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We show how work can be extracted from number-state coherence in a two-mode Bose-Einstein condensate. With careful tuning of parameters, a sequence of thermodynamically reversible steps transforms a Glauber coherent state into a thermal state with the same energy probability distribution. The work extracted during this process arises entirely from the removal of quantum coherence. More generally, we characterise quantum (from coherence) and classical (remaining) contributions to work output, and find that in this system the quantum contribution can be dominant over a broad range of parameters. The proportion of quantum work output can be further enhanced by squeezing the initial coherent state. Due to the many-body nature of the system, the work from coherence can equivalently be understood as work from entanglement., Comment: 9 pages + refs, 3 figures

In the easy-plane phase, a ferromagnetic spin-1 Bose-Einstein condensate is magnetized in a plane transverse to the applied Zeeman field. This phase supports polar-core spin vortices (PCVs), which consist of phase windings of transverse magnetization. Here we show that spin-changing collisions cause a PCV to accelerate down density gradients in an inhomogeneous condensate. The dynamics is well-described by a simplified model adapted from scalar systems, which predicts the dependence of the dynamics on trap tightness and quadratic Zeeman energy. In a harmonic trap, a PCV accelerates radially to the condensate boundary, in stark contrast to the azimuthal motion of vortices in a scalar condensate. In a trap that has a local potential maximum at the centre, the PCV exhibits oscillations around the trap centre, which persist for a remarkably long time. The oscillations coincide with the emission and reabsorption of axial spin waves, which reflect off the condensate boundary., Comment: 13 pages + refs, 6 figures

The two-dimensional One-Component Plasma (OCP) is a foundational model of the statistical mechanics of interacting particles, describing phenomena common to astrophysics, turbulence, and the Fractional Quantum Hall Effect (FQHE). Despite an extensive literature, the phase diagram of the 2D OCP is still a subject of some controversy. Here we develop a "vortex matter" simulator to realize the logarithmic-interaction OCP experimentally by exploiting the topological character of quantized vortices in a thin superfluid layer. Precision optical-tweezer control of the location of quantized vortices enables direct preparation of the OCP ground state with or without defects, and heating from acoustic excitations allows the observation of the melting transition from the solid Wigner crystal through the liquid phase. We present novel theoretical analysis that is in quantitative agreement with experimental observations, and demonstrates how equilibrium states are achieved through the system dynamics. This allows a precise measurement of the superfluid-thermal cloud mutual friction and heating coefficients. This platform provides a route towards solving a number of open problems in systems with long-range interactions. At equilibrium, it could distinguish between the competing scenarios of grain boundary melting and KTHNY theory. Dynamical simulators could test the existence of predicted edge-wave solitons which form a hydrodynamic analogue of topological edge states in the FQHE., Comment: 9 pages, 9 figures

We introduce a simple, experimentally realizable protocol that can prepare any specific superposition of permutationally invariant qubit states, also known as Dicke states. The protocol is comprised entirely of global rotations and globally applied non-linear phase gates -- it does not require local addressability or ancilla qubits -- and hence can be readily implemented in a variety of experimental platforms, including trapped-ion quantum simulators and cavity QED systems. We demonstrate the utility of our protocol by numerically preparing several states with theoretical infidelities $1-\mathcal{F}<10^{-4}$: (i) metrologically useful $N$-qubit Dicke states in $\mathcal{O}(1)$ gate steps, (ii) the $N = 9$ qubit codewords of the Ruskai code with $P = 4$ gate steps, and (iii) the $N = 13$ qubit Gross codewords in $P = 7$ gate steps. Focusing on trapped-ion platforms, we estimate that the protocol achieves fidelities $\gtrsim 95\%$ in the presence of typical experimental noise levels, thus providing a pathway to the preparation of a variety of useful highly-entangled quantum states., Comment: 6 pages, 3 figures

