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The interpretation of nuclear magnetic resonance (NMR) data is of interest in a number of fields. In \"{O}gren [Eur. Phys. J. B (2014) 87: 255] local boundary conditions for random walk simulations of NMR relaxation in digital domains were presented. Here, we have applied those boundary conditions to large, three-dimensional (3D) porous media samples. We compared the random walk results with known solutions and then applied them to highly structured 3D domains, from images derived using synchrotron radiation CT scanning of North Sea chalk samples. As expected, there were systematic errors caused by digitalization of the pore surfaces so we quantified those errors, and by using linear local boundary conditions, we were able to significantly improve the output. We also present a technique for treating numerical data prior to input into the ESPRIT algorithm for retrieving Laplace components of time series from NMR data (commonly called $T$-inversion).

The $^{12}\text{C}(\alpha,\gamma){}^{16}\text{O}$ reaction plays a central role in astrophysics, but its cross section at energies relevant for astrophysical applications is only poorly constrained by laboratory data. The reduced $\alpha$ width, $\gamma_{11}$, of the bound $1^-$ level in $^{16}$O is particularly important to determine the cross section. The magnitude of $\gamma_{11}$ is determined via sub-Coulomb $\alpha$-transfer reactions or the $\beta$-delayed $\alpha$ decay of $^{16}$N, but the latter approach is presently hampered by the lack of sufficiently precise data on the $\beta$-decay branching ratios. Here we report improved branching ratios for the bound $1^-$ level [$b_{\beta,11} = (5.02\pm 0.10)\times 10^{-2}$] and for $\beta$-delayed $\alpha$ emission [$b_{\beta\alpha} = (1.59\pm 0.06)\times 10^{-5}$]. Our value for $b_{\beta\alpha}$ is 33% larger than previously held, leading to a substantial increase in $\gamma_{11}$. Our revised value for $\gamma_{11}$ is in good agreement with the value obtained in $\alpha$-transfer studies and the weighted average of the two gives a robust and precise determination of $\gamma_{11}$, which provides significantly improved constraints on the $^{12}$C$(\alpha,\gamma)$ cross section in the energy range relevant to hydrostatic He burning., Comment: 6 pages, 5 figures

The quantification of surface area between mineral and reactive fluid is essential in environmental applications of reactive transport modelling. This quantity evolves with microstructures and is difficult to predict because the mechanisms for the generation and destruction of reactive surface remain elusive. The challenge of accounting for the inherent heterogeneities of natural porous media in numerical simulation further complicates the problem. Here we first show a direct observation of reactive surface generation in chalk under circumneutral to alkaline pH using in situ X-ray microtomography. The momentary increase of reactive surface area cannot be explained by a change in fluid accessibility or by surface roughening stemming from mineralogical heterogeneity. We then combine greyscale nanotomography data with numerical simulations to show that similar temporal behaviour can be observed over a wide range of pH as porous media dissolve in imposed flow field. We attribute the observation to the coupling between fluid flow and mineral dissolution and argue that the extent of surface generation is strongly correlated with the advective penetration depth of reactants. To conclude, we demonstrate the applicability of using a macroscopic Damk\"ohler number as an indicator for the phenomenon and discuss its environmental significance beyond geologic carbon storage., Comment: 32 pages, 8 figures

Growth of wormholes in porous media can lead to self-organization of flow networks with an overwhelming geometric complexity. Despite decades of study, the mechanism by which a dominant wormhole develops its path during growth remains elusive. Here we show that the trajectory of a growing wormhole can be predicted by identifying the flowpath with a so-called minimum cumulative surface. Our theoretical analysis indicates that the cumulative surface determines the position of the dissolution front. We then show, using numerical simulation based on greyscale nanotomography data, that the tip of an advancing pore always follows the migration of the most far reaching dissolution front. Finally, we show the good accord between theory and the observation with in situ microtomography. Our result suggests that wormholing is a deterministic process rather than, as classical theories imply, a stochastic one that can only be analysed statistically. Our results shed new light on engineering of artificial flow systems by exploiting self-organization in natural porous materials., Comment: 22 pages, 5 figures

