Interacting fermions in synthetic non-Abelian gauge fields

Generation and study of synthetic gauge fields has enhanced the possibility of using cold atom systems as quantum emulators of condensed matter Hamiltonians. In this article we describe the physics of interacting spin -1/2 fermions in synthetic non-Abelian gauge fields which induce a Rashba spin-orbit interaction on the motion of the fermions. We show that the fermion system can evolve to a Bose-Einstein condensate of a novel boson which we call rashbon. The rashbon-rashbon interaction is shown to be independent of the interaction between the constituent fermions. We also show that spin-orbit coupling can help enhancing superfluid transition temperature of weak superfluids to the order of Fermi temperature. A non-Abelian gauge field, when used in conjunction with another potential, can generate interesting Hamiltonians such as that of a magnetic monopole

Online Algorithms with Discrete Visibility - Exploring Unknown Polygonal Environments

The context of this work is the exploration of unknown polygonal environments with obstacles. Both the outer boundary and the boundaries of obstacles are piecewise linear. The boundaries can be nonconvex. The exploration problem can be motivated by the following application. Imagine that a robot has to explore the interior of a collapsed building, which has crumbled due to an earthquake, to search for human survivors. It is clearly impossible to have a knowledge of the building's interior geometry prior to the exploration. Thus, the robot must be able to see, with its onboard vision sensors, all points in the building's interior while following its exploration path. In this way, no potential survivors will be missed by the exploring robot. The exploratory path must clearly reflect the topology of the free space, and, therefore, such exploratory paths can be used to guide future robot excursions (such as would arise in our example from a rescue operation)

Zaciskające zapalenie osierdzia imitujące ciężką restenozę zastawki mitralnej u chorego po leczeniu chirurgicznym choroby reumatycznej serca

Pericardial constriction is a rare, but well documented complication following cardiac surgery. It has been reported following coronary artery bypass grafting (CABG), cardiac surgery for congenital heart diseases and very rarely following closed mitral commissurotomy. We hereby report a case of chronic constrictive pericarditis following closed mitral commissurotomy mimicking mitral restenosis with refractory heart failure

Online Algorithms with Discrete Visibility - Exploring Unknown Polygonal Environments

The context of this work is the exploration of unknown polygonal environments with obstacles. Both the outer boundary and the boundaries of obstacles are piecewise linear. The boundaries can be nonconvex. The exploration problem can be motivated by the following application. Imagine that a robot has to explore the interior of a collapsed building, which has crumbled due to an earthquake, to search for human survivors. It is clearly impossible to have a knowledge of the building's interior geometry prior to the exploration. Thus, the robot must be able to see, with its onboard vision sensors, all points in the building's interior while following its exploration path. In this way, no potential survivors will be missed by the exploring robot. The exploratory path must clearly reflect the topology of the free space, and, therefore, such exploratory paths can be used to guide future robot excursions (such as would arise in our example from a rescue operation)

Quantitative theory of triplet pairing in the unconventional superconductor LaNiGa2

The exceptionally low-symmetry crystal structures of the time-reversal symmetry-breaking superconductors LaNiC2 and LaNiGa2 lead to an internally antisymmetric nonunitary triplet state as the only possibility compatible with experiments. We argue that this state has a distinct signature: a double-peak structure in the density of states (DOS) which resolves in the spin channel in a particular way. We construct a detailed model of LaNiGa2 capturing its electronic band structure and magnetic properties ab initio. The pairing mechanism is described via a single adjustable parameter. The latter is fixed by the critical temperature Tc allowing parameter-free predictions. We compute the electronic specific heat and find excellent agreement with experiment. The size of the ordered moment in the superconducting state is compatible with zero-field muon spin relaxation experiments and the predicted spin-resolved DOS suggests the spin splitting is within the reach of present experimental technology

Recent progress on superconductors with time-reversal symmetry breaking

Superconductivity and magnetism are antagonistic states of matter. The presence of spontaneous magnetic fields inside the superconducting state is, therefore, an intriguing phenomenon prompting extensive experimental and theoretical research. In this review, we discuss recent experimental discoveries of unconventional superconductors which spontaneously break time-reversal symmetry and theoretical efforts in understanding their properties. We discuss the main experimental probes and give an extensive account of theoretical approaches to understand the order parameter symmetries and the corresponding pairing mechanisms including the importance of multiple bands

Baryon squishing in synthetic dimensions by effectiveSU(M)gauge fields

The “synthetic dimension” proposal [A. Celi et al., Phys. Rev. Lett. 112, 043001 (2014)] uses atoms with M internal states (“flavors”) in a one dimensional (1D) optical lattice, to realize a hopping Hamiltonian equivalent to the Hofstadter model (tight-binding model with a given magnetic flux per plaquette) on an M-sites-wide square lattice strip. We investigate the physics of SU (M) symmetric interactions in the synthetic dimension system. We show that this system is equivalent to particles [with SU (M) symmetric interactions] experiencing a SU (M) Zeeman field at each lattice site and a non-Abelian SU (M) gauge potential that affects their hopping. This equivalence brings out the possibility of generating nonlocal interactions between particles at different sites of the optical lattice. In addition, the gauge field induces a flavor-orbital coupling, which mitigates the “baryon breaking” effect of the Zeeman field. For M particles, concomitantly, the SU (M) singlet baryon which is site localized in the usual 1D optical lattice, is deformed to a nonlocal object (“squished baryon”). We conclusively demonstrate this effect by analytical arguments and exact (numerical) diagonalization studies. Our study promises a rich many-body phase diagram for this system. It also uncovers the possibility of using the synthetic dimension system to laboratory realize condensed-matter models such as the SU (M) random flux model, inconceivable in conventional experimental systems

Trapped fermions in a synthetic non-Abelian gauge field

On increasing the coupling strength ($\lambda$) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density \rho \sim \kf^3 undergoes a change at a critical value, \lambda_T \approx \kf [Phys. Rev. B {\bf 84}, 014512 (2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-\half fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulae for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a {\em characteristic fashion with increasing $\lambda$}. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud for all gauge field configurations, which are anisotropic in general. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling $\lambda$. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians (eg. quantum hall spherical geometry) by using a non-Abelian gauge field in conjunction with another potential.Comment: 10 Pages, 4 figure