We consider the far-from-equilibrium quantum transport dynamics in a 1D Josephson junction chain of multi-mode Bose-Einstein condensates. We develop a theoretical model to examine the experiment of R. Labouvie et al. [Phys. Rev. Lett. 115, 050601 (2015)], wherein the phenomenon of negative differential conductivity (NDC) was reported in the refilling dynamics of an initially depleted site within the chain. We demonstrate that a unitary c-field description can quantitatively reproduce the experimental results over the full range of tunnel couplings, and requires no fitted parameters. With a view towards atomtronic implementations, we further demonstrate that the filling is strongly dependent on spatial phase variations stemming from quantum fluctuations. Our findings suggest that the interpretation of the device in terms of NDC is invalid outside of the weak coupling regime. Within this restricted regime, the device exhibits a hybrid behaviour of NDC and the AC Josephson effect. A simplified circuit model of the device will require an approach tailored to atomtronics that incorporates quantum fluctuations., Comment: 5 + 6 pages, 4 + 7 figures

We demonstrate a method for generating persistent currents in Bose-Einstein condensates by using a Gaussian process learner to experimentally control the stirring of the superfluid. The learner optimizes four different outcomes of the stirring process: (O.I) targeting and (O.II) maximization of the persistent current winding number; and (O.III) targeting and (O.IV) maximization with time constraints. The learner optimizations are determined based on the achieved winding number and the number of spurious vortices introduced by stirring. We find that the learner is successful in optimizing the stirring protocols, although the optimal stirring profiles vary significantly depending strongly on the choice of cost function and scenario. These results suggest that stirring is robust and persistent currents can be reliably generated through a variety of stirring approaches., Comment: 12 pages, 8 figures, 1 table

We show that ferromagnetic interactions can enhance the adiabatic performance of a quantum spin chain engine at low temperatures. The enhancement in work output is particular pronounced, increasing exponentially with interaction strength. The performance enhancement occurs in the paramagnetic phase and is qualitatively explained by considering just the ground and first excited state, in which case the system exhibits bipartite entanglement. As the temperature is increased, thermal occupation of higher energy levels diminishes performance. We find that these thermal fluctuations are smallest for long-range interactions, resulting in the highest efficiency. Diabatic work extraction degrades performance due to quantum friction. We identify an approximate, experimentally realisable counterdiabatic drive that can mitigate friction for weak interactions., Comment: 4 pages + refs + supplement, 3 figures

We demonstrate the use of a ring-shaped Bose-Einstein condensate as a rotation sensor by measuring the interference between two counter-propagating phonon modes imprinted azimuthally around the ring. We observe rapid decay of the excitations, quantified by quality factors of at most $Q \approx 27$. We numerically model our experiment using the c-field methodology, allowing us to estimate the parameters that maximise the performance of our sensor. We explore the damping mechanisms underlying the observed phonon decay, and identify two distinct Landau scattering processes that each dominate at different driving amplitudes and temperatures. Our simulations reveal that $Q$ is limited by strong damping of phonons even in the zero temperature limit. We perform an experimental proof-of-principle rotation measurement using persistent currents imprinted around the ring. We demonstrate a rotation sensitivity of up to $\Delta \Omega \approx 0.3$ rad/s from a single image, with a theoretically achievable value of $\Delta \Omega \approx 0.04$ rad/s in the atomic shot-noise limit. This is a significant improvement over the shot-noise-limited $\Delta \Omega \approx 1$ rad/s sensitivity obtained by Marti et al. [Phys. Rev. A 91, 013602 (2015)] for a similar setup., Comment: 22 pages, 10 figures

We characterize the mechanisms of vortex pinning in a superfluid thin film described by the two-dimensional Gross-Pitaevskii equation. We consider a vortex "scattering experiment" whereby a single vortex in a superfluid flow interacts with a circular, uniform pinning potential. By an analogy with linear dielectrics, we develop an analytical hydrodynamic approximation that predicts vortex trajectories, the vortex fixed point and the unpinning velocity. We then solve the Gross-Pitaevskii equation to validate this model, and build a phase portrait of vortex pinning. We identify two different dynamical pinning mechanisms marked by distinctive phonon emission signatures: one enabled by acoustic radiation and another mediated by vortex dipoles nucleated within the pin. Relative to obstacle size, we find that pinning potentials on the order of the healing length are more effective for vortex capture. Our results could be useful in mitigating the negative effects of drag due to vortices in superfluid channels, in analogy to maximising supercurrents in type-II superconductors., Comment: 5+4 pages, 4+5 figures, supplemental videos: https://www.youtube.com/watch?v=l8E8RdydaY0

