We report a study of three-dimensional (3D) localization of ultracold atoms suspended against gravity, and released in a 3D optical disordered potential with short correlation lengths in all directions. We observe density profiles composed of a steady localized part and a diffusive part.Our observations are compatible with the self-consistent theory of Anderson localization, taking into account the specific features of the experiment, and in particular the broad energy distribution of the atoms placed in the disordered potential. The localization we observe cannot be interpreted as trapping of particles with energy below the classical percolation threshold. 1Anderson localization (AL) was proposed more than 50 years ago [1] to understand how disorder can lead to the total cancellation of conduction in certain materials. It is a purely quantum, one-particle effect, which can be interpreted as due to interference between the various amplitudes associated with the scattering paths of a matter wave propagating among impurities [2]. Anderson localization is predicted to strongly depend on the dimension [3]. In the three-dimensional (3D) case, a mobility edge is predicted, which corresponds to an energy threshold separating localized from extended states. Determining the precise behavior of the mobility edge remains a challenge for numerical simulations, microscopic theory and experiments [2]. The quest for AL has been pursued not only in condensed matter physics [4], but also in wave physics [5]: for instance with light waves [6][7][8][9], microwaves [10,11] and acoustic waves [12]. Following theoretical proposals [13][14][15][16][17][18], recent experiments [19,20] have shown that ultracold atoms in optical disorder constitute a remarkable system to study 1D localization [21][22][23]. Here, we report a study of 3D localization of ultracold atoms suspended against gravity, and released in a 3D optical disordered potential with short correlation lengths in all directions. We observe density profiles composed of a steady localized part and a diffusive part. Our observations are compatible with the self-consistent theory of AL [24], taking into account the specific features of the experiment, and in particular the broad energy distribution of the atoms placed in the disordered potential. The localization we observe cannot be interpreted as trapping of particles with energy below the classical percolation threshold.Our scheme (Fig. 1a) is a generalization of the one that allowed us to demonstrate AL in 1D [15,19]. It involves a dilute Bose-Einstein condensate (BEC) with several 10 4 atoms of 87 Rb, initially in a shallow quasi-isotropic Gaussian optical trap, released and suddenly submitted to an optical disordered potential generated by a laser speckle [25]. The atoms, in the |F = 2, m F = −2 hyperfine state of the ground electronic state, are suspended by a magnetic gradient that compensates gravity (the residual component of the magnetic potential is isotropic and repulsive, of the form −mω 2 r 2 /2, with ω = ...

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We establish the phase diagram of the strongly-interacting Bose-Hubbard model defined on a two-leg ladder geometry in the presence of a homogeneous flux. Our work is motivated by a recent experiment [Atala et al., Nature Phys. 10, 588 (2014)], which studied the same system, in the complementary regime of weak interactions. Based on extensive density matrix renormalization group simulations and a bosonization analysis, we fully explore the parameter space spanned by filling, inter-leg tunneling, and flux. As a main result, we demonstrate the existence of gapless and gapped Meissner and vortex phases, with the gapped states emerging in Mott-insulating regimes. We calculate experimentally accessible observables such as chiral currents and vortex patterns.Introduction. The quantum states of interacting electrons in the presence of spin-orbit coupling and magnetic fields are attracting significant attention in condensed matter physics because of their connection to Quantum Hall physics [1], topological insulators [2-4] and the emergence of unusual excitations in low dimensions [5,6]. Recent progress with quantum gas experiments has led to the realization of artificial gauge fields [7], both in the continuum [8][9][10] and for bosons in optical lattices [11][12][13][14], paving the way for future experiments on the interplay of interactions, dimensionality, and gauge fields in a systematic manner. This has motivated theoretical research into the physics of strongly interacting particles in the presence of abelian and non-abelian gauge fields and various questions such as the Quantum Hall effect with bosons [15][16][17][18][19][20][21][22], unusual quantum magnetism [23][24][25][26], and the emergence of topologically protected phases [27][28][29] have been addressed.

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The interplay between spontaneous symmetry breaking in many-body systems, the wavelike nature of quantum particles and lattice effects produces an extraordinary behavior of the chiral current of bosonic particles in the presence of a uniform magnetic flux defined on a two-leg ladder. While noninteracting as well as strongly interacting particles, stirred by the magnetic field, circulate along the system's boundary in the counterclockwise direction in the ground state, interactions stabilize vortex lattices. These states break translational symmetry, which can lead to a reversal of the circulation direction. Our predictions could readily be accessed in quantum gas experiments with existing setups or in arrays of Josephson junctions.

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We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex fluids, vortex lattices, charge density waves, and the biased-ladder phase. Our work focuses on the subset of these states that breaks a discrete symmetry. We use density matrix renormalization group simulations to demonstrate the existence of three vortex-lattice states at different vortex densities and we characterize the phase transitions from these phases into neighboring states. Furthermore, we provide an intuitive explanation of the chiral-current reversal effect that is tied to some of these vortex lattices. We also study a charge-density-wave state that exists at 1/4 particle filling at large interaction strengths and flux values close to half a flux quantum. By changing the system parameters, this state can transition into a completely gapped vortex-lattice Mott-insulating state. We elucidate the stability of these phases against nearest-neighbor interactions on the rungs of the ladder relevant for experimental realizations with a synthetic lattice dimension. A charge-density-wave state at 1/3 particle filling can be stabilized for flux values close to half a flux quantum and for very strong on-site interactions in the presence of strong repulsion on the rungs. Finally, we analytically describe the emergence of these phases in the low-density regime, and, in particular, we obtain the boundaries of the biased-ladder phase, i.e., the phase that features a density imbalance between the legs. We make contact with recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.

We present DeepVesselNet, an architecture tailored to the challenges faced when extracting vessel trees and networks and corresponding features in 3-D angiographic volumes using deep learning. We discuss the problems of low execution speed and high memory requirements associated with full 3-D networks, high-class imbalance arising from the low percentage (<3%) of vessel voxels, and unavailability of accurately annotated 3-D training data—and offer solutions as the building blocks of DeepVesselNet. First, we formulate 2-D orthogonal cross-hair filters which make use of 3-D context information at a reduced computational burden. Second, we introduce a class balancing cross-entropy loss function with false-positive rate correction to handle the high-class imbalance and high false positive rate problems associated with existing loss functions. Finally, we generate a synthetic dataset using a computational angiogenesis model capable of simulating vascular tree growth under physiological constraints on local network structure and topology and use these data for transfer learning. We demonstrate the performance on a range of angiographic volumes at different spatial scales including clinical MRA data of the human brain, as well as CTA microscopy scans of the rat brain. Our results show that cross-hair filters achieve over 23% improvement in speed, lower memory footprint, lower network complexity which prevents overfitting and comparable accuracy that does not differ from full 3-D filters. Our class balancing metric is crucial for training the network, and transfer learning with synthetic data is an efficient, robust, and very generalizable approach leading to a network that excels in a variety of angiography segmentation tasks. We observe that sub-sampling and max pooling layers may lead to a drop in performance in tasks that involve voxel-sized structures. To this end, the DeepVesselNet architecture does not use any form of sub-sampling layer and works well for vessel segmentation, centerline prediction, and bifurcation detection. We make our synthetic training data publicly available, fostering future research, and serving as one of the first public datasets for brain vessel tree segmentation and analysis.