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 ≈ 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 ≈ 0.3 rad s^{-1} ΔΩ≈0.3rads−1 from a single image, with a theoretically achievable value of \Delta \Omega ≈ 0.04 rad s^{-1} ΔΩ≈0.04rads−1 in the atomic shot-noise limit. This is a significant improvement over the shot-noise-limited \Delta \Omega ≈ 1 rad s^{-1} ΔΩ≈1rads−1 sensitivity obtained by Marti et al. [Phys. Rev. A 91, 013602 (2015)] for a similar setup.

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.

Atomtronics deals with matter-wave circuits of ultra-cold atoms manipulated through magnetic or laser-generated guides with different shapes and intensities. In this way, new types of quantum networks can be constructed, in which coherent fluids are controlled with the know-how developed in the atomic and molecular physics community. In particular, quantum devices with enhanced precision, control and flexibility of their operating conditions can be accessed. Concomitantly, new quantum simulators and emulators harnessing on the coherent current flows can also be developed. Here, we survey the landscape of atomtronics-enabled quantum technology and draw a roadmap for the field in the near future. We review some of the latest progresses achieved in matter-wave circuits design and atom-chips. Atomtronic networks are deployed as promising platforms for probing many-body physics with a new angle and a new twist. The latter can be done both at the level of equilibrium and non-equilibrium situations. Numerous relevant problems in mesoscopic physics, like persistent currents and quantum transport in circuits of fermionic or bosonic atoms, are studied through a new lens. We summarize some of the atomtronics quantum devices and sensors. Finally, we discuss alkali-earth and Rydberg atoms as potential platforms for the realization of atomtronic circuits with special features.

All light has structure, but only recently it has become possible to construct highly controllable and precise potentials so that most laboratories can harness light for their specific applications. In this chapter, we review the emerging techniques for high-resolution and configurable optical trapping of ultracold atoms. We focus on optical deflectors and spatial light modulators in the Fourier and direct imaging configurations. These optical techniques have enabled significant progress in studies of superfluid dynamics, single-atom trapping, and underlie the emerging field of atomtronics. The chapter is intended as a complete guide to the experimentalist for understanding, selecting, and implementing the most appropriate optical trapping technology for a given application. After introducing the basic theory of optical trapping and image formation, we describe each of the above technologies in detail, providing a guide to the fundamental operation of optical deflectors, digital micromirror devices, and liquid crystal spatial light modulators. We also describe the capabilities of these technologies for manipulation of trapped ultracold atoms, where the potential is dynamically modified to enable experiments, and where time-averaged potentials can realise more complex traps. The key considerations when implementing time-averaged traps are described.

B.J. Mommers, 2 A. Pritchard, 2 T.A. Bell, 2 R.N. Kohn, Jr., S.E. Olson, M. Baker, 2, 1 and M.W.J. Bromley 2 Centre for Engineered Quantum Systems, The University of Queensland, St Lucia, Australia School of Mathematics and Physics, The University of Queensland, St Lucia, Australia Space Dynamics Laboratory, Albuquerque, New Mexico 87106, USA Air Force Research Laboratory, Kirtland AFB, New Mexico 87117, USA Quantum Technologies, Cyber and Electronic Warfare Division, Defence Science and Technology Group, Brisbane, Australia School of Sciences, University of Southern Queensland, Toowoomba, Australia

2-component BEC, confined in an all optical line trap, we use a spin-dependent optical barrier beam to localise one of the spin components. By time-averaging the beam we can furthermore create multiple spin sites.

We show that an acoustic circuit model quantitatively predicts superfluid transport through a channel. With large initial excitation, we show that typical phase-slip model of the dissipation must be extended to include turbulence. © 2020 The Author(s)

We experimentally study the emergence of high-energy equilibrium states in a chiral vortex gas of like-circulation vortices realized within a disk-shaped atomic Bose-Einstein condensate. In contrast to the familiar triangular Abrikosov lattice, the lowest-energy state of the superfluid in a rotating frame, we observe the formation of rotating vortex equilibria that are highly disordered and have significant energy per vortex. Experimental stirring protocols realize equilibrium states at both positive and negative absolute temperatures of the vortex gas. At sufficiently high energies the system exhibits a symmetry breaking transition, resulting in an off-axis equilibrium phase that no longer shares the symmetry of the container. By initializing vortices in a non-equilibrium distribution with sufficient energy, relaxation to equilibrium is observed within experimental timescales and an off-axis equilibrium state emerges at negative absolute temperature. The observed equilibria are in close agreement with mean field theory of the microcanonical ensemble of the vortex gas.

