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The prototypical superfluid, Helium-4 ($^4$He), transitions to its superfluid state below ~2 K. In contrast, its isotopic counterpart Helium-3 ($^3$He) has a transition temperature of ~2 mK. This thousand-fold disparity is due to the nature of the superfluid transition; while $^4$He Bose condenses directly, the fermionic $^3$He atoms must first form composite bosons through Cooper pairing. The $p$-wave, spin-triplet pairing of the $^3$He atoms gives rise to many possible superfluid phases, though only two distinct phases are realized in the bulk.

Recent experimental and theoretical advances have suggested that a third phase emerges when superfluid $^3$He is confined to a slab --- a pair-density-wave (PDW) phase. Analogous to a supersolid, the PDW phase is characterized by the spontaneous breaking of translational symmetry that coexists with superfluid order. The precise spatial structure of this &quot;superfluid crystal&quot; has been the subject of ongoing debate: existing theories favor a unidirectional PDW, the stripe phase, while recent nuclear magnetic resonance (NMR) experiments seem to indicate a two-dimensional PDW with square or hexagonal symmetry. In this talk, I will outline a mechanism, based on Landau&#39;s theory of weak crystallization, which stabilizes a two-dimensional PDW with the hexagonal symmetry of a triangular lattice.

CAP Virtual Congress 2021

Triangular Pair-Density-Wave in Confined Superfluid 3He

crystal

helium-3

superfluid

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The prototypical superfluid, Helium-4 ($^4$He), transitions to its superfluid state below ~2 K. In contrast, its isotopic counterpart Helium-3 ($^3$He) has a transition temperature of ~2 mK. This thousand-fold disparity is due to the nature of the superfluid transition; while $^4$He Bose condenses directly, the fermionic $^3$He atoms must first form composite bosons through Cooper pairing. The $p$-wave, spin-triplet pairing of the $^3$He atoms gives rise to many possible superfluid phases, though only two distinct phases are realized in the bulk.

Recent experimental and theoretical advances have suggested that a third phase emerges when superfluid $^3$He is confined to a slab --- a pair-density-wave (PDW) phase. Analogous to a supersolid, the PDW phase is characterized by the spontaneous breaking of translational symmetry that coexists with superfluid order. The precise spatial structure of this "superfluid crystal" has been the subject of ongoing debate: existing theories favor a unidirectional PDW, the stripe phase, while recent nuclear magnetic resonance (NMR) experiments seem to indicate a two-dimensional PDW with square or hexagonal symmetry. In this talk, I will outline a mechanism, based on Landau's theory of weak crystallization, which stabilizes a two-dimensional PDW with the hexagonal symmetry of a triangular lattice.

technical paper

The main advantage of hybrid PET-MR imaging systems is the ability to correlate anatomical with metabolic information directly. The bulk of commercially available PET-MR systems are quite large and expensive and mostly used on humans rather than for preclinical animal studies. This has led to a gap of knowledge in PET-MR imaging of small animal models used in preclinical research. Our work takes advantage of a new imaging system developed by Cubresa called 'NuPET'. This device is a MR-compatible PET scanner placed around the subject while they are within the toroidal bore of a MR scanner. With this equipment we are attempting to demonstrate the selective activation of serotonergic neurons in living rodent brains. To specify which neurons are to be activated, we use Designed Receptors Exclusively Activated by Designer Drug (DREADD) technology. These DREADDs are designer G-protein-coupled receptors. Neurons at the site of a stereotactic injection are transfected with a viral vector containing the proteins necessary to force expression of DREADDs in genetically modified rats. These may then be activated by administering the designer drug clozapine-N-oxide (CNO). This technique allows for precise spatiotemporal control of receptor signaling in vivo. Over two experiments (N=5, N=2) we have attempted to image the effect of DREADDs-mediated excitation of 5-HT neurons in rats. Voxel-based analysis of the data thus far show no confirmed statistically significant differences between rats given saline and those given CNO. Numerous methodological issues have been discovered within the experimental design, and are being addressed for a new trial of the technique and technology.

