Topological Superfluid in one-dimensional Ultracold Atomic System with Spin-Orbit Coupling

We propose a one-dimensional Hamiltonian $H_{1D}$ which supports Majorana fermions when $d_{x^{2}-y^{2}}$-wave superfluid appears in the ultracold atomic system and obtain the phase-separation diagrams both for the time-reversal-invariant case and time-reversal-symmetry-breaking case. From the phase-separation diagrams, we find that the single Majorana fermions exist in the topological superfluid region, and we can reach this region by tuning the chemical potential $\mu$ and spin-orbit coupling $\alpha_{R}$. Importantly, the spin-orbit coupling has realized in ultracold atoms by the recent experimental achievement of synthetic gauge field, therefore, our one-dimensional ultra-cold atomic system described by $H_{1D}$ is a promising platform to find the mysterious Majorana fermions.Comment: 5 papers, 2 figure

Recent developments in unconventional superconductivity theory

The review of recent developments in the unconventional superconductivity theory is given. In the fist part I consider the physical origin of the Kerr rotation polarization of light reflected from the surface of superconducting $Sr_2RuO_4$. Then the comparison of magneto-optical responses in superconductors with orbital and spin spontaneous magnetization is presented. The latter result is applied to the estimation of the magneto-optical properties of neutral superfluids with spontaneous magnetization. The second part is devoted to the natural optical activity or gyrotropy properties of noncentrosymmetric metals in their normal and superconducting states. The temperature behavior of the gyrotropy coefficient is compared with the temperature behavior of paramagnetic susceptibility determining the noticeable increase of the paramagnetic limiting field in noncentrosymmetric superconductors. In the last chapter I describe the order parameter and the symmetry of superconducting state in the itinerant ferromagnet with orthorhombic symmetry. Finally the Josephson coupling between two adjacent ferromagnet superconducting domains is discussed.Comment: 15 page

Life after charge noise: recent results with transmon qubits

We review the main theoretical and experimental results for the transmon, a superconducting charge qubit derived from the Cooper pair box. The increased ratio of the Josephson to charging energy results in an exponential suppression of the transmon's sensitivity to 1/f charge noise. This has been observed experimentally and yields homogeneous broadening, negligible pure dephasing, and long coherence times of up to 3 microseconds. Anharmonicity of the energy spectrum is required for qubit operation, and has been proven to be sufficient in transmon devices. Transmons have been implemented in a wide array of experiments, demonstrating consistent and reproducible results in very good agreement with theory.Comment: 6 pages, 4 figures. Review article, accepted for publication in Quantum Inf. Pro

Topological superfluid 3^3He-B: fermion zero modes on interfaces and in the vortex core

Many quantum condensed matter systems are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, topology allows us to determine generic features of their fermionic spectrum, which are robust to perturbation and interaction. We discuss the nodeless 3D system, such as superfluid $^3$He-B, vacuum of Dirac fermions, and relativistic singlet and triplet supercondutors which may arise in quark matter. The systems, which have nonzero value of topological invariant, have gapless fermions on the boundary and in the core of quantized vortices. We discuss the index theorem which relates fermion zero modes on vortices with the topological invariants in combined momentum and coordinate space.Comment: paper is prepared for Proceedings of the Workshop on Vortices, Superfluid Dynamics, and Quantum Turbulence held on 11-16 April 2010, Lammi, Finlan

Density Waves in Layered Systems with Fermionic Polar Molecules

A layered system of two-dimensional planes containing fermionic polar molecules can potentially realize a number of exotic quantum many-body states. Among the predictions, are density-wave instabilities driven by the anisotropic part of the dipole-dipole interaction in a single layer. However, in typical multilayer setups it is reasonable to expect that the onset and properties of a density-wave are modified by adjacent layers. Here we show that this is indeed the case. For multiple layers the critical strength for the density-wave instability decreases with the number of layers. The effect depends on density and is more pronounced in the low density regime. The lowest solution of the instability corresponds to the density waves in the different layers being in-phase, whereas higher solutions have one or several adjancet layers that are out of phase. The parameter regime needed to explore this instability is within reach of current experiments.Comment: 7 pages, 4 figures. Final version in EPJD, EuroQUAM special issue "Cold Quantum Matter - Achievements and Prospects

Bound Chains of Tilted Dipoles in Layered Systems

Ultracold polar molecules in multilayered systems have been experimentally realized very recently. While experiments study these systems almost exclusively through their chemical reactivity, the outlook for creating and manipulating exotic few- and many-body physics in dipolar systems is fascinating. Here we concentrate on few-body states in a multilayered setup. We exploit the geometry of the interlayer potential to calculate the two- and three-body chains with one molecule in each layer. The focus is on dipoles that are aligned at some angle with respect to the layer planes by means of an external eletric field. The binding energy and the spatial structure of the bound states are studied in several different ways using analytical approaches. The results are compared to stochastic variational calculations and very good agreement is found. We conclude that approximations based on harmonic oscillator potentials are accurate even for tilted dipoles when the geometry of the potential landscape is taken into account.Comment: 10 pages, 6 figures. Submitted to Few-body Systems special issue on Critical Stability, revised versio

Self-consistent field theory of polarized BEC: dispersion of collective excitation

We suggest the construction of a set of the quantum hydrodynamics equations for the Bose-Einstein condensate (BEC), where atoms have the electric dipole moment. The contribution of the dipole-dipole interactions (DDI) to the Euler equation is obtained. Quantum equations for the evolution of medium polarization are derived. Developing mathematical method allows to study effect of interactions on the evolution of polarization. The developing method can be applied to various physical systems in which dynamics is affected by the DDI. Derivation of Gross-Pitaevskii equation for polarized particles from the quantum hydrodynamics is described. We showed that the Gross-Pitaevskii equation appears at condition when all dipoles have the same direction which does not change in time. Comparison of the equation of the electric dipole evolution with the equation of the magnetization evolution is described. Dispersion of the collective excitations in the dipolar BEC, either affected or not affected by the uniform external electric field, is considered using our method. We show that the evolution of polarization in the BEC leads to the formation of a novel type of the collective excitations. Detailed description of the dispersion of collective excitations is presented. We also consider the process of wave generation in the polarized BEC by means of a monoenergetic beam of neutral polarized particles. We compute the possibilities of the generation of Bogoliubov and polarization modes by the dipole beam.Comment: 16 pages, 15 figures. arXiv admin note: substantial text overlap with arXiv:1106.082

Layers of Cold Dipolar Molecules in the Harmonic Approximation

We consider the N-body problem in a layered geometry containing cold polar molecules with dipole moments that are polarized perpendicular to the layers. A harmonic approximation is used to simplify the hamiltonian and bound state properties of the two-body inter-layer dipolar potential are used to adjust this effective interaction. To model the intra-layer repulsion of the polar molecules, we introduce a repulsive inter-molecule potential that can be parametrically varied. Single chains containing one molecule in each layer, as well as multi-chain structures in many layers are discussed and their energies and radii determined. We extract the normal modes of the various systems as measures of their volatility and eventually of instability, and compare our findings to the excitations in crystals. We find modes that can be classified as either chains vibrating in phase or as layers vibrating against each other. The former correspond to acoustic and the latter to optical phonons. Instabilities can occur for large intra-layer repulsion and produce diverging amplitudes of molecules in the outer layers. Lastly, we consider experimentally relevant regimes to observe the structures.Comment: 17 pages, 20 figures, accepted versio