it possible to detect weak electric fields inside the fiber. In this Letter, we show that by combining highly excited Rydberg states with higher-order optical modes, we can gain insight into the distribution and underlying effects of these electric fields. Comparisons between experimental findings and simulations indicate that the fields are caused by the dipole moments of atoms adsorbed on the hollow-core wall. Knowing the origin of the electric fields is an important step towards suppressing them in future HC-PCF experiments. Furthermore, a better understanding of the influence of adatoms will be advantageous for optimizing electric-field-sensitive experiments carried out in the vicinity of nearby surfaces.

Versatile, high-power 460 nm laser system for Rydberg excitation of ultracold potassium

We present a versatile laser system which provides more than 1.5 W of narrowband light, tunable in the range from 455-463 nm. It consists of a commercial titanium-sapphire laser which is frequency doubled using resonant cavity second harmonic generation and stabilized to an external reference cavity. We demonstrate a wide wavelength tuning range combined with a narrow linewidth and low intensity noise. This laser system is ideally suited for atomic physics experiments such as two-photon excitation of Rydberg states of potassium atoms with principal quantum numbers n > 18. To demonstrate this we perform two-photon spectroscopy on ultracold potassium gases in which we observe an electromagnetically induced transparency resonance corresponding to the 35s_1/2 state and verify the long-term stability of the laser system. Additionally, by performing spectroscopy in a magneto-optical trap we observe strong loss features corresponding to the excitation of s, p, d and higher-l states accessible due to a small electric field.

Rydberg-atom based radio-frequency electrometry using frequency modulation spectroscopy in room temperature vapor cells

Rydberg atom-based electrometry enables traceable electric field measurements with high sensitivity over a large frequency range, from gigahertz to terahertz. Such measurements are particularly useful for the calibration of radio frequency and terahertz devices, as well as other applications like near field imaging of electric fields. We utilize frequency modulated spectroscopy with active control of residual amplitude modulation to improve the signal to noise ratio of the optical readout of Rydberg atom-based radio frequency electrometry. Matched filtering of the signal is also implemented. Although we have reached similarly, high sensitivity with other read-out methods, frequency modulated spectroscopy is advantageous because it is well-suited for building a compact, portable sensor. In the current experiment, ∼3 µV cm^-1 Hz^-1/2 sensitivity is achieved and is found to be photon shot noise limited.

Control of Spatial Correlations between Rydberg Excitations using Rotary Echo

We manipulate correlations between Rydberg excitations in cold atom samples using a rotary-echo technique in which the phase of the excitation pulse is flipped at a selected time during the pulse. The correlations are due to interactions between the Rydberg atoms. We measure the resulting change in the spatial pair correlation function of the excitations via direct position-sensitive atom imaging. For zero detuning of the lasers from the interaction-free Rydberg-excitation resonance, the pair-correlation value at the most likely nearest-neighbor Rydberg-atom distance is substantially enhanced when the phase is flipped at the middle of the excitation pulse. In this case, the rotary echo eliminates most uncorrelated (unpaired) atoms, leaving an abundance of correlated atom pairs at the end of the sequence. In off-resonant cases, a complementary behavior is observed. We further characterize the effect of the rotary-echo excitation sequence on the excitation-number statistics.

Facilitation Dynamics and Localization Phenomena in Rydberg Lattice Gases with Position Disorder

We explore the dynamics of Rydberg excitations in an optical tweezer array under antiblockade (or facilitation) conditions. Because of the finite temperature the atomic positions are randomly spread, an effect that leads to quenched correlated disorder in the interatomic interaction strengths. This drastically affects the facilitation dynamics as we demonstrate experimentally on the elementary example of two atoms. To shed light on the role of disorder in a many-body setting we show that here the dynamics is governed by an Anderson-Fock model, i.e., an Anderson model formulated on a lattice with sites corresponding to many-body Fock states. We first consider a one-dimensional atom chain in a limit that is described by a one-dimensional Anderson-Fock model with disorder on every other site, featuring both localized and delocalized states. We then illustrate the effect of disorder experimentally in a situation in which the system maps on a two-dimensional Anderson-Fock model on a trimmed square lattice. We observe a clear suppression of excitation propagation, which we ascribe to the localization of the many-body wave functions in Hilbert space.

Multicritical behavior in dissipative Ising models

We analyze theoretically the many-body dynamics of a dissipative Ising model in a transverse field using a variational approach. We find that the steady-state phase diagram is substantially modified compared to its equilibrium counterpart, including the appearance of a multicritical point belonging to a different universality class. Building on our variational analysis, we establish a field-theoretical treatment corresponding to a dissipative variant of a Ginzburg-Landau theory, which allows us to compute the upper critical dimension of the system. Finally, we present a possible experimental realization of the dissipative Ising model using ultracold Rydberg gases.

Direct observation of ultrafast many-body electron dynamics in an ultracold Rydberg gas

Many-body correlations govern a variety of important quantum phenomena such as the emergence of superconductivity and magnetism. Understanding quantum many-body systems is thus one of the central goals of modern sciences. Here we demonstrate an experimental approach towards this goal by utilizing an ultracold Rydberg gas generated with a broadband picosecond laser pulse. We follow the ultrafast evolution of its electronic coherence by time-domain Ramsey interferometry with attosecond precision. The observed electronic coherence shows an ultrafast oscillation with a period of 1 femtosecond, whose phase shift on the attosecond timescale is consistent with many-body correlations among Rydberg atoms beyond mean-field approximations. This coherent and ultrafast many-body dynamics is actively controlled by tuning the orbital size and population of the Rydberg state, as well as the mean atomic distance. Our approach will offer a versatile platform to observe and manipulate non-equilibrium dynamics of quantum many-body systems on the ultrafast timescale.