The authors wish to acknowledge funding from NSERC partnership grants, Mitacs, Cubresa, and Research Manitoba.

Multi-modal PET-MR imaging of the selective activation of serotonergic neurons in living rodent brains with DREADD technology

Multiquark states have been of great interest among hadronic physicists, and despite the big breakthrough that came in 2003 with the discovery of the charmonium-like tetraquark candidate X(3872), their internal quark structure (e.g., molecular versus diquark clusters) are not well-understood yet. QCD sum-rule mass estimates for multiquark states can provide insights on possible internal quark structures. Previous research suggests that the next-to-leading order (NLO) corrections to QCD sum-rule mass determinations are quite different in heavy and light multiquark states. 
The study of these multiquark systems can give us another approach to understand strong interactions at the elementary level and at different energy scales. The goal of this research is a detailed examination of the NLO corrections to mass estimates of the light scalar tetraquarks using QCD sum-rules.

NLO effects on light tetraquark mass estimates using QCD sum rules

We present some analytic results that describe the gluon field, or glasma, that exists at very early times after a collision of relativistic heavy ions at proper time $\tau=0$. We use a Colour Glass Condensate approach, and perform an expansion in $\tau$. We show that the expansion to order $\tau^6$ can be trusted to about $\tau=0.05$ fm/c. We calculate the transverse and longitudinal pressures and show that for $\tau < 0.05$ fm/c they move towards their equilibrium values of one third of the energy density. We study the spatial eccentricity of the plasma, and the Fourier coefficients of the azimuthal momentum distribution. Our results for the Fourier coefficients are larger than  expected, which contradicts the usual assumption that anisotropy is mostly generated during the hydrodynamic evolution of the plasma. We  find a significant correlation between the elliptic flow coefficient and the eccentricity, which indicates that the spatial inhomogeneity introduced by the initial geometry is effectively transmitted to the azimuthal distribution of the gluon momentum field, even at very early times. This result is interesting because correlations of this kind are  characteristic of the onset of hydrodynamic behaviour. We also calculate the angular momentum of the glasma and obtain results that are many orders of magnitude smaller than the initial angular momentum of two ions colliding with non-zero impact parameter. This indicates that most of the angular momentum carried by the valence quarks is not transmitted to the glasma. The result is significant because it contradicts the picture of a rapidly rotating initial glasma state,  but agrees with the current lack of experimental evidence for a global polarization effect in the hyperons and vector mesons produced in heavy ion collisions.

Characteristics of early time gluon fields in relativistic heavy ion collisions

I will discuss different notions of nonrelativistic strings and their target space geometries. The first example comes from a self-contained corner of string theory dubbed nonrelativistic string theory, which is closely related to string theory in the discrete light-cone quantization. The appropriate spacetime geometry for nonrelativistic string theory is a stringy generalization of Newton-Cartan geometry. The second example involves sigma models at a Lifshitz point, which describe strings moving in bimetric spacetime. In the limit when the two metrics coincide, the relativistic sigma model that underlies string theory can be recovered. This study of Lifshitz-type sigma models also provides useful insights for constructing a quantum theory of membranes.

Nonrelativistic Strings and Exotic Geometries

Despite the constant stream of black hole merger observations, black hole mergers are not yet fully understood. The phenomenon seems simple enough, but the details of how the two apparent horizons end up as one horizon is unclear due to the non-linear nature of the merger process. Recent numerical work has shown that there is a merger of self-intersecting Marginally Outer-Trapped Surfaces (MOTS) during the black hole merger. Following papers have investigated further into MOTS in a simpler and static scenario, that of a Schwarzschild black hole. Such cases require less machinery and are solved with everyday computers. Those numerical calculations show an infinite number of self-intersecting MOTS hidden within the apparent horizon, as well as open surfaces (MOTOS). The importance of Schwarzschild MOTS are not to be undermined due to its relative simplicity as such MOTS describe an extreme-mass-ratio black hole merger, where one of the black holes is far more massive than the other. In this talk, I will discuss the current understanding of black hole mergers as have numerically been shown and my work investigating Schwarzschild MOTS in maximally-extended Kruskal-Szekeres coordinates.

