Phase diagram of the bose Hubbard model

The first reliable analytic calculation of the phase diagram of the bose gas on a $d$-dimensional lattice with on-site repulsion is presented. In one dimension, the analytic calculation is in excellent agreement with the numerical Monte Carlo results. In higher dimensions, the deviations from the Monte Carlo calculations are larger, but the correct shape of the Mott insulator lobes is still obtained. Explicit expressions for the energy of the Mott and the ``defect'' phase are given in a strong-coupling expansion.Comment: RevTeX 3.

Deep Learning Technique for Detecting and Analysing Ischemic Stroke Using MRI Images

The quantitative analysis of cerebral MRI images plays a pivotal role in stroke diagnosis and treatment. Deep learning, particularly CNNs, with their robust learning capabilities, offer an effective tool for lesion detection. To address the unique properties of stroke injuries and automate detection processes, we compiled a dataset of brain MRI images from various medical sources, representing patients affected by ischemic strokes. Different deep learning-based networks, including “Single Shot Multibox Detector (SSD)”, “Region-based CNN with ResNet101 (RCNN-ResNet101)”, “RCNN with VGG16 (RCNN- VGG16)”, and “YOLOV3”, were employed for automated lesion detection. The evaluation focused on achieving optimal precision in comparison to existing methods across Diffused Weight, Flair, and T1 modalities of MRI datasets. The developed technique involves extracting deep features during the encoding stage, followed by the minimization of features using fully connected layers. Significant handcrafted features, such as Local Binary Pattern (LBP) and Gray Level Co-occurrence Matrix (GLCM), were incorporated alongside deep features. The concatenation of these features was implemented to maximize the dimension of the feature vector. This concatenated vector was then used to train and test the performance of various classifiers. Binary classification was employed to categorize brain images into normal or stroke affected. Initially, SoftMax was used as the default classifier. The performance of each classifier was individually evaluated, and the best-performing classifier was selected to confirm the overall effectiveness of the proposed technique. This all-encompassing strategy not only leverages deep learning for automatic lesion detection but also integrates handcrafted features and diverse classifiers to improve the precision and dependability of stroke detection across various brain MRI image modalities

Oscillating Superfluidity of Bosons in Optical Lattices

We follow up on a recent suggestion by C. Orzel et. al., Science, 291, 2386 (2001), whereby bosons in an optical lattice would be subjected to a sudden parameter change from the Mott to the superfluid phase. We analyze the Bose Hubbard model with a modified coherent states path integral which can escribe - both - phases. The saddle point theory yields collective oscillations of the uniform superfluid order parameter. These would be seen in time resolved interference patterns made by the released gas. We calculate the collective oscillation's damping rate by phason pair emission. In two dimensions the overdamped region largely overlaps with the quantum critical region. Measurements of critical dynamics on the Mott side are proposed.Comment: 4 pages 1 eps figures; Final version as appears in PRL. Added discussion on spontaneous generation of vortice

Vortex configurations of bosons in an optical lattice

The single vortex problem in a strongly correlated bosonic system is investigated self-consistently within the mean-field theory of the Bose-Hubbard model. Near the superfluid-Mott transition, the vortex core has a tendency toward the Mott-insulating phase, with the core particle density approaching the nearest commensurate value. If the nearest neighbor repulsion exists, the charge density wave order may develop locally in the core. The evolution of the vortex configuration from the strong to weak coupling regions is studied. This phenomenon can be observed in systems of rotating ultra-cold atoms in optical lattices and Josephson junction arraysComment: 4 pages, 4 figs, Accepted by Physics Review

Mott-Hubbard Transition of Bosons in Optical Lattices with Three-body Interactions

In this paper, the quantum phase transition between superfluid state and Mott-insulator state is studied based on an extended Bose-Hubbard model with two- and three-body on-site interactions. By employing the mean-field approximation we find the extension of the insulating 'lobes' and the existence of a fixed point in three dimensional phase space. We investigate the link between experimental parameters and theoretical variables. The possibility to obverse our results through some experimental effects in optically trapped Bose-Einstein Condensates(BEC) is also discussed.Comment: 7 pages, 4 figures; to be appear in Phys. Rev.

Atomic Bose-Fermi mixtures in an optical lattice

A mixture of ultracold bosons and fermions placed in an optical lattice constitutes a novel kind of quantum gas, and leads to phenomena, which so far have been discussed neither in atomic physics, nor in condensed matter physics. We discuss the phase diagram at low temperatures, and in the limit of strong atom-atom interactions, and predict the existence of quantum phases that involve pairing of fermions with one or more bosons, or, respectively, bosonic holes. The resulting composite fermions may form, depending on the system parameters, a normal Fermi liquid, a density wave, a superfluid liquid, or an insulator with fermionic domains. We discuss the feasibility for observing such phases in current experiments.Comment: 4 pages, 1 eps figure, misprints correcte

Reentrant Phenomenon in Quantum Phase Diagram of Optical Boson Lattice

We calculate the location of the quantum phase transitions of a bose gas trapped in an optical lattice as a function of effective scattering length a_{\eff} and temperature $T$. Knowledge of recent high-loop results on the shift of the critical temperature at weak couplings is used to locate a {\em nose} in the phase diagram above the free Bose-Einstein critical temperature $T_c^{(0)}$, thus predicting the existence of a reentrant transition {\em above} $T_c^{(0)}$, where a condensate should form when {\em increasing} a_{\eff}. At zero temperature, the transition to the normal phase produces the experimentally observed Mott insulator.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.htm

Ultracold atoms in optical lattices

Bosonic atoms trapped in an optical lattice at very low temperatures, can be modeled by the Bose-Hubbard model. In this paper, we propose a slave-boson approach for dealing with the Bose-Hubbard model, which enables us to analytically describe the physics of this model at nonzero temperatures. With our approach the phase diagram for this model at nonzero temperatures can be quantified.Comment: 29 pages, 10 figure

Quantum phase transitions of light

Recently, condensed matter and atomic experiments have reached a length-scale and temperature regime where new quantum collective phenomena emerge. Finding such physics in systems of photons, however, is problematic, as photons typically do not interact with each other and can be created or destroyed at will. Here, we introduce a physical system of photons that exhibits strongly correlated dynamics on a meso-scale. By adding photons to a two-dimensional array of coupled optical cavities each containing a single two-level atom in the photon-blockade regime, we form dressed states, or polaritons, that are both long-lived and strongly interacting. Our zero temperature results predict that this photonic system will undergo a characteristic Mott insulator (excitations localised on each site) to superfluid (excitations delocalised across the lattice) quantum phase transition. Each cavity's impressive photon out-coupling potential may lead to actual devices based on these quantum many-body effects, as well as observable, tunable quantum simulators. We explicitly show that such phenomena may be observable in micro-machined diamond containing nitrogen-vacancy colour centres and superconducting microwave strip-line resonators.Comment: 11 pages, 5 figures (2 in colour