Magnus Ögren

Zeno effect and switching of solitons in nonlinear couplers

The Zeno effect is investigated for soliton type pulses in a nonlinear directional coupler with dissipation. The effect consists in increase of the coupler transparency with increase of the dissipative losses in one of the arms. It is shown that localized dissipation can lead to switching of solitons between the arms. Power losses accompanying the switching can be fully compensated by using a combination of dissipative and active (in particular, parity-time-symmetric) segments.

Atom-atom correlations in colliding Bose-Einstein condensates

We analyze atom-atom correlations in the s-wave scattering halo of two colliding condensates. By developing a simple perturbative approach, we obtain explicit analytic results for the collinear (CL) and back-to-back (BB) correlations corresponding to realistic density profiles of the colliding condensates with interactions. The results in the short-time limit are in agreement with the first-principles simulations using the positive-P representation and provide analytic insights into the experimental observations of Perrin et al. [Phys. Rev. Lett. 99, 150405 (2007)]. For long collision durations, we predict that the BB correlation becomes broader than the CL correlation.

First-principles quantum dynamics for fermions: Application to molecular dissociation

We demonstrate that the quantum dynamics of a many-body Fermi-Bose system can be simulated using a Gaussian phase-space representation method. In particular, we consider the application of the mixed fermion-boson model to ultracold quantum gases and simulate the dynamics of dissociation of a Bose-Einstein condensate of bosonic dimers into pairs of fermionic atoms. We quantify deviations of atom-atom pair correlations from Wicks factorization scheme, and show that atom-molecule and molecule-molecule correlations grow with time, in clear departures from pairing mean-field theories. As a first-principles approach, the method provides benchmarking of approximate approaches and can be used to validate dynamical probes for characterizing strongly correlated phases of fermionic systems.

Stochastic simulations of fermionic dynamics with phase-space representations

A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains well-bounded, which defines a useful simulation time. We analyse the application of the Gaussian phase-space representation to the dynamics of the dissociation of an ultra-cold molecular gas. We show how the choice of mapping to stochastic differential equations can be used to tailor the stochastic behaviour, and thus the useful simulation time. In the phase-space approach, it is only averages of stochastic trajectories that have a direct physical meaning. Whether particular constants of the motion are satisfied by individual trajectories depends on the choice of mapping, as we show in examples

Uniform semiclassical trace formula for U(3) → SO(3) symmetry breaking

We develop a uniform semiclassical trace formula for the density of states of a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term . This term breaks the U(3) symmetry of the ...

There's more to the multimedia effect than meets the eye : is seeing pictures believing?

Textbooks in applied mathematics often use graphs to explain the meaning of formulae, even though their benefit is still not fully explored. To test processes underlying this assumed multimedia effect we collected performance scores, eye movements, and think-aloud protocols from students solving problems in vector calculus with and without graphs. Results showed no overall multimedia effect, but instead an effect to confirm statements that were accompanied by graphs, irrespective of whether these statements were true or false. Eye movement and verbal data shed light on this surprising finding. Students looked proportionally less at the text and the problem statement when a graph was present. Moreover, they experienced more mental effort with the graph, as indicated by more silent pauses in thinking aloud. Hence, students actively processed the graphs. This, however, was not sufficient. Further analysis revealed that the more students looked at the statement, the better they performed. Thus, in the multimedia condition the graph drew students’ attention and cognitive capacities away from focusing on the statement. A good alternative strategy in the multimedia condition was to frequently look between graph and problem statement, and thus to integrate their information. In conclusion, graphs influence where students look and what they process, and may even mislead them into believing accompanying information. Thus, teachers and textbook designers should be very critical on when to use graphs and carefully consider how the graphs are integrated with other parts of the problem.

Numerical solution of the stationary multicomponent nonlinear Schrödinger equation with a constraint on the angular momentum.

We formulate a damped oscillating particle method to solve the stationary nonlinear Schrödinger equation (NLSE). The ground-state solutions are found by a converging damped oscillating evolution equation that can be discretized with symplectic numerical techniques. The method is demonstrated for three different cases: for the single-component NLSE with an attractive self-interaction, for the single-component NLSE with a repulsive self-interaction and a constraint on the angular momentum, and for the two-component NLSE with a constraint on the total angular momentum. We reproduce the so-called yrast curve for the single-component case, described in [A. D. Jackson et al., Europhys. Lett. 95, 30002 (2011)], and produce for the first time an analogous curve for the two-component NLSE. The numerical results are compared with analytic solutions and competing numerical methods. Our method is well suited to handle a large class of equations and can easily be adapted to further constraints and components.

Faraday waves in quasi-one-dimensional superfluid Fermi-Bose mixtures

The generation of Faraday waves in superfluid Fermi-Bose mixtures in elongated traps is investigated. The generation of waves is achieved by periodically changing a parameter of the system in time. ...

Self-consistent Ginzburg–Landau theory for transport currents in superconductors

Abstract We elaborate on boundary conditions for Ginzburg–Landau (GL) theory in the case of external currents. We implement a self-consistent theory within the finite element method (FEM) and present numerical results for a two-dimensional rectangular geometry. We emphasize that our approach can in principle also be used for general geometries in three-dimensional superconductors.

Role of spatial inhomogeneity in dissociation of trapped molecular condensates

We theoretically analyze dissociation of a harmonically trapped Bose-Einstein condensate of molecular dimers and examine how the spatial inhomogeneity of the molecular condensate affects the conversion dynamics and the atom-atom pair correlations in the short-time limit. Both fermionic and bosonic statistics of the constituent atoms are considered. Using the undepleted molecular-field approximation, we obtain explicit analytic results for the asymptotic behavior of the second-order correlation functions and for the relative number squeezing between the dissociated atoms in one, two, and three spatial dimensions. Comparison with the numerical results shows that the analytic approach employed here captures the main underlying physics and provides useful insights into the dynamics of dissociation for conversion efficiencies up to 10%. The results show explicitly how the strength of atom-atom correlations and relative number squeezing degrade with the reduction of the size of the molecular condensate.