Ultra long spin decoherence times in graphene quantum dots with a small number of nuclear spins

We study the dynamics of an electron spin in a graphene quantum dot, which is interacting with a bath of less than ten nuclear spins via the anisotropic hyperfine interaction. Due to substantial progress in the fabrication of graphene quantum dots, the consideration of such a small number of nuclear spins is experimentally relevant. This choice allows us to use exact diagonalization to calculate the longtime average of the electron spin as well as its decoherence time. We investigate the dependence of spin observables on the initial states of nuclear spins and on the position of nuclear spins in the quantum dot. Moreover, we analyze the effects of the anisotropy of the hyperfine interaction for different orientations of the spin quantization axis with respect to the graphene plane. Interestingly, we then predict remarkable long decoherence times of more than 10ms in the limit of few nuclear spins.Comment: 13 pages, 10 figures, corrected typos, clarified estimation of decoherence times (results unchanged), extended discussion of spin preparation schem

Thermal electron spin flip in quantum dots

We study a thermally induced spin flip of an electron spin located in a semiconductor quantum dot. This interesting effect arises from an intriguing interplay between the Zeeman coupling to an external magnetic field and the hyperfine interaction with the surrounding nuclear spins. By considering a minimal model, we explain the main mechanism driving this spin flip and analyze its dependence on the strength of the external magnetic field, the number of nuclear spins and the ratio of the electron and nuclear Zeeman energies, respectively. Finally we show, that this minimal model can be applied to experimentally relevant QDs in III-V heterostructures, where we explicitly predict the temperature at which the spin flip occurs.Comment: 9 pages, 5 figures; included generalized calculations, which additionally consider the so-called flip-flop terms; three additional appendices; two additional figures; changes in the main text in order to include our new result

Proton MR Spectroscopy of Neural Stem Cells: Does the Proton-NMR Peak at 1.28 ppm Function As a Biomarker for Cell Type or State?

Recently, a peak at 1.28 ppm in proton magnetic resonance spectroscopy (^1H-MRS) of neural stem cells (NSCs) was introduced as a noninterventional biomarker for neurogenesis in vivo. This would be an urgently needed requisite for translational studies in humans regarding the beneficial role of adult neurogenesis for the structural and functional integrity of the brain. However, many concerns have risen about the validity of the proposed signal as a specific marker for NSCs. The peak has also been related to cell-type-independent phenomena such as apoptosis or necrosis. Thus, we compared the 1.28-ppm peak in various immature stem cell populations, including embryonic stem cells, mouse embryonic fibroblasts, embryonic stem cell– and induced pluripotent stem cell–derived NSCs, ex vivo isolated embryonic NSCs, as well as mature and tumor cell types from different germ layers. To correlate the integral peak intensity with cell death, we induced both apoptosis with camptothecin and necrosis with sodium azide. A peak at 1.28 ppm was found in most cell types, and in most, but not all, NSCH cultures, demonstrating no specificity for NSCs. The intensities of the 1.28-ppm resonance significantly correlated with the rate of apoptosis, but not with the rate of necrosis, cell cycle phase distribution, cell size, or type. Multiple regression analysis displayed a significant predictive value of the peak intensity for apoptosis only. In this context, its specificity for apoptosis as a major selection process during neurogenesis may suggest this resonance as an indirect marker for neurogenesis in vivo

Tan relations in one dimension

We derive exact relations that connect the universal $C/k^4$-decay of the momentum distribution at large $k$ with both thermodynamic properties and correlation functions of two-component Fermi gases in one dimension with contact interactions. The relations are analogous to those obtained by Tan in the three-dimensional case and are derived from an operator product expansion of the one- and two-particle density matrix. They extend earlier results by Olshanii and Dunjko [Phys. Rev. Lett. 91, 090401 (2003)] for the bosonic Lieb-Liniger gas. As an application, we calculate the pair distribution function at short distances and the dimensionless contact in the limit of infinite repulsion. The ground state energy approaches a universal constant in this limit, a behavior that also holds in the three-dimensional case. In both one and three dimensions, a Stoner instability to a saturated ferromagnet for repulsive fermions with zero range interactions is ruled out at any finite coupling.Comment: 8 figures, 27 pages - Updated to status of published versio