Developing theoretical models for nonequilibrium quantum systems poses significant challenges. Here we develop and study a multimode model of a driven-dissipative Josephson junction chain of atomic Bose-Einstein condensates, as realised in the experiment of Labouvie et al. [Phys. Rev. Lett. 116, 235302 (2016)]. The model is based on c-field theory, a beyond-mean-field approach to Bose-Einstein condensates that incorporates fluctuations due to finite temperature and dissipation. We find the c-field model is capable of capturing all key features of the nonequilibrium phase diagram, including bistability and a critical slowing down in the lower branch of the bistable region. Our model is closely related to the so-called Lugiato-Lefever equation, and thus establishes new connections between nonequilibrium dynamics of ultracold atoms with nonlinear optics, exciton-polariton superfluids, and driven damped sine-Gordon systems., Comment: 12 pages, 10 figures

We experimentally study emergence of microcanonical equilibrium states in the turbulent relaxation dynamics of a two-dimensional chiral vortex gas. Same-sign vortices are injected into a quasi-two-dimensional disk-shaped atomic Bose-Einstein condensate using a range of mechanical stirring protocols. The resulting long-time vortex distributions are found to be in excellent agreement with the meanfield Poisson-Boltzmann equation for the system describing the microcanonical ensemble at fixed energy $\cal{H}$ and angular momentum $\cal{M}$. The equilibrium states are characterized by the corresponding thermodynamic variables of inverse temperature $\hat{\beta}$ and rotation frequency $\hat{\omega}$. We are able to realize equilibria spanning the full phase diagram of the vortex gas, including on-axis states near zero-temperature, infinite temperature, and negative absolute temperatures. At sufficiently high energies the system exhibits a symmetry-breaking transition, resulting in an off-axis equilibrium phase at negative absolute temperature that no longer shares the symmetry of the container. We introduce a point-vortex model with phenomenological damping and noise that is able to quantitatively reproduce the equilibration dynamics., Comment: V1: 16 pages, 7 figures, 6 in main text

Accelerating beams are wave packets which appear to spontaneously accelerate without external potentials or applied forces. Since their first physical realisation in the form of Airy beams, they have found applications on various platforms, spanning from optics to plasma physics. We investigate the dynamics of examples of finite-energy accelerating beams derived from catastrophe theory. We use a Madelung transformation in momentum-space, combined with a wavelet transformed analysis, to demonstrate that the beams' properties arise from a special type of vanishing self-interference. We identify the modes responsible for the wave packet's acceleration and we derive the general acceleration for higher-order cupsoid-related beams. We also demonstrate how bright solitons resulting from nonlinear Airy beams can be unambiguously detected using the wavelet transform. This methodology will allow for a better understanding of nontrivial wave packet dynamics.

A large ensemble of quantum vortices in a superfluid may itself be treated as a novel kind of fluid that exhibits anomalous hydrodynamics. Here we consider the dynamics of vortex clusters with thermal friction, and present an analytic solution that uncovers a new universality class in the out-of-equilibrium dynamics of dissipative superfluids. We find that the long-time dynamics of the vorticity distribution is an expanding Rankine vortex (i.e.~top-hat distribution) independent of initial conditions. This highlights a fundamentally different decay process to classical fluids, where the Rankine vortex is forbidden by viscous diffusion. Numerical simulations of large ensembles of point vortices confirm the universal expansion dynamics, and further reveal the emergence of a frustrated lattice structure marked by strong correlations. We present experimental results in a quasi-two-dimensional Bose-Einstein condensate that are in excellent agreement with the vortex fluid theory predictions, demonstrating that the signatures of vortex fluid theory can be observed with as few as $N\sim 11$ vortices. Our theoretical, numerical, and experimental results establish the validity of the vortex fluid theory for superfluid systems., Comment: V1: 6 pages, 3 figures in main text. 5 pages, 5 figures in supplemental material. V2: Updated in response to reviewer comments: Improved introduction and discussion, additional simulation data provided in supplemental materials

