Two-component superfluid hydrodynamics of neutron star cores

We consider the hydrodynamics of the outer core of a neutron star under conditions when both neutrons and protons are superfluid. Starting from the equation of motion for the phases of the wave functions of the condensates of neutron pairs and proton pairs we derive the generalization of the Euler equation for a onecomponent fluid. These equations are supplemented by the conditions for conservation of neutron number and proton number. Of particular interest is the effect of entrainment, the fact that the current of one nucleon species depends on the momenta per nucleon of both condensates. We find that the nonlinear terms in the Euler-like equation contain contributions that have not always been taken into account in previous applications of superfluid hydrodynamics. We apply the formalism to determine the frequency of oscillations about a state with stationary condensates and states with a spatially uniform counterflow of neutrons and protons. The velocities of the coupled sound-like modes of neutrons and protons are calculated from properties of uniform neutron star matter evaluated on the basis of chiral effective field theory. We also derive the condition for the two-stream instability to occur.Comment: Final version. 9 pages, 5 figure

Dipole and monopole modes in the Bose-Hubbard model in a trap

The lowest-lying collective modes of a trapped Bose gas in an optical lattice are studied in the Bose-Hubbard model. An exact diagonalization of the Hamiltonian is performed in a one-dimensional five-particle system in order to find the lowest few eigenstates. Dipole and breathing character of the eigenstates is confirmed in the limit where the tunneling dominates the dynamics, but under Mott-like conditions the excitations do not correspond to oscillatory modes.Comment: 19 pages, 11 figures; submitted to Phys. Rev.

Bogoliubov Theory and Lee-Huang-Yang Corrections in Spin-1 and Spin-2 Bose-Einstein Condensates in the Presence of the Quadratic Zeeman Effect

We develop Bogoliubov theory of spin-1 and spin-2 Bose-Einstein condensates (BECs) in the presence of a quadratic Zeeman effect, and derive the Lee-Huang-Yang (LHY) corrections to the ground-state energy, sound velocity, and quantum depletion. We investigate all the phases of spin-1 and spin-2 BECs that can be realized experimentally. We also examine the stability of each phase against quantum fluctuations and the quadratic Zeeman effect. Furthermore, we discuss a relationship between the number of symmetry generators that are spontaneously broken and that of Nambu-Goldstone (NG) modes. It is found that in the spin-2 nematic phase there are special Bogoliubov modes that have gapless linear dispersion relations but do not belong to the NG modes.Comment: v3: 62 pages, 18 figure

Effects of thermal and quantum fluctuations on the phase diagram of a spin-1 87Rb Bose-Einstein condensate

We investigate effects of thermal and quantum fluctuations on the phase diagram of a spin-1 87Rb Bose-Einstein condensate (BEC) under a quadratic Zeeman effect. Due to the large ratio of spinindependent to spin-dependent interactions of 87Rb atoms, the effect of noncondensed atoms on the condensate is much more significant than that in scalar BECs. We find that the condensate and spontaneous magnetization emerge at different temperatures when the ground state is in the brokenaxisymmetry phase. In this phase, a magnetized condensate induces spin coherence of noncondensed atoms in different magnetic sublevels, resulting in temperature-dependent magnetization of the noncondensate. We also examine the effect of quantum fluctuations on the order parameter at absolute zero, and find that the ground-state phase diagram is significantly altered by quantum depletion.Comment: Comment: 21 pages, 7 figures Comment: 20 pages, 7 figures, paper reconstructed, nomenclature changed, references added, grammatical errors correcte