The many marginally outer trapped surfaces of Schwarzschild spacetime

Topological insulators are an interesting class of materials which host distinct zero/low-energy states at their boundaries. These symmetry-protected states can, for example, arise as Majorana zero-modes in various superconducting systems and have potential applications in quantum error correction. However, experimental study and verification of such zero-modes remains a challenge. Considering a toy-system based on the Su-Schrieffer-Heeger (SSH) model coupled to one end with a semi-infinite conducting lead, we propose a measurement method for gapped topological states through a study of the decoherence dynamics of a quantum dot or qubit. Decoherence rates along the length of the SSH chain vary proportionally to the edge states and allow for both the identification and spatial characterisation of such states.

Quantum dots as probes for topological materials

We use Langevin dynamics (LD) simulations to investigate single file diffusion (SFD) in a dilute solution of flexible linear polymers inside a narrow tube. The transition from single-file diffusion, where the mean-square displacement scales like $\langle x^2 \rangle \sim t^{1/2}$, to normal diffusion with $\langle x^2 \rangle \sim t$, is studied as a function of the system parameters, such as the width of the channel, the polymer concentration and the polymer size. Based on our simulation results and scaling arguments, we propose a phase diagram describing the different diffusion regimes. We also map this problem onto a one-dimensional Lattice Random Walk algorithm where the diffusing object represents the polymer's center of mass. In order to model the polymers entanglement and disentanglement processes we allow several objects to temporarily share the same lattice site and diffuse together. Extension of our work to polydisperse polymer solutions, one-dimensional electrophoresis, ring polymers and DNA mapping are discussed.

The Limits of Polymer Single File Dynamics: A phase diagram

Temporal diffusion spectroscopy (TDS) has been used to infer axon sizes using geometric models that assume axons are cylinders. A celery sample was imaged to test if the importance of other geometric models. The vascular bundles and collenchyma tissue (~20 μm cells) in celery can be modeled as containing cylindrical cells. Whereas the parenchyma cells are rounder and are 3-4 times larger in diameter. Thus we imaged celery to test TDS with oscillating gradient spin echo (OGSE) to see if the spherical cell model and cylindrical cell model infer significantly different cell sizes to determine how important the geometrical model is.
A small section of a celery stalk was cut to fit inside a 15 mL sample tube filled with water. The image slice was chosen to be perpendicular to the length of the celery stalk. The sample was imaged using a 7T Bruker AvanceIII NMR system with Paravision 5.0 and BGA6 gradient set with a maximum gradient strength of 430357 Hz/cm, and a 3.5 cm diameter bird cage RF coil. Each 20 ms apodised cosine gradient pulse ranged from n = 1-20, in steps of 1. Two different gradient strengths were used for each frequency and gradient pulses were separated by 24.52 ms. A 1mm thick slice was acquired with the following imaging parameters: 2 averages, 2.56 cm FOV, TR = 1250 ms, TE = 50 ms, matrix 128 x 128, 200 μm in plane resolution, acquisition time 26.67 minutes per scan (scans performed = 40, 17.78 hours).
The inferred diameters of cells in celery (14±6μm to 20±12μm) were not statistically different when using the two different geometric models. This is the first step toward understanding the importance of geometric models for TDS.
The authors wish to acknowledge funding from NSERC and Mitacs.

