A quantum engine in the BEC-BCS crossover.

Heat engines convert thermal energy into mechanical work both in the classical and quantum regimes1. However, quantum theory offers genuine non-classical forms of energy, different from heat, which so far have not been exploited in cyclic engines. Here we experimentally realize a quantum many-body engine fuelled by the energy difference between fermionic and bosonic ensembles of ultracold particles that follows from the Pauli exclusion principle2. We employ a harmonically trapped superfluid gas of 6Li atoms close to a magnetic Feshbach resonance3 that allows us to effectively change the quantum statistics from Bose-Einstein to Fermi-Dirac, by tuning the gas between a Bose-Einstein condensate of bosonic molecules and a unitary Fermi gas (and back) through a magnetic field4-10. The quantum nature of such a Pauli engine is revealed by contrasting it with an engine in the classical thermal regime and with a purely interaction-driven device. We obtain a work output of several 106 vibrational quanta per cycle with an efficiency of up to 25%. Our findings establish quantum statistics as a useful thermodynamic resource for work production.

Observing the loss and revival of long-range phase coherence through disorder quenches.

Relaxation of quantum systems is a central problem in nonequilibrium physics. In contrast to classical systems, the underlying quantum dynamics results not only from atomic interactions but also from the long-range coherence of the many-body wave function. Experimentally, nonequilibrium states of quantum fluids are usually created using moving objects or laser potentials, directly perturbing and detecting the system's density. However, the fate of long-range phase coherence for hydrodynamic motion of disordered quantum systems is less explored, especially in three dimensions. Here, we unravel how the density and phase coherence of a Bose-Einstein condensate of 6Li2 molecules respond upon quenching on or off an optical speckle potential. We find that, as the disorder is switched on, long-range phase coherence breaks down one order of magnitude faster than the density of the quantum gas responds. After removing it, the system needs two orders of magnitude longer times to reestablish quantum coherence, compared to the density response. We compare our results with numerical simulations of the Gross-Pitaevskii equation on large three-dimensional grids, finding an overall good agreement. Our results shed light on the importance of long-range coherence and possibly long-lived phase excitations for the relaxation of nonequilibrium quantum many-body systems.

Coherent and Dephasing Spectroscopy for Single-Impurity Probing of an Ultracold Bath.

We report Ramsey spectroscopy on the clock states of individual Cs impurities immersed in an ultracold Rb bath. We record both the interaction-driven phase evolution and the decay of fringe contrast of the Ramsey interference signal to obtain information about bath density or temperature nondestructively. The Ramsey fringe is modified by a differential shift of the collisional energy when the two Cs states superposed interact with the Rb bath. This differential shift is directly affected by the mean gas density and the details of the Rb-Cs interspecies scattering length, affecting the phase evolution and the contrast of the Ramsey signal. Additionally, we enhance the temperature dependence of the phase shift preparing the system close to a low-magnetic-field Feshbach resonance where the s-wave scattering length is significantly affected by the collisional (kinetic) energy. Analyzing coherent phase evolution and decay of the Ramsey fringe contrast, we probe the Rb cloud's density and temperature. Our results point at using individual impurity atoms as nondestructive quantum probes in complex quantum systems.

Ultracold Bose Gases in Dynamic Disorder with Tunable Correlation Time.

We study experimentally the dissipative dynamics of ultracold bosonic gases in a dynamic disorder potential with tunable correlation time. First, we measure the heating rate of thermal clouds exposed to the dynamic potential and present a model of the heating process, revealing the microscopic origin of dissipation from a thermal, trapped cloud of bosons. Second, for Bose-Einstein condensates, we measure the particle loss rate induced by the dynamic environment. Depending on the correlation time, the losses are either dominated by heating of residual thermal particles or the creation of excitations in the superfluid, a notion we substantiate with a rate model. Our results illuminate the interplay between superfluidity and time-dependent disorder and on more general grounds establish ultracold atoms as a platform for studying spatiotemporal noise and time-dependent disorder.

Continuous-Time Random Walk for a Particle in a Periodic Potential.