The mean-field Gross-Pitaevskii equation with repulsive interactions exhibits frictionless flow when stirred by an obstacle below a critical velocity. Here we go beyond the mean-field approximation to examine the influence of quantum fluctuations on this threshold behaviour in a one-dimensional Bose gas in a ring. Using the truncated Wigner approximation, we perform simulations of ensembles of trajectories where the Bose gas is stirred with a repulsive obstacle below the mean-field critical velocity. We observe the probabilistic formation of grey solitons which subsequently decay, leading to an increase in the momentum of the fluid. The formation of the first soliton leads to a soliton cascade, such that the fluid rapidly accelerates to minimise the speed difference with the obstacle. We measure the initial rate of momentum transfer, and relate it to macroscopic tunnelling between quantised flow states in the ring., Comment: v2: 10 pages, 8 figures. Published version with added references and improvements in response to referees

We numerically model experiments on the superfluid critical velocity of an elongated, harmonically trapped Bose-Einstein condensate as reported by [P. Engels and C. Atherton, Phys. Rev. Lett. 99, 160405 (2007)]. These experiments swept an obstacle formed by an optical dipole potential through the long axis of the condensate at constant velocity. Their results found an increase in the resulting density fluctuations of the condensate above an obstacle velocity of $v\approx 0.3$ mm/s, suggestive of a superfluid critical velocity substantially less than the average speed of sound. However, our analysis shows that the that the experimental observations of Engels and Atherton are in fact consistent with a superfluid critical velocity equal to the local speed of sound. We construct a model of energy transfer to the system based on the local density approximation to explain the experimental observations, and propose and simulate experiments that sweep potentials through harmonically trapped condensates at a constant fraction of the local speed of sound. We find that this leads to a sudden onset of excitations above a critical fraction, in agreement with the Landau criterion for superfluidity., Comment: 14 pages, 13 figures, comments welcome

Time-averaged trapping potentials have played an important role in the development of the field of ultracold atoms. Despite their widespread application, there is not yet a complete understanding of when a system can be considered time-averaged. Here we use Floquet theory to analyse the lowest energy state of time-periodic trapping potentials, and characterise the transition from a localised state in a slowly moving trap to a delocalised state in a rapidly oscillating time-averaged potential. We investigate how the driving parameters affect the density and phase of the Floquet ground state, and provide a quantitative measure of the degree to which they can be considered time-averaged. We study a number of simple representative systems, and comment on the features affecting the experimental realisation of time-averaged trapping potentials., Comment: v2: Manuscript improved with feedback, 12 pages, 7 figures, further comments welcome

X-waves are an example of a localized wave packet solution of the homogeneous wave equation, and can potentially arise in any area of physics relating to wave phenomena, such as acoustics, electromagnetism, or quantum mechanics. They have been predicted in condensed matter systems such as atomic Bose-Einstein condensates in optical lattices, and were recently observed in exciton-polariton condensates. Here we show that polariton X-waves result from an interference between two separating wave packets that arise from the combination of a locally hyperbolic dispersion relation and nonlinear interactions. We show that similar X-wave structures could also be observed in expanding spin-orbit coupled Bose-Einstein condensates.

We numerically model decaying quantum turbulence in two-dimensional disk-shaped Bose-Einstein condensates, and investigate the effects of finite temperature on the turbulent dynamics. We prepare initial states with a range of condensate temperatures, and imprint equal numbers of vortices and antivortices at randomly chosen positions throughout the fluid. The initial states are then subjected to unitary time-evolution within the c-field methodology. For the lowest condensate temperatures, the results of the zero temperature Gross-Pitaevskii theory are reproduced, whereby vortex evaporative heating leads to the formation of Onsager vortex clusters characterised by a negative absolute vortex temperature. At higher condensate temperatures the dissipative effects due to vortex-phonon interactions tend to drive the vortex gas towards positive vortex temperatures dominated by the presence of vortex dipoles. We associate these two behaviours with the system evolving toward an anomalous non-thermal fixed point, or a Gaussian thermal fixed point, respectively., Comment: 20 pages, 6 figures, SciPost format. Updated version includes a new section with further analysis and an additional figure

We experimentally realize a highly tunable superfluid oscillator circuit in a quantum gas of ultracold atoms and develop and verify a simple lumped-element description of this circuit. At low oscillator currents, we demonstrate that the circuit is accurately described as a Helmholtz resonator, a fundamental element of acoustic circuits. At larger currents, the breakdown of the Helmholtz regime is heralded by a turbulent shedding of vortices and density waves. Although a simple phase-slip model offers qualitative insights into the circuit's resistive behavior, our results indicate deviations from the phase-slip model. A full understanding of the dissipation in superfluid circuits will thus require the development of empirical models of the turbulent dynamics in this system, as have been developed for classical acoustic systems., Comment: 12 pages, 9 figures

