We present an application of dark-field imaging that enables in situ detection of two-dimensional vortex distributions in single-component Bose-Einstein condensates (BECs). By rotating a $^{87}\mathrm{Rb}$ BEC in a magnetic trap, we generate a triangular lattice of vortex cores in the BEC, with core diameters on the order of 400 nm and cores separated by approximately $9\ensuremath{\mu}\mathrm{m}$. We have experimentally confirmed that the positions of the vortex cores near the BEC center can be determined without the need for ballistic expansion of the BEC. Our imaging method should allow for the determination of arbitrary distributions of vortices and other superfluid density defects in cases where expansion of the BEC is either impractical or would significantly alter the physical characteristics and appearance of vortices or defects. Our method is also a step toward real-time measurements of complex two-dimensional vortex dynamics within a single BEC.
We present an application of dark-field imaging that enables in situ detection of two-dimensional vortex distributions in single-component Bose-Einstein condensates (BECs). By rotating a 87Rb BEC in a magnetic trap, we generate a triangular lattice of vortex cores in the BEC, with core diameters on the order of 400 nm and cores separated by approximately 9\ensuremathμm. We have experimentally confirmed that the positions of the vortex cores near the BEC center can be determined without the need for ballistic expansion of the BEC. Our imaging method should allow for the determination of arbitrary distributions of vortices and other superfluid density defects in cases where expansion of the BEC is either impractical or would significantly alter the physical characteristics and appearance of vortices or defects. Our method is also a step toward real-time measurements of complex two-dimensional vortex dynamics within a single BEC.
Bose-Einstein condensates (BECs), with their superfluid behavior, quantized vortices, and high-level of control over trap geometry and other system parameters provide a compelling environment for studies of quantum fluid dynamics. Recently there has been an influx of theoretical and numerical progress in understanding the superfluid dynamics associated with two-dimensional quantum turbulence, with expectations that complementary experiments will soon be realized. In this dissertation I present progress in the development of an experimental toolkit that will enable such experimental studies of two-dimensional quantum turbulence. My approach to developing this toolkit has been twofold: first, efforts aimed at the development of experimental techniques for generating large disordered vortex distributions within a BEC; and second, efforts directed towards the design, implementation, and characterization of a quantum vortex microscope. Quantum turbulence in a superfluid is generally regarded as a disordered tangle of quantized vortices in three dimensions, or a disordered planar distribution of quantized vortices in two dimensions. However, not all vortex distributions, even large disordered ones, are expected to exhibit robust signatures of quantum turbulence. Identification and development of techniques for controlled forcing or initialization of turbulent vortex distributions is now underway. In this dissertation, I will discuss experimental techniques that were examined during the course of my dissertation research, namely generation of large disordered distributions of vortices, and progress towards injecting clusters of vortices into a BEC. Complimentary to vortex generation is the need to image these vortex distributions. The nondeterministic nature of quantum turbulence and other far-from-equilibrium superfluid dynamics requires the development of new imaging techniques that allow one to obtain information about vortex dynamics from a single BEC. To this end, the first vortex microscope constructed as part of my dissertation research enabled the first in situ images of quantized vortices in a single-component BEC, obtained without prior expansion. I have further developed and characterized a second vortex microscope, which has enabled the acquisition of multiple in situ images of a lattice of vortex cores, as well as the acquisition of single in situ images of vortex cores in a BEC confined in a weak hybrid trap. In this dissertation, I will discuss the state-of-the-art of imaging vortices and other superfluid phenomena in the University of Arizona BEC lab, as indicated by the examined performance of the quantum vortex microscope.
Abstract Quantum vortices in atomic Bose–Einstein condensates (BECs) are topological defects characterized by quantized circulation of particles around them. In experimental studies, vortices are commonly detected by time-of-flight imaging, where their density-depleted cores are enlarged. In this work, we describe a machine learning-based method for detecting vortices in experimental BEC images, particularly focusing on turbulent condensates containing irregularly distributed vortices. Our approach employs a convolutional neural network (CNN) trained solely on synthetic simulated images, eliminating the need for manual labeling of the vortex positions as ground truth. We find that the CNN achieves accurate vortex detection in real experimental images, thereby facilitating analysis of large experimental datasets without being constrained by specific experimental conditions. This novel approach represents a significant advancement in studying quantum vortex dynamics and streamlines the analysis process in the investigation of turbulent BECs.