Continuous-time random walks offer powerful coarse-grained descriptions of transport processes. We here microscopically derive such a model for a Brownian particle diffusing in a deep periodic potential. We determine both the waiting-time and the jump-length distributions in terms of the parameters of the system, from which we analytically deduce the non-Gaussian characteristic function. We apply this continuous-time random walk model to characterize the underdamped diffusion of single cesium atoms in a one-dimensional optical lattice. We observe excellent agreement between experimental and theoretical characteristic functions, without any free parameter.

Tailored Single-Atom Collisions at Ultralow Energies.

We employ collisions of individual atomic cesium (Cs) impurities with an ultracold rubidium (Rb) gas to probe atomic interaction with hyperfine- and Zeeman-state sensitivity. Controlling the Rb bath's internal state yields access to novel phenomena observed in interatomic spin exchange. These can be tailored at ultralow energies, owing to the excellent experimental control over all relevant energy scales. First, detecting spin-exchange dynamics in the Cs hyperfine-state manifold, we resolve a series of previously unreported Feshbach resonances at magnetic fields below 300 mG, separated by energies as low as h×15 kHz. The series originates from a coupling to molecular states with binding energies below h×1 kHz and wave function extensions in the micrometer range. Second, at magnetic fields below ≈100 mG, we observe the emergence of a new reaction path for alkali atoms, where in a single, direct collision between two atoms two quanta of angular momentum can be transferred. This path originates from the hyperfine analog of dipolar spin-spin relaxation. Our work yields control of subtle ultralow-energy features of atomic collision dynamics, opening new routes for advanced state-to-state chemistry, for controlling spin exchange in quantum many-body systems for solid-state simulations, or for determination of high-precision molecular potentials.

Quantum Spin Dynamics of Individual Neutral Impurities Coupled to a Bose-Einstein Condensate.

We report on spin dynamics of individual, localized neutral impurities immersed in a Bose-Einstein condensate. Single cesium atoms are transported into a cloud of rubidium atoms and thermalize with the bath, and the ensuing spin exchange between localized impurities with quasispin F_{i}=3 and bath atoms with F_{b}=1 is resolved. Comparing our data to numerical simulations of spin dynamics, we find that, for gas densities in the Bose-Einstein condensate regime, the dynamics is dominated by the condensed fraction of the cloud. We spatially resolve the density overlap of impurities and gas by the spin population of impurities. Finally, we trace the coherence of impurities prepared in a coherent superposition of internal states when coupled to a gas of different densities. For our choice of states, we show that, despite high bath densities and, thus, fast thermalization rates, the impurity coherence is not affected by the bath, realizing a regime of sympathetic cooling while maintaining internal state coherence. Our work paves the way toward the nondestructive probing of quantum many-body systems via localized impurities.

Individual Tracer Atoms in an Ultracold Dilute Gas.

We report on the experimental investigation of individual Cs atoms impinging on a dilute cloud of ultracold Rb atoms with variable density. We study the relaxation of the initial nonthermal state and detect the effect of single collisions which has so far eluded observation. We show that, after few collisions, the measured spatial distribution of the tracer atoms is correctly described by a Langevin equation with a velocity-dependent friction coefficient, over a large range of Knudsen numbers. Our results extend the simple and effective Langevin treatment to the realm of light particles in dilute gases. The experimental technique developed opens up the microscopic exploration of a novel regime of diffusion at the level of individual collisions.

Digital atom interferometer with single particle control on a discretized space-time geometry.

Engineering quantum particle systems, such as quantum simulators and quantum cellular automata, relies on full coherent control of quantum paths at the single particle level. Here we present an atom interferometer operating with single trapped atoms, where single particle wave packets are controlled through spin-dependent potentials. The interferometer is constructed from a sequence of discrete operations based on a set of elementary building blocks, which permit composing arbitrary interferometer geometries in a digital manner. We use this modularity to devise a space-time analogue of the well-known spin echo technique, yielding insight into decoherence mechanisms. We also demonstrate mesoscopic delocalization of single atoms with a separation-to-localization ratio exceeding 500; this result suggests their utilization beyond quantum logic applications as nano-resolution quantum probes in precision measurements, being able to measure potential gradients with precision 5 x 10(-4) in units of gravitational acceleration g.

Indication of critical scaling in time during the relaxation of an open quantum system.