Comparison of Cylindrical and Spherical Geometric Models to Infer Cell Sizes in a Celery Sample

In any application where a radiation detector is utilized in a mixed radiation field, there is an inherent issue of separating the signal from the background. This research focuses on the separation of neutron and gamma-ray events in a liquid scintillator. The standard solution to this issue leverages the fact that the secondary particles generated in neutron and photon interactions are different; the former being nuclear recoils, typically protons in organic scintillators, and the latter being electrons or positrons in the case of pair production. The charge deposition characteristics of these secondary particles provide the basis for Pulse Shape Discrimination (PSD) as a means of event classification.

The work presented focuses on the development of a machine learning algorithm for use in the problem of pulse shape discrimination. The signals generated from gamma ray and neutron interactions inside the liquid scintillator used are comprised of three characteristic scintillation decay times: 3.16 ns, 32.3 ns, and 270 ns. The proportion of scintillation light generated from these three characteristic times is dictated by the stopping power of the particle traversing the scintillator, generating distinguishable signals for photon interactions relative to neutron interactions. Typically PSD is performed by allowing two different charge collection windows and comparing the amount of charge collected in both; tail-to-total integration. This work utilizes current generation machine vision algorithms for the task of event classification, where the PMT output from the scintillator will be utilized as the input to the machine vision algorithm. Current generation algorithms allow for feature extraction performed simultaneously at differing spatial extents, which enables the algorithm to extract valuable information about the signal from all three time scales present in the scintillator, 3, 30, and 300 ns. This new application of machine vision algorithms will be coupled with a current generation digitizer operating with 12 bit precision and sampling at 3.2 GS/s. This opens up the possibility of utilizing information from the rising edge of the signal, which is on the order of a few nanoseconds.

Training of this algorithm was performed in a supervised manner, which requires that labeled sets of data be provided for the algorithm to learn from. Any improperly labeled data utilized, diminishes the performance of the algorithm, making correctly labeled data paramount to success. Performing this for neutron and gamma-ray events in the scintillator is quite difficult due to the complications mentioned for event classification. The solution used in this project is to utilize an isotopic source of neutrons, PuBe. The PuBe source produces prompt gamma rays in conjunction with neutrons in some decays, with energies greater than 4 MeV. These prompt gamma rays can serve as an event trigger for detection of neutrons in a secondary detector, providing relative certainty that detected events within an appropriate time window are indeed neutron events. Producing a high degree of purity in the training data.

Development and Implementation of a Machine Learning Algorithm for Pulse Shape Discrimination

Laser-induced breakdown spectroscopy (LIBS) is a laser-based spectrochemical technique that allows a near-instantaneous measurement of the elemental composition of a target by making time-resolved spectroscopic analyses of laser-induced ablation plasmas. Utilizing nanosecond laser pulses and a broadband high-resolution Echelle spectrometer, high signal-to-noise optical emission spectra can be obtained from almost any desired target.

Recently it has been shown by others that ablation of a non-metallic target that has been coated with metallic (gold or silver) nanoparticles causes an increase in optical emission intensity due to the creation of a plasma with a higher temperature and higher electron density. This process is called “nanoparticle enhanced” LIBS or NELIBS. In our laboratory we have begun investigating whether cheaper and easier to acquire monodisperse metallic microparticles can be used to enhance the emission from bacterial cells when they are deposited upon a nitrocellulose paper filter medium.

This presentation will detail our efforts to build a small deposition chamber to reliably and reproducibly deposit a known mass of commercially obtained one micron silver microparticles. The silver microparticles must also be uniformly deposited over the surface of the 9 mm diameter filter medium (achieving a uniform surface mass density) to insure that the enhancement is consistent over the one millimeter diameter circular bacterial deposition area in the center of the filter. 

A nominal surface coverage density of 0.026 μg/mm^2 of silver microparticles was achieved, resulting in a silver ablation mass of 110 pg per laser shot. Using this mass surface density, enhancement of the emission from the different elements present in the bacterial cells was observed and was found to not be consistent, varying from an enhancement factor of 1 up to 8. Efforts to exploit and further develop this phenomenon for detecting lower numbers of bacterial cells will be described.

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Triangular Pair-Density-Wave in Confined Superfluid 3He

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