Studying long-range interactions in the controlled environment of trapped ultracold gases can help our understanding of fundamental many-body physics. Here the authors excite a gas of Rydberg atoms with a ps laser pulse, demonstrating behaviour consistent with many-body correlations beyond mean-field.

Emergent kinetic constraints, ergodicity breaking, and cooperative dynamics in noisy quantum systems

Kinetically constrained spin systems play an important role in understanding key properties of the dynamics of slowly relaxing materials, such as glasses. Recent experimental studies have revealed that manifest kinetic constraints govern the evolution of strongly interacting gases of highly excited atoms in a noisy environment. Motivated by this development we explore which types of kinetically constrained dynamics can generally emerge in quantum spin systems subject to strong noise and show how, in this framework, constraints are accompanied by conservation laws. We discuss an experimentally realizable case of a lattice gas, where the interplay between those and the geometry of the lattice leads to collective behavior and time-scale separation even at infinite temperature. This is in contrast to models of glass-forming substances which typically rely on low temperatures and the consequent suppression of thermal activation.

Observation of Rydberg-Atom Macrodimers: Micrometer-Sized Diatomic Molecules

Long-range metastable molecules consisting of two cesium atoms in high Rydberg states have been observed in an ultracold gas. A sequential three-photon two-color photoassociation scheme is employed to form these molecules in states, which correlate to np(n+1)s dissociation asymptotes. Spectral signatures of bound molecular states are clearly resolved at the positions of avoided crossings between long-range van der Waals potential curves. The experimental results are in agreement with simulations based on a detailed model of the long-range multipole-multipole interactions of Rydberg-atom pair states. We show that a full model is required to accurately predict the occurrence of bound Rydberg macrodimers. The macrodimers are distinguished from repulsive molecular states by their behavior with respect to spontaneous ionization and possible decay channels are discussed.

Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations

Stochastic processes with absorbing states feature examples of nonequilibrium universal phenomena. While the classical regime has been thoroughly investigated in the past, relatively little is known about the behavior of these nonequilibrium systems in the presence of quantum fluctuations. Here, we theoretically address such a scenario in an open quantum spin model which, in its classical limit, undergoes a directed percolation phase transition. By mapping the problem to a nonequilibrium field theory, we show that the introduction of quantum fluctuations stemming from coherent, rather than statistical, spin flips alters the nature of the transition such that it becomes first order. In the intermediate regime, where classical and quantum dynamics compete on equal terms, we highlight the presence of a bicritical point with universal features different from the directed percolation class in a low dimension. We finally propose how this physics could be explored within gases of interacting atoms excited to Rydberg states.

Anomalous Broadening in Driven Dissipative Rydberg Systems

We observe interaction-induced broadening of the two-photon 5s-18s transition in ^{87}Rb atoms trapped in a 3D optical lattice. The measured linewidth increases by nearly 2 orders of magnitude with increasing atomic density and excitation strength, with corresponding suppression of resonant scattering and enhancement of off-resonant scattering. We attribute the increased linewidth to resonant dipole-dipole interactions of 18s atoms with blackbody induced population in nearby np states. Over a range of initial atomic densities and excitation strengths, the transition width is described by a single function of the steady-state density of Rydberg atoms, and the observed resonant excitation rate corresponds to that of a two-level system with the measured, rather than natural, linewidth. The broadening mechanism observed here is likely to have negative implications for many proposals with coherently interacting Rydberg atoms.

Self-similar nonequilibrium dynamics of a many-body system with power-law interactions

The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases, which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations-often referred to as the blockade radius-is not a static but rather a dynamic quantity.

Observation of interference effects via four-photon excitation of highly excited Rydberg states in thermal cesium vapor

We report on the observation of electromagnetically induced transparency (EIT) and absorption (EIA) of highly excited Rydberg states in thermal Cs vapor using a four-step excitation scheme. The advantage of this four-step scheme is that the final transition to the Rydberg state has a large dipole moment and one can achieve similar Rabi frequencies to two- or three-step excitation schemes using two orders of magnitude less laser power. This scheme enables new applications such as dephasing free Rydberg excitation. The observed lineshapes are in good agreement with simulations based on multilevel optical Bloch equations.

Sub-Poissonian Statistics of Jamming Limits in Ultracold Rydberg Gases

Several recent experiments have established by measuring the Mandel Q parameter that the number of Rydberg excitations in ultracold gases exhibits sub-Poissonian statistics. This effect is attributed to the Rydberg blockade that occurs due to the strong interatomic interactions between highly excited atoms. Because of this blockade effect, the system can end up in a state in which all particles are either excited or blocked: a jamming limit. We analyze appropriately constructed random-graph models that capture the blockade effect, and derive formulae for the mean and variance of the number of Rydberg excitations in jamming limits. This yields an explicit relationship between the Mandel Q parameter and the blockade effect, and comparison to measurement data shows strong agreement between theory and experiment.