Near continuous phase transitions, universal power-law scaling, characterized by critical exponents, emerges. This behavior reflects the singular responses of physical systems to continuous control parameters like temperature or external fields. Universal scaling extends to non-equilibrium dynamics in isolated quantum systems after a quench, where time takes the role of the control parameter. Our research unveils critical scaling in time also during the relaxation dynamics of an open quantum system. Here we experimentally realize such a system by the spin of individual Cesium atoms dissipatively coupled through spin-exchange processes to a bath of ultracold Rubidium atoms. Through a finite-size scaling analysis of the entropy dynamics via numerical simulations, we identify a critical point in time in the thermodynamic limit. This critical point is accompanied by the divergence of a characteristic length, which is described by critical exponents that turn out to be unaffected by system specifics.

Dynamics of single neutral impurity atoms immersed in an ultracold gas.

We report on controlled doping of an ultracold Rb gas with single neutral Cs impurity atoms. Elastic two-body collisions lead to a rapid thermalization of the impurity inside the Rb gas, representing the first realization of an ultracold gas doped with a precisely known number of impurity atoms interacting via s-wave collisions. Inelastic interactions are restricted to a single three-body recombination channel in a highly controlled and pure setting, which allows us to determine the Rb-Rb-Cs three-body loss rate with unprecedented precision. Our results pave the way for a coherently interacting hybrid system of individually controllable impurities in a quantum many-body system.

Bayesian feedback control of a two-atom spin-state in an atom-cavity system.

We experimentally demonstrate real-time feedback control of the joint spin-state of two neutral cesium atoms inside a high finesse optical cavity. The quantum states are discriminated by their different cavity transmission levels. A Bayesian update formalism is used to estimate state occupation probabilities as well as transition rates. We stabilize the balanced two-atom mixed state, which is deterministically inaccessible, via feedback control and find very good agreement with Monte Carlo simulations. On average, the feedback loop achieves near optimal conditions by steering the system to the target state marginally exceeding the time to retrieve information about its state.

Fiber-tip endoscope for optical and microwave control.

We present a robust, fiber-based endoscope with a silver direct-laser-written structure for radio frequency (RF) emission next to the optical fiber facet. Thereby, we are able to excite and probe a sample, such as nitrogen-vacancy (NV) centers in diamond, with RF and optical signals simultaneously and specifically measure the fluorescence of the sample fully through the fiber. At our targeted frequency range of around 2.9 GHz, the facet of the fiber core is in the near-field of the RF-guiding silver structure, which comes with the advantage of an optimal RF intensity decreasing rapidly with the distance. By creating a silver structure on the cladding of the optical fiber, we achieve the minimal possible distance between an optically excited and detected sample and an antenna structure without affecting the optical performance of the fiber. This allows us to realize a high RF amplitude at the sample's position when considering an endoscope solution with integrated optical and RF access. The capabilities of the endoscope are quantified by optically detected magnetic resonance (ODMR) measurements of an NV-doped microdiamond that we probe as a practical use case. We demonstrate a magnetic sensitivity of our device of 17.8 nT/Hz when measuring the ODMR exclusively through our fiber and compare the sensitivity to a measurement using a confocal microscope. Moreover, the application of our device is not limited to NV centers in diamonds. Similar endoscope-like devices combining optical excitation and detection with radio frequency or microwave antenna could be used as a powerful tool for measuring a variety of fluorescent particles that have so far only been investigated with bulky and large optical setups. Furthermore, our endoscope points toward precise distance measurements based on Rabi oscillations.

Spatial quantum noise interferometry in expanding ultracold atom clouds.

In a pioneering experiment, Hanbury Brown and Twiss (HBT) demonstrated that noise correlations could be used to probe the properties of a (bosonic) particle source through quantum statistics; the effect relies on quantum interference between possible detection paths for two indistinguishable particles. HBT correlations--together with their fermionic counterparts--find numerous applications, ranging from quantum optics to nuclear and elementary particle physics. Spatial HBT interferometry has been suggested as a means to probe hidden order in strongly correlated phases of ultracold atoms. Here we report such a measurement on the Mott insulator phase of a rubidium Bose gas as it is released from an optical lattice trap. We show that strong periodic quantum correlations exist between density fluctuations in the expanding atom cloud. These spatial correlations reflect the underlying ordering in the lattice, and find a natural interpretation in terms of a multiple-wave HBT interference effect. The method should provide a useful tool for identifying complex quantum phases of ultracold bosonic and fermionic atoms.

