Publisher Correction: Signatures of self-organized criticality in an ultracold atomic gas.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

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 properties2-9. Although self-organized criticality is sometimes captured by simple models that feature a critical point as an attractor for the dynamics10-15, the connection to real-world systems is exceptionally hard to test quantitatively16-21. 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.

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.

Unitary and Nonunitary Quantum Cellular Automata with Rydberg Arrays.

We propose a physical realization of quantum cellular automata (QCA) using arrays of ultracold atoms excited to Rydberg states. The key ingredient is the use of programmable multifrequency couplings which generalize the Rydberg blockade and facilitation effects to a broader set of nonadditive, unitary and nonunitary (dissipative) conditional interactions. Focusing on a 1D array we define a set of elementary QCA rules that generate complex and varied quantum dynamical behavior. Finally, we demonstrate theoretically that Rydberg QCA is ideally suited for variational quantum optimization protocols and quantum state engineering by finding parameters that generate highly entangled states as the steady state of the quantum dynamics.

Realization of a Rydberg-Dressed Ramsey Interferometer and Electrometer.

We present the experimental realization and characterization of a Ramsey interferometer based on optically trapped ultracold potassium atoms, where one state is continuously coupled by an off-resonant laser field to a highly excited Rydberg state. We show that the observed interference signals can be used to precisely measure the Rydberg atom-light coupling strength as well as the population and coherence decay rates of the Rydberg-dressed states with subkilohertz accuracy and for Rydberg state fractions as small as one part in 10^{6}. We also demonstrate an application for measuring small, static electric fields with high sensitivity. This provides the means to combine the outstanding coherence properties of Ramsey interferometers based on atomic ground states with a controllable coupling to strongly interacting states, thus expanding the number of systems suitable for metrological applications and many-body physics studies.

Diffusive to Nonergodic Dipolar Transport in a Dissipative Atomic Medium.

We investigate the dipole-mediated transport of Rydberg impurities through an ultracold gas of atoms prepared in an auxiliary Rydberg state. In one experiment, we continuously probe the system by coupling the auxiliary Rydberg state to a rapidly decaying state that realizes a dissipative medium. In situ imaging of the impurities reveals diffusive spreading controlled by the intensity of the probe laser. By preparing the same density of hopping partners, but then switching off the dressing fields, the spreading is effectively frozen. This is consistent with numerical simulations, which indicate the coherently evolving system enters a nonergodic extended phase. This opens the way to study transport and localization phenomena in systems with long-range hopping and controllable dissipation.

Relaxation of an Isolated Dipolar-Interacting Rydberg Quantum Spin System.

How do isolated quantum systems approach an equilibrium state? We experimentally and theoretically address this question for a prototypical spin system formed by ultracold atoms prepared in two Rydberg states with different orbital angular momenta. By coupling these states with a resonant microwave driving, we realize a dipolar XY spin-1/2 model in an external field. Starting from a spin-polarized state, we suddenly switch on the external field and monitor the subsequent many-body dynamics. Our key observation is density dependent relaxation of the total magnetization much faster than typical decoherence rates. To determine the processes governing this relaxation, we employ different theoretical approaches that treat quantum effects on initial conditions and dynamical laws separately. This allows us to identify an intrinsically quantum component to the relaxation attributed to primordial quantum fluctuations.

Growth and annual survival estimates to examine the ecology of larval lamprey and the implications of ageing error in fitting models.

This study used existing western brook lamprey Lampetra richardsoni age information to fit three different growth models (i.e. von Bertalanffy, Gompertz and logistic) with and without error in age estimates. Among these growth models, there was greater support for the logistic and Gompertz models than the von Bertalanffy model, regardless of ageing error assumptions. The von Bertalanffy model, however, appeared to fit the data well enough to permit survival estimates; using length-based estimators, annual survival varied between 0·64 (95% credibility interval: 0·44-0·79) and 0·81 (0·79-0·83) depending on ageing and growth process error structure. These estimates are applicable to conservation and management of L. richardsoni and other western lampreys (e.g. Pacific lamprey Entosphenus tridentatus) and can potentially be used in the development of life-cycle models for these species. These results also suggest that estimators derived from von Bertalanffy growth models should be interpreted with caution if there is high uncertainty in age estimates.

Correlated Exciton Transport in Rydberg-Dressed-Atom Spin Chains.

We investigate the transport of excitations through a chain of atoms with nonlocal dissipation introduced through coupling to additional short-lived states. The system is described by an effective spin-1/2 model where the ratio of the exchange interaction strength to the reservoir coupling strength determines the type of transport, including coherent exciton motion, incoherent hopping, and a regime in which an emergent length scale leads to a preferred hopping distance far beyond nearest neighbors. For multiple impurities, the dissipation gives rise to strong nearest-neighbor correlations and entanglement. These results highlight the importance of nontrivial dissipation, correlations, and many-body effects in recent experiments on the dipole-mediated transport of Rydberg excitations.

