Landau levels and the Thomas-Fermi structure of rapidly rotating Bose-Einstein condensates

We show that, within mean-field theory, the density profile of a rapidly rotating harmonically trapped Bose-Einstein condensate is of the Thomas-Fermi form as long as the number of vortices is much larger than unity. Two forms of the condensate wave function are explored: i) the lowest Landau level (LLL) wave function with a regular lattice of vortices multiplied by a slowly varying envelope function, which gives rise to components in higher Landau levels; ii) the LLL wave function with a nonuniform vortex lattice. From variational calculations we find it most favorable energetically to retain the LLL form of the wave function but to allow the vortices to deviate slightly from a regular lattice. The predicted distortions of the lattice are small, but in accord with recent measurements at lower rates of rotation.Comment: 4 pages, 2 figures, to appear in Phys. Rev. Lett. (extend the arguments of cond-mat/0402167

Bose-Einstein condensate in a rapidly rotating non-symmetric trap

A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional harmonic trap can be described with the lowest Landau-level set of single-particle states. The condensate wave function psi(x,y) is a Gaussian exp(-r^2/2), multiplied by an analytic function f(z) of the complex variable z= x+ i y. The criterion for a quantum phase transition to a non-superfluid correlated many-body state is usually expressed in terms of the ratio of the number of particles to the number of vortices. Here, a similar description applies to a rapidly rotating non-symmetric two-dimensional trap with arbitrary quadratic anisotropy (omega_x^2 < omega_y^2). The corresponding condensate wave function psi(x,y) is a complex anisotropic Gaussian with a phase proportional to xy, multiplied by an analytic function f(z), where z = x + i \beta_- y is a stretched complex variable and 0< \beta_- <1 is a real parameter that depends on the trap anisotropy and the rotation frequency. Both in the mean-field Thomas-Fermi approximation and in the mean-field lowest Landau level approximation with many visible vortices, an anisotropic parabolic density profile minimizes the energy. An elongated condensate grows along the soft trap direction yet ultimately shrinks along the tight trap direction. The criterion for the quantum phase transition to a correlated state is generalized (1) in terms of N/L_z, which suggests that a non-symmetric trap should make it easier to observe this transition or (2) in terms of a "fragmented" correlated state, which suggests that a non-symmetric trap should make it harder to observe this transition. An alternative scenario involves a crossover to a quasi one-dimensional condensate without visible vortices, as suggested by Aftalion et al., Phys. Rev. A 79, 011603(R) (2009).Comment: 20 page

Mechanism of d_{x^2-y^2}-wave superconductivity based on doped hole induced spin texture in high T_c cuprates

A mechanism of d_{x^2-y^2}-wave superconductivity is proposed for the high-T_c cuprates based on a spin texture with non-zero topological density induced by doped holes through Zhang-Rice singlet formation. The pairing interaction arises from the magnetic Lorentz force like interaction between the holes and the spin textures. The stability of the pairing state against the vortex-vortex interaction and the Coulomb repulsion is examined. The mechanism suggests appearance of a p-wave pairing component by introducing anisotropy in the CuO_2 plane.Comment: 9 pages, 3 figures; added references, corrected minor error

Effective bosonic hamiltonian for excitons : a too naive concept

Excitons, being made of two fermions, may appear from far as bosons. Their close-to-boson character is however quite tricky to handle properly. Using our commutation technique especially designed to deal with interacting close-to-boson particles, we here calculate the exact expansion in Coulomb interaction of theexciton-exciton correlations, and show that a naive effective bosonic hamiltonian for excitons cannot produce these X-X correlations correctly

Medical applications of nasa-developed science and technology quarterly progress report no. 2, 30 apr. - 31 jul. 1965

Medical applications of aerospace science and technolog

An effective theory of Feshbach resonances and many-body properties of Fermi gases

