There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

/pdf/many-body-physics-with-ultracold-gases-552s10zfdn.pdf

Many-Body Physics with Ultracold Gases

Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

Super-resolution microscopy has revolutionized the fields of chemistry and biology by resolving features at the molecular level. Such techniques can be either "stochastic," gaining resolution through precise localization of point source emitters, or "deterministic," leveraging the nonlinear optical response of a sample to improve resolution. In atomic physics, deterministic methods can be applied to reveal the atomic wavefunction and to perform quantum control. Here we demonstrate super-resolution imaging based on nonlinear response of atoms to an optical pumping pulse. With this technique the atomic density distribution can be resolved with a point spread function FWHM of 32(4) nm and a localization precision below 1 nm. The short optical pumping pulse of 1.4 $\mu$s enables us to resolve fast atomic dynamics within a single lattice site. A byproduct of our scheme is the emergence of moire patterns on the atomic cloud, which we show to be immensely magnified images of the atomic density in the lattice. Our work represents a general approach to accessing the physics of cold atoms at the nanometer scale, and can be extended to higher dimensional lattices and bulk systems for a variety of atomic and molecular species.

Super-resolution microscopy of cold atoms in an optical lattice

Quantum phase transitions, transitions between many-body ground states, are of extensive interest in research ranging from condensed-matter physics to cosmology
 1–4
 . Key features of the phase transitions include a stage with rapidly growing new order, called inflation in cosmology
 5
 , followed by the formation of topological defects
 6–8
 . How inflation is initiated and evolves into topological defects remains a hot topic of debate. Ultracold atomic gas offers a pristine and tunable platform to investigate quantum critical dynamics
 9–21
 . We report the observation of coherent inflationary dynamics across a quantum critical point in driven Bose–Einstein condensates. The inflation manifests in the exponential growth of density waves and populations in well-resolved momentum states. After the inflation stage, extended coherent dynamics is evident in both real and momentum space. We present an intuitive description of the quantum critical dynamics in our system and demonstrate the essential role of phase fluctuations in the formation of topological defects. An ultracold quantum gas experiment shows that, when it crosses the many-body phase transition, the original ground state can evolve coherently into the new emergent phase, reflecting the initial global coherence presented in the system.

Coherent inflationary dynamics for Bose–Einstein condensates crossing a quantum critical point

We report a new scheme to create weakly bound Cs$_2$ molecules from an atomic Bose-Einstein condensate. The method is based on switching the magnetic field to a narrow Feshbach resonance and yields a high atom-molecule conversion efficiency of more than 30%, a factor of three higher than obtained with conventional magnetic-field ramps. The Cs$_2$ molecules are created in a single $g$-wave rotational quantum state. The observed dependence of the conversion efficiency on the magnetic field and atom density shows scattering processes beyond two-body coupling to occur in the vicinity of the Feshbach resonance.

Efficient creation of molecules from a cesium Bose-Einstein condensate

Correlations in interacting many-body systems are key to the study of quantum matter. The complexity of the correlations typically grows quickly as the system evolves and thus presents a challenge for experimental characterization and intuitive understanding. In a strongly driven Bose-Einstein condensate, we observe the high-harmonic generation of matter-wave jets with complex correlations as a result of bosonic stimulation. Based on a pattern recognition scheme, we identify a pattern of correlations that reveals the underlying secondary scattering processes and higher-order correlations. We show that pattern recognition offers a versatile strategy to visualize and analyze the quantum dynamics of a many-body system.

https://science.sciencemag.org/content/sci/363/6426/521.full.pdf

Correlations in high-harmonic generation of matter-wave jets revealed by pattern recognition

A new superresolution imaging technique reveals the behavior of cold atoms in an optical lattice with a spatial resolution of 32 nm and moir\'e patterns that are hugely magnified images of the microscopic atomic density distribution itself.

Cheng Chin

Papers

Super-resolution microscopy of cold atoms in an optical lattice

Coherent inflationary dynamics for Bose–Einstein condensates crossing a quantum critical point

Efficient creation of molecules from a cesium Bose-Einstein condensate

Correlations in high-harmonic generation of matter-wave jets revealed by pattern recognition

Superresolution Microscopy of Cold Atoms in an Optical Lattice