Dynamics of the Mott Insulator to Superfluid quantum phase transition in the truncated Wigner approximation

The quantum phase transition from the Mott insulator state to the superfluid in the Bose-Hubbard model is investigated. We research one, two and three dimensional lattices in the truncated Wigner approximation. We compute both kinetic and potential energy and they turn out to have a power law behaviour as a function of the transition rate, with the power equal to 1/3. The same applies to the total energy in a system with a harmonic trap, which is usually present in the experimental set-up. These observations are in agreement with the experiment of [8], where such scalings were also observed and the power of the decay was numerically close to 1/3. The results confirm the Kibble-Zurek (adiabatic-impulse-adiabatic approximation) scenario for this transition.Comment: 14 pages, 11 figures; Laser Physics Workshop (LPHYS'12) Proceedings, Calgary 201

Spin-Imbalanced Fermi Superfluidity in a Lieb Lattice Hubbard Model

We obtain a phase diagram of the spin imbalanced Hubbard model on the Lieb lattice, which is known to feature a flat band in its single-particle spectrum. Using the BCS mean-field theory for multiband systems, we find a variety of superfluid phases with imbalance. In particular, we find four different types FFLO phases, i.e. superfluid phases with periodic spatial modulation. They differ by the magnitude and direction of the centre-of-mass momentum of Cooper pairs. We also see a large region of stable Sarma phase, where the density imbalance is associated with zero Cooper pair momentum. In the mechanism responsible for the formation of those phases, the crucial role is played by the flat band, wherein particles can readjust their density at zero energy cost. The multiorbital structure of the unit cell is found to stabilize the Sarma phase by allowing for a modulation of the order parameter within a unit cell. We also study the effect of finite temperature and a lattice with staggered hopping parameters on the behaviour of these phases.Comment: 10 pages, 10 figure

A ring of BEC pools as a trap for persistent flow

Mott insulator - superfluid transition in a periodic lattice of Josephson junctions can be driven by tunneling rate increase. Resulting winding numbers $W$ of the condensate wavefunction decrease with increasing quench time in accord with the Kibble-Zurek mechanism (KZM). However, in very slow quenches Bose-Hubbard dynamics rearranges wavefunction phase so that its random walk cools, $\bar{W^2}$ decreases and eventually the wavefunction becomes too cold to overcome potential barriers separating different $W$. Thus, in contrast with KZM, in very slow quenches $\bar{W^2}$ is set by random walk with "critical" step size, independently of $\tau_Q$.Comment: Decompressed version to appear in Phys. Rev.

Quench from Mott Insulator to Superfluid

We study a linear ramp of the nearest-neighbor tunneling rate in the Bose-Hubbard model driving the system from the Mott insulator state into the superfluid phase. We employ the truncated Wigner approximation to simulate linear quenches of a uniform system in 1,2, and 3 dimensions, and in a harmonic trap in 3 dimensions. In all these setups the excitation energy decays like one over third root of the quench time. The -1/3 scaling arises from an impulse-adiabatic approximation - a variant of the Kibble-Zurek mechanism - describing a crossover from non-adiabatic to adiabatic evolution when the system begins to keep pace with the increasing tunneling rate.Comment: 10 pages, 13 figures; version published in Phys. Rev.

Excitation energy after a smooth quench in a Luttinger liquid

Low energy physics of quasi-one-dimensional ultracold atomic gases is often described by a gapless Luttinger liquid (LL). It is nowadays routine to manipulate these systems by changing their parameters in time but, no matter how slow the manipulation is, it must excite a gapless system. We study a smooth change of parameters of the LL (a smooth "quench") with a variable quench time and find that the excitation energy decays with an inverse power of the quench time. This universal exponent is -2 at zero temperature, and -1 for slow enough quenches at finite temperature. The smooth quench does not excite beyond the range of validity of the low energy LL description.Comment: 5 pages, 2 figures; minor changes, version published in Phys. Rev.

Observation of Solitonic Vortices in Bose-Einstein Condensates

We observe solitonic vortices in an atomic Bose-Einstein condensate after free expansion. Clear signatures of the nature of such defects are the twisted planar density depletion around the vortex line, observed in absorption images, and the double dislocation in the interference pattern obtained through homodyne techniques. Both methods allow us to determine the sign of the quantized circulation. Experimental observations agree with numerical simulations. These solitonic vortices are the decay product of phase defects of the BEC order parameter spontaneously created after a rapid quench across the BEC transition in a cigar-shaped harmonic trap and are shown to have a very long lifetime.Comment: 7 pages, 7 figure

Solitonic Vortices in Bose-Einstein Condensates

We analyse, theoretically and experimentally, the nature of solitonic vortices (SV) in an elongated Bose-Einstein condensate. In the experiment, such defects are created via the Kibble-Zurek mechanism, when the temperature of a gas of sodium atoms is quenched across the BEC transition, and are imaged after a free expansion of the condensate. By using the Gross-Pitaevskii equation, we calculate the in-trap density and phase distributions characterizing a SV in the crossover from an elongate quasi-1D to a bulk 3D regime. The simulations show that the free expansion strongly amplifies the key features of a SV and produces a remarkable twist of the solitonic plane due to the quantized vorticity associated with the defect. Good agreement is found between simulations and experiments.Comment: 6 pages, 4 figure

Model of the distribution of diastolic left ventricular posterior wall thickness in healthy adults and its impact on the behavior of a string of virtual cardiomyocytes

Correlation of the thickness of the left ventricular posterior wall (LVPWd) with various parameters, including age, gender, weight and height, was investigated in this study using regression models. Multicenter derived database comprised over 4,000 healthy individuals. The developed models were further utilized in the in vitro-in vivo (IVIV) translation of the drug cardiac safety data with use of the mathematical model of human cardiomyocytes operating at the virtual healthy population level. LVPWd was assumed to be equivalent to the length of one-dimensional string of virtual cardiomyocyte cells which was presented, as other physiological factors, to be a parameter influencing the simulated pseudo-ECG (pseudoelectrocardiogram), QTcF and $\Delta$QTcF, both native and modified by exemplar drug (disopyramide) after $I_{Kr}$ current disruption. Simulation results support positive correlation between the LVPWd and QTcF/$\Delta$QTc. Developed models allow more detailed description of the virtual population and thus inter-individual variability influence on the drug cardiac safet