Two-dimensional superfluidity and quantum turbulence are directly connected to the microscopic dynamics of quantized vortices. However, surface effects have prevented direct observations of coherent vortex dynamics in strongly-interacting two-dimensional systems. Here, we overcome this challenge by confining a two-dimensional droplet of superfluid helium at microscale on the atomically-smooth surface of a silicon chip. An on-chip optical microcavity allows laser-initiation of vortex clusters and nondestructive observation of their decay in a single shot. Coherent dynamics dominate, with thermal vortex diffusion suppressed by six orders-of-magnitude. This establishes a new on-chip platform to study emergent phenomena in strongly-interacting superfluids, test astrophysical dynamics such as those in the superfluid core of neutron stars in the laboratory, and construct quantum technologies such as precision inertial sensors., Comment: Main text - 12 pages, 4 figures. Supplementary materials - 25 pages, 13 figures

We study the nonequilibrium dynamics of the quantum Newton's cradle in a one-dimensional (1D) Bose gas in the weakly-interacting quasicondensate regime. This is the opposite regime to the original quantum Newton's cradle experiment of Kinoshita et al. [Nature 440, 900 (2006)], which was realized in the strongly interacting 1D Bose gas. Using finite temperature c-field methods, we calculate the characteristic relaxation rates to the final equilibrium state. Hence, we identify the different dynamical regimes of the system in the parameter space that characterizes the strength of interatomic interactions, the initial temperature, and the magnitude of the Bragg momentum used to initiate the collisional oscillations of the cradle. In all parameter regimes, we find that the system relaxes to a final equilibrium state for which the momentum distribution is consistent with a thermal distribution. For sufficiently large initial Bragg momentum, the system can undergo hundreds of repeated collisional oscillations before reaching the final thermal equilibrium. The corresponding thermalization timescales can reach tens of seconds, which is an order of magnitude smaller than in the strongly interacting regime., Comment: Final published version; 14 pages, 10 figures

Rapidly scanning magnetic and optical dipole traps have been widely utilised to form time-averaged potentials for ultracold quantum gas experiments. Here we theoretically and experimentally characterise the dynamic properties of Bose-Einstein condensates in ring-shaped potentials that are formed by scanning an optical dipole beam in a circular trajectory. We find that unidirectional scanning leads to a non-trivial phase profile of the condensate that can be approximated analytically using the concept of phase imprinting. While the phase profile is not accessible through in-trap imaging, time-of-flight expansion manifests clear density signatures of an in-trap phase step in the condensate, coincident with the instantaneous position of the scanning beam. The phase step remains significant even when scanning the beam at frequencies two orders of magnitude larger than the characteristic frequency of the trap. We map out the phase and density properties of the condensate in the scanning trap, both experimentally and using numerical simulations, and find excellent agreement. Furthermore, we demonstrate that bidirectional scanning eliminated the phase gradient, rendering the system more suitable for coherent matter wave interferometry., Comment: 10 pages, 7 figures

Adding energy to a system through transient stirring usually leads to more disorder. In contrast, point-like vortices in a bounded two-dimensional fluid are predicted to reorder above a certain energy, forming persistent vortex clusters. Here we realize experimentally these vortex clusters in a planar superfluid: a $^{87}$Rb Bose-Einstein condensate confined to an elliptical geometry. We demonstrate that the clusters persist for long times, maintaining the superfluid system in a high energy state far from global equilibrium. Our experiments explore a regime of vortex matter at negative absolute temperatures, and have relevance to the dynamics of topological defects, two-dimensional turbulence, and systems such as helium films, nonlinear optical materials, fermion superfluids, and quark-gluon plasmas., Comment: 14 pages, 4 Figures, 9 Supplemental Figures. The definitive version of this article was published in Science Vol. 364, Issue 6447, pp. 1264-1267, 28 Jun 2019. doi:10.1126/science.aat5718

Negative effective masses can be realised by engineering the dispersion relation in a variety of quantum systems. A recent experiment with spin-orbit coupled Bose-Einstein condensates has shown that a negative effective mass can halt the free expansion of the condensate and produce fringes in the density [M. Khamehchi et al., Phys. Rev. Lett. 118, 155301 (2017)]. Here, we show that the observed fringes are due to the negativity of only one of the two effective mass parameters that characterise the dispersion, which leads to previously predicted self-interference of the wave packet. We show how confgurations are nevertheless accessible to spin-orbit coupled Bose-Einstein condensates where both mass parameters controlling the propagation and diffusion of the condensate are negative, resulting in the novel phenomenon of counter-propagating self-interfering packets.