Dispersion and decay of collective modes in neutron star cores

We calculate the frequencies of collective modes of neutrons, protons and electrons in the outer core of neutron stars. The neutrons and protons are treated in a hydrodynamic approximation and the electrons are regarded as collisionless. The coupling of the nucleons to the electrons leads to Landau damping of the collective modes and to significant dispersion of the low-lying modes. We investigate the sensitivity of the mode frequencies to the strength of entrainment between neutrons and protons, which is not well characterized. The contribution of collective modes to the thermal conductivity is evaluated.Comment: 10 pages, 4 figure

p-Wave stabilization of three-dimensional Bose-Fermi solitons

We explore bright soliton solutions of ultracold Bose-Fermi gases, showing that the presence of p-wave interactions can remove the usual collapse instability and support stable soliton solutions that are global energy minima. A variational model that incorporates the relevant s- and p-wave interactions in the system is established analytically and solved numerically to probe the dependencies of the solitons on key experimental parameters. Under attractive s-wave interactions, bright solitons exist only as meta-stable states susceptible to collapse. Remarkably, the presence of repulsive p-wave interactions alleviates this collapse instability. This dramatically widens the range of experimentally-achievable soliton solutions and indicates greatly enhanced robustness. While we focus specifically on the boson-fermion pairing of 87Rb and 40K, the stabilization inferred by repulsive p-wave interactions should apply to the wider remit of ultracold Bose-Fermi mixtures.Comment: 9 pages, 6 figure

Bose-Einstein Condensates in Spin-Orbit Coupled Optical Lattices: Flat Bands and Superfluidity

Recently spin-orbit (SO) coupled superfluids in free space or harmonic traps have been extensively studied, motivated by the recent experimental realization of SO coupling for Bose-Einstein condensates (BEC). However, the rich physics of SO coupled BEC in optical lattices has been largely unexplored. In this paper, we show that in suitable parameter region the lowest Bloch state forms an isolated flat band in a one dimensional (1D) SO coupled optical lattice, which thus provides an experimentally feasible platform for exploring the recently celebrated topological flat band physics in lattice systems. We show that the flat band is preserved even with the mean field interaction in BEC. We investigate the superfluidity of the BEC in SO coupled lattices through dynamical and Landau stability analysis, and show that the BEC is stable on the whole flat band.Comment: 5 pages, 4 figures, to appear in Phys. Rev.

Superfluid liquid crystals: pasta phases in neutron star crusts

The pasta phases predicted to occur near the inner boundary of the crust of a neutron star resemble liquid crystals, a smectic A in the case of sheet-like nuclei (lasagna) and the columnar phase in the case of rod-like nuclei (spaghetti). An important difference compared with usual liquid crystals is that the nucleons are superfluid. We develop the hydrodynamic equations for this system and use them to study collective oscillations. Nucleon superfluidity leads to important qualitative differences in the spectra of these oscillations and also increases their frequencies compared with ordinary liquid crystals. We discuss a number of directions for future work.Comment: 7 page

Groundstate and Collective Modes of a Spin-Polarized Dipolar Bose-Einstein Condensate in a Harmonic Trap

We report new results for the Thomas-Fermi groundstate and the quadrupolar modes of density oscillations of a spin- polarized dipolar interacting Bose-Einstein condensate for the case when the external magnetic field is not orientated parallel to a principal axis of a harmonic anisotropic trap.Comment: Final version, published in Physical Review

Spectral Properties and Lifetimes of Neutral Spin-1/2-Fermions in a Magnetic Guide

We investigate the resonant motion of neutral spin-1/2-fermions in a magnetic guide. A wealth of unitary and anti-unitary symmetries is revealed in particular giving rise to a two-fold degeneracy of the energy levels. To compute the energies and decay widths of a large number of resonances the complex scaling method is employed. We discuss the dependence of the lifetimes on the angular momentum of the resonance states. In this context the existence of so-called quasi-bound states is shown. In order to approximately calculate the resonance energies of such states a radial Schr\"odinger equation is derived which improves the well-known adiabatic approximation. The effects of an additionally applied homogeneous Ioffe field on the resonance energies and decay widths are also considered. The results are applied to the case of the $^6\text{Li}$ atom in the $F=1/2$ hyperfine ground state.Comment: accepted for publication in PR