Quantum simulation of energy transport with embedded Rydberg aggregates.

We show that an array of ultracold Rydberg atoms embedded in a laser driven background gas can serve as an aggregate for simulating exciton dynamics and energy transport with a controlled environment. Energetic disorder and decoherence introduced by the interaction with the background gas atoms can be controlled by the laser parameters. This allows for an almost ideal realization of a Haken-Reineker-Strobl-type model for energy transport. The transport can be monitored using the same mechanism that provides control over the environment. The degree of decoherence is traced back to information gained on the excitation location through the monitoring, turning the setup into an experimentally accessible model system for studying the effects of quantum measurements on the dynamics of a many-body quantum system.

Full counting statistics of laser excited Rydberg aggregates in a one-dimensional geometry.

We experimentally study the full counting statistics of few-body Rydberg aggregates excited from a quasi-one-dimensional atomic gas. We measure asymmetric excitation spectra and increased second and third order statistical moments of the Rydberg number distribution, from which we determine the average aggregate size. Estimating rates for different excitation processes we conclude that the aggregates grow sequentially around an initial grain. Direct comparison with numerical simulations confirms this conclusion and reveals the presence of liquidlike spatial correlations. Our findings demonstrate the importance of dephasing in strongly correlated Rydberg gases and introduce a way to study spatial correlations in interacting many-body quantum systems without imaging.

Spontaneous avalanche ionization of a strongly blockaded Rydberg gas.

We report the sudden and spontaneous evolution of an initially correlated gas of repulsively interacting Rydberg atoms to an ultracold plasma. Under continuous laser coupling we create a Rydberg ensemble in the strong blockade regime, which at longer times undergoes an ionization avalanche. By combining optical imaging and ion detection, we access the full information on the dynamical evolution of the system, including the rapid increase in the number of ions and a sudden depletion of the Rydberg and ground state densities. Rydberg-Rydberg interactions are observed to strongly affect the dynamics of plasma formation. Using a coupled rate-equation model to describe our data, we extract the average energy of electrons trapped in the plasma, and an effective cross section for ionizing collisions between Rydberg atoms and atoms in low-lying states. Our results suggest that the initial correlations of the Rydberg ensemble should persist through the avalanche. This would provide the means to overcome disorder-induced heating, and offer a route to enter new strongly coupled regimes.

Sub-Poissonian statistics of Rydberg-interacting dark-state polaritons.

We observe individual dark-state polaritons as they propagate through an ultracold atomic gas involving Rydberg states coupled via an electromagnetically induced transparency resonance. Strong long-range interactions between Rydberg excitations give rise to a blockade between polaritons, resulting in large optical nonlinearities and modified polariton number statistics. By combining optical imaging and high-fidelity detection of the Rydberg polaritons we investigate both aspects of this coupled atom-light system. We map out the full nonlinear optical response as a function of atomic density and follow the temporal evolution of polaritons through the atomic cloud. In the blockade regime, the statistical fluctuations of the polariton number drop well below the quantum noise limit. The low level of fluctuations indicates that photon correlations modified by the strong interactions have a significant backaction on the Rydberg atom statistics.

Interaction enhanced imaging of individual Rydberg atoms in dense gases.

We propose a new all-optical method to image individual Rydberg atoms embedded within dense gases of ground state atoms. The scheme exploits interaction-induced shifts on highly polarizable excited states of probe atoms, which can be spatially resolved via an electromagnetically induced transparency resonance. Using a realistic model, we show that it is possible to image individual Rydberg atoms with enhanced sensitivity and high resolution despite photon-shot noise and atomic density fluctuations. This new imaging scheme could be extended to other impurities such as ions, and is ideally suited to equilibrium and dynamical studies of complex many-body phenomena involving strongly interacting particles. As an example we study blockade effects and correlations in the distribution of Rydberg atoms optically excited from a dense gas.

Crossover from 2D to 3D in a weakly interacting Fermi gas.

We have studied the transition from two to three dimensions in a low temperature weakly interacting 6Li Fermi gas. Below a critical atom number N(2D) only the lowest transverse vibrational state of a highly anisotropic oblate trapping potential is occupied and the gas is two dimensional. Above N(2D) the Fermi gas enters the quasi-2D regime where shell structure associated with the filling of individual transverse oscillator states is apparent. This dimensional crossover is demonstrated through measurements of the cloud size and aspect ratio versus atom number.