We use the coordinate Bethe ansatz to study the Lieb-Liniger model of a one-dimensional gas of bosons on a finite-sized ring interacting via an attractive delta-function potential. We calculate zero-temperature correlation functions for seven particles in the vicinity of the crossover to a localized solitonic state and study the dynamics of a system of four particles quenched to attractive interactions from the ideal-gas ground state. We determine the time evolution of correlation functions, as well as their temporal averages, and discuss the role of bound states in shaping the postquench correlations and relaxation dynamics., Comment: v1: Original submission to SciPost Physics. v2: Improvements to text based on referee comments

We introduce a new method of statistical analysis to characterise the dynamics of turbulent fluids in two dimensions. We establish that, in equilibrium, the vortex distributions can be uniquely connected to the temperature of the vortex gas, and apply this vortex thermometry to characterise simulations of decaying superfluid turbulence. We confirm the hypothesis of vortex evaporative heating leading to Onsager vortices proposed in Phys. Rev. Lett. 113, 165302 (2014), and find previously unidentified vortex power-law distributions that emerge from the dynamics., Comment: 8 pages, 9 figures

The problem of understanding how a coherent, macroscopic Bose-Einstein condensate (BEC) emerges from the cooling of a thermal Bose gas has attracted significant theoretical and experimental interest over several decades. The pioneering achievement of BEC in weakly-interacting dilute atomic gases in 1995 was followed by a number of experimental studies examining the growth of the BEC number, as well as the development of its coherence. More recently there has been interest in connecting such experiments to universal aspects of nonequilibrium phase transitions, in terms of both static and dynamical critical exponents. Here, the spontaneous formation of topological structures such as vortices and solitons in quenched cold-atom experiments has enabled the verification of the Kibble-Zurek mechanism predicting the density of topological defects in continuous phase transitions, first proposed in the context of the evolution of the early universe. This chapter reviews progress in the understanding of BEC formation, and discusses open questions and future research directions in the dynamics of phase transitions in quantum gases., Comment: Unedited version of chapter to appear in "Universal Themes of Bose-Einstein Condensation", edited by D. W. Snoke, N. P. Proukakis and P. B. Littlewood (Cambridge University Press). Comments are invited and appreciated

Interferometric measurements with matter waves are established techniques for sensitive gravimetry, rotation sensing, and measurement of surface interactions, but compact interferometers will require techniques based on trapped geometries. In a step towards the realization of matter wave interferometers in toroidal geometries, we produce a large, smooth ring trap for Bose-Einstein condensates using rapidly scanned time-averaged dipole potentials. The trap potential is smoothed by using the atom distribution as input to an optical intensity correction algorithm. Smooth rings with a diameter up to 300 $\mu$m are demonstrated. We experimentally observe and simulate the dispersion of condensed atoms in the resulting potential, with good agreement serving as an indication of trap smoothness. Under time of flight expansion we observe low energy excitations in the ring, which serves to constrain the lower frequency limit of the scanned potential technique. The resulting ring potential will have applications as a waveguide for atom interferometry and studies of superfluidity.

We present a model of a spin-squeezed rotation sensor utilising the Sagnac effect in a spin-1 Bose-Einstein condensate in a ring trap. The two input states for the interferometer are seeded using Raman pulses with Laguerre-Gauss beams and are amplified by the bosonic enhancement of spin-exchange collisions, resulting in spin-squeezing and potential quantum enhancement in the interferometry. The ring geometry has an advantage over separated beam path atomic rotation sensors due to the uniform condensate density. We model the interferometer both analytically and numerically for realistic experimental parameters and find that significant quantum enhancement is possible, but this enhancement is partially degraded when working in a regime with strong atomic interactions., Comment: 13 pages, 9 figures