FrOoDo: Framework for Out-of-Distribution Detection

FrOoDo is an easy-to-use and flexible framework for Out-of-Distribution detection tasks in digital pathology. It can be used with PyTorch classification and segmentation models, and its modular design allows for easy extension. The goal is to automate the task of OoD Evaluation such that research can focus on the main goal of either designing new models, new methods or evaluating a new dataset. The code can be found at https://github.com/MECLabTUDA/FrOoDo

Spin decoherence in graphene quantum dots due to hyperfine interaction

Carbon based systems are prominent candidates for a solid-state spin-qubit due to weak spin-orbit and hyperfine interactions in combination with a low natural abundance of spin carrying isotopes. We consider the effect of the hyperfine interaction on the coherence of an electron-spin localized in a graphene quantum dot. It is known, that the hyperfine interaction in these systems is anisotropic promising interesting physics. We calculate the dynamics of an electron spin surrounded by a bath of nuclear spins in a non-Markovian approach using a generalized master equation. Considering a general form of the hyperfine interaction, we are able to extend the range of validity of our results to other systems beyond graphene. For large external magnetic fields, we find within Born approximation that the electron spin state is conserved up to small corrections, which oscillate with a frequency determined by the hyperfine interaction. The amplitude of these oscillations decays with a power law, where its initial value depends on the specific form of the anisotropy. Analyzing this in more detail, we identify two distinct classes of anisotropy, which can be both found in graphene depending on the orientation of the external magnetic field with respect to the carbon layer.Comment: 19 pages, 7 figure

Spin-Imbalance in a One-Dimensional Fermi Gas

Superconductivity and magnetism generally do not coexist. Changing the relative number of up and down spin electrons disrupts the basic mechanism of superconductivity, where atoms of opposite momentum and spin form Cooper pairs. Nearly forty years ago Fulde and Ferrell and Larkin and Ovchinnikov proposed an exotic pairing mechanism (FFLO) where magnetism is accommodated by formation of pairs with finite momentum. Despite intense theoretical and experimental efforts, however, polarized superconductivity remains largely elusive. Here we report experimental measurements of density profiles of a two spin mixture of ultracold 6Li atoms trapped in an array of one dimensional (1D) tubes, a system analogous to electrons in 1D wires. At finite spin imbalance, the system phase separates with an inverted phase profile in comparison to the three-dimensional case. In 1D we find a partially polarized core surrounded by wings composed of either a completely paired BCS superfluid or a fully polarized Fermi gas, depending on the degree of polarization. Our observations are in quantitative agreement with theoretical calculations in which the partially polarized phase is found to be a 1D analogue of the FFLO state. This study demonstrates how ultracold atomic gases in 1D may be used to create non-trivial new phases of matter, and also paves the way for direct observation and further study of the FFLO phase.Comment: 30 pages, 7 figure

From Pointwise to Powerhouse: Initialising Neural Networks with Generative Models

Traditional initialisation methods, e.g. He and Xavier, have been effective in avoiding the problem of vanishing or exploding gradients in neural networks. However, they only use simple pointwise distributions, which model one-dimensional variables. Moreover, they ignore most information about the architecture and disregard past training experiences. These limitations can be overcome by employing generative models for initialisation. In this paper, we introduce two groups of new initialisation methods. First, we locally initialise weight groups by employing variational autoencoders. Secondly, we globally initialise full weight sets by employing graph hypernetworks. We thoroughly evaluate the impact of the employed generative models on state-of-the-art neural networks in terms of accuracy, convergence speed and ensembling. Our results show that global initialisations result in higher accuracy and faster initial convergence speed. However, the implementation through graph hypernetworks leads to diminished ensemble performance on out of distribution data. To counteract, we propose a modification called noise graph hypernetwork, which encourages diversity in the produced ensemble members. Furthermore, our approach might be able to transfer learned knowledge to different image distributions. Our work provides insights into the potential, the trade-offs and possible modifications of these new initialisation methods