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.

Sub-Poissonian atom-number fluctuations by three-body loss in mesoscopic ensembles.

We show that three-body loss of trapped atoms leads to sub-Poissonian atom-number fluctuations. We prepare hundreds of dense ultracold ensembles in an array of magnetic microtraps which undergo rapid three-body decay. The shot-to-shot fluctuations of the number of atoms per trap are sub-Poissonian, for ensembles comprising 50-300 atoms. The measured relative variance or Fano factor F=0.53+/-0.22 agrees very well with the prediction by an analytic theory (F=3/5) and numerical calculations. These results will facilitate studies of quantum information science with mesoscopic ensembles.

Preventing obesity at weaning: parental views about the EMPOWER programme.

BACKGROUND: Infant growth and lifestyle are now recognized as being critical determinants of later obesity. EMPOWER (Empowering Parents to Prevent Obesity at Weaning: Exploratory Research) was developed as an intervention for parents whose babies are at high risk. Delivered by specially trained health visitors, it is underpinned by the Family Partnership Model and uses a strengths-based, solution-focused way of working with families. METHODS: Mothers of babies participating in the pilot of EMPOWER in Leeds were recruited to take part in a study to examine perceptions about the programme's acceptability and usefulness. Interviews were taped and transcribed, and thematic analysis undertaken. RESULTS: Families talked positively about the approach of the EMPOWER health visitor with her emphasis on listening, partnership working and shared problem-solving. Parents particularly valued the use of a non-judgemental approach, which they felt had helped them to discuss openly, sensitive issues such as weight and diet. They identified a number of important benefits ranging from increased knowledge about the most appropriate types and amount of food to feed their toddler, to more far-reaching changes within the family as a whole, including modifications to their own diet and lifestyle. Programmes of this nature were perceived as more valuable than the standard help that is currently available. CONCLUSION: The EMPOWER programme appears to be both acceptable and valued by targeted parents and a potentially effective means of supporting high-risk families to prevent their children from developing obesity. An exploratory randomized controlled trial is now underway to ascertain the feasibility of conducting a definitive phase 3 trial.

Effects of the Diabetes Manual 1:1 structured education in primary care.

AIMS: To determine the effects of the Diabetes Manual on glycaemic control, diabetes-related distress and confidence to self-care of patients with Type 2 diabetes. METHODS: A cluster randomized, controlled trial of an intervention group vs. a 6-month delayed-intervention control group with a nested qualitative study. Participants were 48 urban general practices in the West Midlands, UK, with high population deprivation levels and 245 adults with Type 2 diabetes with a mean age of 62 years recruited pre-randomization. The Diabetes Manual is 1:1 structured education designed for delivery by practice nurses. Measured outcomes were HbA(1c), cardiovascular risk factors, diabetes-related distress measured by the Problem Areas in Diabetes Scale and confidence to self-care measured by the Diabetes Management Self-Efficacy Scale. Outcomes were assessed at baseline and 26 weeks. RESULTS: There was no significant difference in HbA(1c) between the intervention group and the control group [difference -0.08%, 95% confidence interval (CI) -0.28, 0.11]. Diabetes-related distress scores were lower in the intervention group compared with the control group (difference -4.5, 95% CI -8.1, -1.0). Confidence to self-care Scores were 11.2 points higher (95% CI 4.4, 18.0) in the intervention group compared with the control group. The patient response rate was 18.5%. CONCLUSIONS: In this population, the Diabetes Manual achieved a small improvement in patient diabetes-related distress and confidence to self-care over 26 weeks, without a change in glycaemic control. Further study is needed to optimize the intervention and characterize those for whom it is more clinically and psychologically effective to support its use in primary care.

Scanning magnetoresistance microscopy of atom chips.

Surface based geometries of microfabricated wires or patterned magnetic films can be used to magnetically trap and manipulate ultracold neutral atoms or Bose-Einstein condensates. We investigate the magnetic properties of such atom chips using a scanning magnetoresistive (MR) microscope with high spatial resolution and high field sensitivity. By comparing MR scans of a permanent magnetic atom chip to field profiles obtained using ultracold atoms, we show that MR sensors are ideally suited to observe small variations of the magnetic field caused by imperfections in the wires or magnetic materials which ultimately lead to fragmentation of ultracold atom clouds. Measurements are also provided for the magnetic field produced by a thin current-carrying wire with small geometric modulations along the edge. Comparisons of our measurements with a full numeric calculation of the current flow in the wire and the subsequent magnetic field show excellent agreement. Our results highlight the use of scanning MR microscopy as a convenient and powerful technique for precisely characterizing the magnetic fields produced near the surface of atom chips.