A quantum heat engine driven by atomic collisions.

Quantum heat engines are subjected to quantum fluctuations related to their discrete energy spectra. Such fluctuations question the reliable operation of thermal machines in the quantum regime. Here, we realize an endoreversible quantum Otto cycle in the large quasi-spin states of Cesium impurities immersed in an ultracold Rubidium bath. Endoreversible machines are internally reversible and irreversible losses only occur via thermal contact. We employ quantum control to regulate the direction of heat transfer that occurs via inelastic spin-exchange collisions. We further use full-counting statistics of individual atoms to monitor quantized heat exchange between engine and bath at the level of single quanta, and additionally evaluate average and variance of the power output. We optimize the performance as well as the stability of the quantum heat engine, achieving high efficiency, large power output and small power output fluctuations.

Objective comparison of methods to decode anomalous diffusion.

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.g., short or noisy trajectories, heterogeneous behaviour, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. To perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams applied their algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, machine-learning-based approaches achieved superior performance for all tasks. The discussion of the challenge results provides practical advice for users and a benchmark for developers.

Optical control of the refractive index of a single atom.

We experimentally demonstrate the elementary case of electromagnetically induced transparency with a single atom inside an optical cavity probed by a weak field. We observe the modification of the dispersive and absorptive properties of the atom by changing the frequency of a control light field. Moreover, a strong cooling effect has been observed at two-photon resonance, increasing the storage time of our atoms twenty-fold to about 16 seconds. Our result points towards all-optical switching with single photons.

Controlled collisions for multi-particle entanglement of optically trapped atoms.

Entanglement lies at the heart of quantum mechanics, and in recent years has been identified as an essential resource for quantum information processing and computation. The experimentally challenging production of highly entangled multi-particle states is therefore important for investigating both fundamental physics and practical applications. Here we report the creation of highly entangled states of neutral atoms trapped in the periodic potential of an optical lattice. Controlled collisions between individual neighbouring atoms are used to realize an array of quantum gates, with massively parallel operation. We observe a coherent entangling-disentangling evolution in the many-body system, depending on the phase shift acquired during the collision between neighbouring atoms. Such dynamics are indicative of highly entangled many-body states; moreover, these are formed in a single operational step, independent of the size of the system.

Tonks-Girardeau gas of ultracold atoms in an optical lattice.

Strongly correlated quantum systems are among the most intriguing and fundamental systems in physics. One such example is the Tonks-Girardeau gas, proposed about 40 years ago, but until now lacking experimental realization; in such a gas, the repulsive interactions between bosonic particles confined to one dimension dominate the physics of the system. In order to minimize their mutual repulsion, the bosons are prevented from occupying the same position in space. This mimics the Pauli exclusion principle for fermions, causing the bosonic particles to exhibit fermionic properties. However, such bosons do not exhibit completely ideal fermionic (or bosonic) quantum behaviour; for example, this is reflected in their characteristic momentum distribution. Here we report the preparation of a Tonks-Girardeau gas of ultracold rubidium atoms held in a two-dimensional optical lattice formed by two orthogonal standing waves. The addition of a third, shallower lattice potential along the long axis of the quantum gases allows us to enter the Tonks-Girardeau regime by increasing the atoms' effective mass and thereby enhancing the role of interactions. We make a theoretical prediction of the momentum distribution based on an approach in which trapped bosons acquire fermionic properties, finding that it agrees closely with the measured distribution.

Microwave control of atomic motion in optical lattices.

We control the quantum mechanical motion of neutral atoms in an optical lattice by driving microwave transitions between spin states whose trapping potentials are spatially offset. Control of this offset with nanometer precision allows for adjustment of the coupling strength between different motional states, analogous to an adjustable effective Lamb-Dicke factor. This is used both for efficient one-dimensional sideband cooling of individual atoms to a vibrational ground state population of 97% and to drive coherent Rabi oscillation between arbitrary pairs of vibrational states. We further show that microwaves can drive well resolved transitions between motional states in maximally offset, shallow lattices, and thus in principle allow for coherent control of long-range quantum transport.