For calculating low-energy properties of a dilute gas of atoms interacting via a Feshbach resonance, we develop an effective theory in which the parameters that enter are an atom-molecule coupling strength and the magnetic moment of the molecular resonance. We demonstrate that for resonances in the fermionic systems $^{6}$Li and $^{40}$K that are under experimental investigation, the coupling is so strong that many-body effects are appreciable even when the resonance lies at an energy large compared with the Fermi energy. We calculate a number of many-body effects, including the effective mass and the lifetime of atomic quasiparticles in the gas.Comment: 4 pages, 1 figure, NORDITA-2003-21 C

Normal Modes of a Vortex in a Trapped Bose-Einstein Condensate

A hydrodynamic description is used to study the normal modes of a vortex in a zero-temperature Bose-Einstein condensate. In the Thomas-Fermi (TF) limit, the circulating superfluid velocity far from the vortex core provides a small perturbation that splits the originally degenerate normal modes of a vortex-free condensate. The relative frequency shifts are small in all cases considered (they vanish for the lowest dipole mode with |m|=1), suggesting that the vortex is stable. The Bogoliubov equations serve to verify the existence of helical waves, similar to those of a vortex line in an unbounded weakly interacting Bose gas. In the large-condensate (small-core) limit, the condensate wave function reduces to that of a straight vortex in an unbounded condensate; the corresponding Bogoliubov equations have no bound-state solutions that are uniform along the symmetry axis and decay exponentially far from the vortex core.Comment: 15 pages, REVTEX, 2 Postscript figures, to appear in Phys. Rev. A. We have altered the material in Secs. 3B and 4 in connection with the normal modes that have |m|=1. Our present treatment satisfies the condition that the fundamental dipole mode of a condensate with (or without) a vortex should have the bare frequency $\omega_\perp

Beyond the Thomas-Fermi approximation for a trapped condensed Bose-Einstein gas

Corrections to the zero-temperature Thomas-Fermi description of a dilute interacting condensed Bose-Einstein gas confined in an isotropic harmonic trap arise due to the presence of a boundary layer near the condensate surface. Within the Bogoliubov approximation, the various contributions to the ground-state condensate energy all have terms of order R^{-4}ln R and R^{-4}, where R is the number-dependent dimensionless condensate radius in units of the oscillator length. The zero-order hydrodynamic density-fluctuation amplitudes are extended beyond the Thomas-Fermi radius through the boundary layer to provide a uniform description throughout all space. The first-order correction to the excitation frequencies is shown to be of order R^{-4}.Comment: 12 pages, 2 figures, revtex. Completely revised discussion of the boundary-layer corrections to collective excitations, and two new figures added. To appear in Phys. Rev. A (October, 1998

An Active-Sterile Neutrino Transformation Solution for r-Process Nucleosynthesis

We discuss how matter-enhanced active-sterile neutrino transformation in both neutrino and antineutrino channels could enable the production of the rapid neutron capture (r-process) nuclei in neutrino-heated supernova ejecta. In this scheme the lightest sterile neutrino would be heavier than the electron neutrino and split from it by a vacuum mass-squared difference roughly between 3 and 70 eV$^2$ and vacuum mixing angle given by $\sin^2 2\theta_{es} > 10^{-4}$.Comment: 27 pages plus twelve figures. Submitted to Phys. Rev.

Many-Body Theory of the Electroweak Nuclear Response

After a brief review of the theoretical description of nuclei based on nonrelativistic many-body theory and realistic hamiltonians, these lectures focus on its application to the analysis of the electroweak response. Special emphasis is given to electron-nucleus scattering, whose experimental study has provided a wealth of information on nuclear structure and dynamics, exposing the limitations of the shell model. The extension of the formalism to the case of neutrino-nucleus interactions, whose quantitative understanding is required to reduce the systematic uncertainty of neutrino oscillation experiments, is also discussed.Comment: Lectures delivered at the DAE-BRNS Workshop on Hadron Physics. Aligarh Muslim University, Aligarh (India), February 18-23, 200