The presence of quantized vortices and a high level of control over trap geometries and other system parameters make dilute-gas Bose-Einstein condensates (BECs) a natural environment for studies of vortex dynamics and quantum turbulence in superfluids, primary interests of the BEC group at the University of Arizona. Such research may lead to deeper understanding of the nature of quantum fluid dynamics and far-from-equilbrium phenomena.Despite the importance of quantized vortex dynamics in the fields of superfluidity, superconductivity and quantum turbulence, direct imaging of vortices in trapped BECs remains a significant technical challenge. This is primarily due to the small size of the vortex core in a trapped gas, which is typically a few hundred nanometers in diameter. In this dissertation I present the design and construction of a new ^87Rb BEC apparatus with the goal of studying vortex dynamics in trapped BECs. The heart of the apparatus is a compact vacuum chamber with a custom, all-glass science cell designed to accommodate the use of commercial high-numerical-aperture microscope objectives for in situ imaging of vortices.The designs for the new system are, in part, based on prior work in our group on in situ imaging of vortices. Here I review aspects of our prior work and discuss some of the successes and limitations that are relevant to the new apparatus. The bulk of the thesis is used to described the major subsystems of the new apparatus which include the vacuum chamber, the laser systems, the magnetic transfer system and the final magnetic trap for the atoms. Finally, I demonstrate the creation of a BEC of ~2x10^6 ^87Rb atoms in our new system and show that the BEC can be transferred into a weak, spherical, magnetic trap with a well defined magnetic field axis that may be useful for future vortex imaging studies.
Abstract Quantum vortices naturally emerge in rotating Bose–Einstein condensates (BECs) and, similarly to their classical counterparts, allow the study of a range of interesting out-of-equilibrium phenomena, such as turbulence and chaos. However, the study of such phenomena requires the determination of the precise location of each vortex within a BEC, which becomes challenging when either only the density of the condensate is available or sources of noise are present, as is typically the case in experimental settings. Here, we introduce a machine-learning-based vortex detector motivated by state-of-the-art object detection methods that can accurately locate vortices in simulated BEC density images. Our model allows for robust and real-time detection in noisy and non-equilibrium configurations. Furthermore, the network can distinguish between vortices and anti-vortices if the phase profile of the condensate is also available. We anticipate that our vortex detector will be advantageous for both experimental and theoretical studies of the static and dynamic properties of vortex configurations in BECs.
A basic challenge in experimental physics is the extraction of information related to variables that are not directly measured. The challenge is particularly severe in quantum systems where one may be interested in correlations of operators that are not diagonal in the measurement basis. In this paper we take a step towards addressing this issue in the context of Boson superfluids, where standard in-situ imaging yields only the spatially resolved density, leaving the phase field - crucial for identifying topological defects such as vortices and confirming superfluidity - indirectly encoded. Previous work has shown that the location of vortices in the phase field may be detected, but has not solved the problems of fully reconstructing the phase or identifying the charge (vortex vs. antivortex). This paper shows that a combination of a deep machine learning (ML) model and classical computer vision post-processing steps can address this gap. We use realistic snapshots of the thermal state of a two-dimensional BEC in a harmonic trap using synthetic data obtained from projected Gross-Pitaevskii equation simulations to train a U-Net-based architecture to infer the absolute values of the phase field gradients from an observed density field, and then employ a separate ML model to locate the positions of the vortex cores and a post-processing graphical analysis to determine with high accuracy the phase field, including the quantized charge of each vortex.
Dilute gas Bose-Einstein condensates (BECs) provide unique and powerful experimental platforms to study fluid turbulence. Some aspects of BEC hydrodynamics are specific to atomic quantum fluids such as quantized vortices and flexible trapping geometries. However, there are features of turbulence that are universal and simpler to understand in such systems. BECs are also of interest in fundamental physics in their own right and a rich synthesis of theory and experiment has yielded powerful numerical methods to simulate and study BEC dynamics. In this dissertation I present two experiments, one conducted and one proposed, describing novel aspects of the generation and detection of vorticity in Bose-Einstein condensates. Models of BEC dynamics at zero temperature are provided by the Gross-Pitaevskii equation. Simple and fast numerical solutions of this equation have yielded a wealth of literature. However, in experimental reality the atomic ensemble exists at a finite temperature and consists of a BEC coexisting with a thermal cloud of non-condensed atoms. The interaction between the condensate and the thermal fraction yields rich and complex physics that require more advanced models. We present an experiment demonstrating the relaxation dynamics of a BEC in a rotating trap perturbed by a repulsive laser barrier. The data provided by this experiment are valuable to further development of theoretical models that incorporate interactions between the BEC and noncondensed atoms. In the field of quantum fluid dynamics, an experimental method to determine the position and circulation of vortices is a highly sought-after capability. Onsager's point-vortex model of turbulence completely determines the kinetic energy spectrum of an incompressible fluid by these degrees of freedom. We present proof-of-principle simulations that describe a new method of spatially sampling the velocity field of a two-dimensional BEC by using an optical lattice analogously to a Shack-Hartmann Wavefront Sensor. Extracting vortex information from the appropriately sampled velocity field can be accomplished either qualitatively or with detection algorithms. This method requires minimal experimental infrastructure and is generally applicable across atomic species. The implications of measuring a condensate velocity field are broad and these initial results provide the first step towards realizing a valuable tool in BEC physics.