The dissolution of porous media in a geologic formation induced by the injection of massive amounts of CO2 can undermine the mechanical stability of the formation structure before carbon mineralization takes place. The geomechanical impact of geologic carbon storage is therefore closely related to the structural sustainability of the chosen reservoir as well as the probability of buoyancy driven CO2 leakage through caprocks. Here we show, with a combination of ex situ nanotomography and in situ microtomography, that the presence of dissolved CO2 in water produces a homogeneous dissolution pattern in natural chalk microstructure. This pattern stems from a greater apparent solubility of chalk and therefore a greater reactive subvolume in a sample. When a porous medium dissolves homogeneously in an imposed flow field, three geomechanical effects were observed: material compaction, fracturing and grain relocation. These phenomena demonstrated distinct feedbacks to the migration of the dissolution front and severely complicated the infiltration instability problem. We conclude that the presence of dissolved CO2 makes the dissolution front less susceptible to spatial and temporal perturbations in the strongly coupled geochemical and geomechanical processes., Comment: 43 pages, 16 figures

We present the first experimental realization of coherent Bragg scattering off a one-dimensional (1D) system -- two strings of atoms strongly coupled to a single photonic mode -- realized by trapping atoms in the evanescent field of a tapered optical fiber (TOF), which also guides the probe light. We report nearly 12% power reflection from strings containing only about one thousand cesium atoms, an enhancement of two orders of magnitude compared to reflection from randomly positioned atoms. This result paves the road towards collective strong coupling in 1D atom-photon systems. Our approach also allows for a straightforward fiber connection between several distant 1D atomic crystals., Comment: 5 pages + supplementary information

We demonstrate preparation and detection of an atom number distribution in a one-dimensional atomic lattice with the variance $-14$ dB below the Poissonian noise level. A mesoscopic ensemble containing a few thousand atoms is trapped in the evanescent field of a nanofiber. The atom number is measured through dual-color homodyne interferometry with a pW-power shot noise limited probe. Strong coupling of the evanescent probe guided by the nanofiber allows for a real-time measurement with a precision of $\pm 8$ atoms on an ensemble of some $10^3$ atoms in a one-dimensional trap. The method is very well suited for generating collective atomic entangled or spin-squeezed states via a quantum non-demolition measurement as well as for tomography of exotic atomic states in a one-dimensional lattice.

We report on the observation of quantum interference of a collective single spin excitation with a spin ensemble of $N_{\text{atom}} =10^5$ atoms. Detection of a single photon scattered from the atoms creates the single spin excitation, a Fock state embedded in the collective spin of the ensemble. The state of the atomic ensemble is then detected by tomography via a quantum non-demolition measurement of the collective spin. A macroscopic difference of the order of $\sqrt{N_{\text{atom}}}$ in the marginal distribution of the collective spin state arises from the interference between the single excited spin and $N_{\text{atom}}$ atoms. The hybrid discrete-continuous processing of the collective spin pave the road towards generation of even more exotic states for quantum information processing, precision measurements and communication., Comment: Published version

We present a proposal and a feasibility study for the creation and quantum state tomography of a single polariton state of an atomic ensemble. The collective non-classical and non-Gaussian state of the ensemble is generated by detection of a single forward scattered photon. The state is subsequently characterized by atomic state tomography performed using strong dispersive light-atoms interaction followed by a homodyne measurement on the transmitted light. The proposal is backed by preliminary experimental results showing projection noise limited sensitivity and a simulation demonstrating the feasibility of the proposed method for detection of a non-classical and non-Gaussian state of the mesoscopic atomic ensemble. This work represents the first attempt of hybrid discrete-continuous variable quantum state processing with atomic ensembles.

The weakly interacting trapped Bose gases have been customarily described using the mean-field approximation in the form of the Gross-Pitaevskii equation. The mean-field approximation, however, has certain limitations, in particular it can not describe correlations between particles. We introduce here an alternative variational approach, based on the correlated Gaussian method, which in its simplest form is as fast and simple as the mean-field approximation, but which allows successive improvements of the trial wave-function by including correlations between particles., Comment: 9 pages, Workshop on Nuclei and Mesoscopic Physics, NSCL MSU, 2004

Few-body correlations often express the distinguishing characteristic features of a many-body system. This thesis studies such correlations within dilute Bose-Einstein condensates in the case of arbitrary negative s-wave scattering length. The N-boson problem is solved by using an ab-initio approach based on correlated Gaussians that allows explicit inclusion of few-body correlations with a computational complexity that is independent of the number of particles. Calculations introducing all higher-order correlations are also done for small systems. In the weakly interacting regime, two-body correlations are not only the simplest but also the most important. By varying the scattering length and comparing the ground state energy for different explicitly correlated trial wave functions this assumption is investigated under both weakly and strongly interacting conditions., Comment: Master thesis, 91 pages