Atomtronics is an emerging field of quantum technology dealing with matter-wave circuits of ultra-cold atoms manipulated in magnetic or laser-generated guides of different shapes and intensity. Atomtronic circuits are promised to define quantum networks of new types in which coherent fluids can be feasibly controlled with the know how of the atomic and molecular physics quantum technology. This way, atomtronics can provide the basis for new quantum devices with enhanced precision, control and flexibility. At the same time, new quantum simulators and emulators harnessing coherent current flows can be defined. Here, we survey the atomtronics-enabled quantum technology and we draw a roadmap on the field for the years to come. The latest progress achieved in matter-wave circuits design and atom-chips are reviewed. Atomtronic networks have been used as platforms to study many-body physics in a new way, both at equilibrium and at non-equilibrium. Relevant problems in mesoscopic physics, like persistent currents and quantum transport in circuits of fermionic or bosonic atoms, have been studied with a new twist. We discuss the state of the art and the perspectives for the quantum devices and sensors implied by coherent matter-wave physics principles. Finally, we discuss alkali-earth and Rydberg atoms as great potential platforms for the realization of atomtronic circuits of a new type.

Microscopic control of BECs is realised through an atom-density based optimisation of optical potentials. These techniques make progress on the long-standing goal of producing smooth and arbitrary potentials for cold atom trapping. © 2019 The Authors.

A gyroscopic measurement scheme is developed using counter-propagating grey solitons generated around optically trapped toroidal atomic superfluids. Digital micromirror spatial light modulator experiments are envisaged to facilitate the future demonstration of this scheme. © 2020 The Author(s)

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.

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. In this study, we experimentally realize these vortex clusters in a planar superfluid: a 87Rb Bose-Einstein condensate confined to an elliptical geometry. We demonstrate that the clusters persist for long time periods, 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 for the dynamics of topological defects, two-dimensional turbulence, and systems such as helium films, nonlinear optical materials, fermion superfluids, and quark-gluon plasmas.

The growth of 3D imaging across a range of sectors has driven a demand for beam steering technology. Fields as diverse as autonomous vehicles and medical imaging can benefit from a high speed, adaptable method of beam steering. We present a monolithic, submicrosecond electro-optic switch as a solution toward the need for reliability, speed, dynamic addressability, and compactness. Here, we demonstrate a laboratory-scale, solid-state light detection and ranging system, using the electro-optic switch to launch modulated coherent light into free space and then to collect the reflected signal. We use coherent detection of the reflected light to simultaneously extract the range and axial velocity of targets at each of the several electronically addressable output ports.

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.

Turbulence in classical fluids is a ubiquitous non-equilibrium phenomenon, yet a complete theoretical description for turbulent flow remains a challenging problem. A useful simplification for ideal two-dimensional (2D) fluids is to describe the turbulent flow with long-range-interacting point vortices, each possessing quantised circulation. In 1949, Onsager applied statistical mechanics to determine the equilibria of this model. He showed that at sufficiently high energies, like-circulation vortices preferentially aggregate into large-scale clusters, and are characterised by a negative absolute temperature. Onsageru0027s theory has been highly influential, providing understanding of diverse quasi-2D systems such as turbulent soap films, guiding-centre plasmas, and self-gravitating systems. It also predicts the striking tendency of 2D turbulence to spontaneously form large-scale, long-lived vortices -- Jupiteru0027s Great Red Spot is a well-known example. However, Onsageru0027s theory doesnu0027t quantitatively apply to classical fluids where vorticity is continuous, and experimental systems demonstrating Onsageru0027s point-vortex statistical mechanics have remained elusive. Here we realise high energy, negative-temperature vortex clusters in a uniform superfluid Bose-Einstein condensate. Our results confirm Onsageru0027s prediction of negative temperature clustered phases of quantum vortices, and demonstrate the utility of point-vortex statistical mechanics in 2D quantum fluids. This work opens future directions for the study of turbulent dynamics and we anticipate exploring the entire phase diagram of 2D quantum vortices, including the formation of clusters from 2D quantum turbulence.

Advances in the control over novel trapping potentials has been a driving factor behind the development of the cold atoms field. As such, the direct imaging of a digital micromirror device (DMD) onto a plane has become a popular technique which has expanded the range of dynamic potentials available for 2D cold atom experiments [1]. One of the drawbacks of this technique is that direct imaging does not allow for correction of aberrations in the projecting optical system, and nonuniformity and imperfections in the illumination field cause imperfection in the projected potential. To this end, we have developed a density-based feedforward optimization technique which uses the grayscaling and dynamic capabilities of the DMD to correct imperfections in the projected trapping potential. This technique can be used to correct for non-uniformity in the trapping potential (See Fig. 1), with unprecendented control over the trapping landscape.

Rapidly scanning magnetic and optical dipole traps have been widely utilized to form time-averaged potentials for ultracold quantum gas experiments. Here we theoretically and experimentally characterize 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 nontrivial 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 2 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 flattens the phase profile, rendering the system more suitable for coherent matter-wave interferometry.