Private Sector

Feder, Ernest

doi:10.1007/978-1-4684-1030-3_23

“…4. This mode is referred to as the "overcritical branch" in [13], and we have observed that it has an elliptical density distribution which is orthogonal to the trap potential, as predicted by numerical simulations [14]. It then nucleates vortices when the eccentricity is too large for the quadrupole mode to be a solution of the hydrodynamic equations.…”

mentioning

confidence: 57%

Vortex Nucleation in Bose-Einstein Condensates in an Oblate, Purely Magnetic Potential

Hodby

¹

,

Hechenblaikner

²

,

Hopkins

³

et al. 2001

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“…It is interesting to estimate at what displacement the vortex velocity becomes supersonic [125]. Assuming the speed of sound varies radially with the local density as c = c 0 1 − r 2 0 /R 2 ⊥ , where…”

Section: Thomas-fermi Regime For Straight Vortex In Disk-shape Trapmentioning

confidence: 99%

Vortices in a trapped dilute Bose-Einstein condensate

Fetter¹,

Svidzinsky²

2001

J. Phys.: Condens. Matter

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We review the theory of vortices in trapped dilute Bose-Einstein condensates and compare theoretical predictions with existing experiments. Mean-field theory based on the time-dependent Gross-Pitaevskii equation describes the main features of the vortex states, and its predictions agree well with available experimental results. We discuss various properties of a single vortex, including its structure, energy, dynamics, normal modes and stability, as well as vortex arrays. When the nonuniform condensate contains a vortex, the excitation spectrum includes unstable ("anomalous") mode(s) with negative frequency. Trap rotation shifts the normal-mode frequencies and can stabilize the vortex. We consider the effect of thermal quasiparticles on vortex normal modes as well as possible mechanisms for vortex dissipation. Vortex states in mixtures and spinor condensates are also discussed.

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“…This is certainly the simplest example of a model Hamiltonian which allows for one to study the interactions between such electron pairs. Further, using a Gorkov derivation of the Ginzburg-Landau equations for an s-wave superconductor, one can show that for the values of | U | /W that we are considering, W = 8t being the (noninteracting) bandwidth, this model also reproduces the short coherence lengths of the Cooper pairs found in the high T c cuprate superconductors [3].…”

Section: Abstract: Attractive Hubbard Model; Quasiparticle Propertiesmentioning

confidence: 67%

“…This is certainly the simplest example of a model Hamiltonian which allows for one to study the interactions between such electron pairs. Further, using a Gorkov derivation of the Ginzburg-Landau equations for an s-wave superconductor, one can show that for the values of | U | /W that we are considering, W = 8t being the (noninteracting) bandwidth, this model also reproduces the short coherence lengths of the Cooper pairs found in the high T c cuprate superconductors [3].We employ the Brueckner Hartree-Fock theory to solve the Bethe-Salpeter equation for the 2D attractive Hubbard model in the ladder approximation [4], reliable for this model at low electron (or hole) densities. This affords us the opportunity to investigate the influence of preformed pairs with arbitrary lifetimes on the normal state properties.…”

mentioning

confidence: 68%

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A unifying theory of the magnetic and transport properties of La2−xSrxCuO4

Lai

¹

,

Gooding

²

1997

Physica B: Condensed Matter

0

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The attractive Hubbard model on a 2-D square lattice is studied at low electronic densities using the ladder approximation for the pair susceptibility. This model includes (i) the short coherence lengths known to exist experimentally in the cuprate superconductors, and (ii) two-particle bound states that correspond to electron pairs. We study the quasiparticle lifetimes in both non self-consistent and self-consistent theories, the latter including interactions between the pairs. We find that if we include the interactions between pairs the quasiparticle lifetimes vary approximately linearly with the inverse temperature, consistent with experiment. Keywords: attractive Hubbard model; quasiparticle propertiesNumerous recent experiments (e.g., neutrons, ARPES, optical, NMR) have shown that in the high T c cuprate superconductors a so-called pseudogap is present [1]. This has led to proposals that electron pairs form at temperatures well above the superconducting transition temperature. However, possibly due to phase fluctuations, a macroscopic phase coherent wave function is not formed, so superconductivity is not encountered [2].This physics motivates our study of the attractive Hubbard model. The Hamiltonian for this system iswhere the lattice sites of a 2-D square lattice are labeled by {i}, the lattice fermion operators are denoted by c i,σ , and neighbouring sites are represented by ij . For any nonzero | U |, two-particle bound states appear, and are physically related to a pair of electrons lowering the system's energy when they exist on the same lattice site. This is certainly the simplest example of a model Hamiltonian which allows for one to study the interactions between such electron pairs. Further, using a Gorkov derivation of the Ginzburg-Landau equations for an s-wave superconductor, one can show that for the values of | U | /W that we are considering, W = 8t being the (noninteracting) bandwidth, this model also reproduces the short coherence lengths of the Cooper pairs found in the high T c cuprate superconductors [3].We employ the Brueckner Hartree-Fock theory to solve the Bethe-Salpeter equation for the 2D attractive Hubbard model in the ladder approximation [4], reliable for this model at low electron (or hole) densities. This affords us the opportunity to investigate the influence of preformed pairs with arbitrary lifetimes on the normal state properties. Haussmann has argued [5] that when one solves this model in this approximation self consistently, one will include pair-pair interactions. These interactions will be, in first order, of a repulsive nature between different pairs.

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Private Sector

Cited by 5 publications

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Vortex Nucleation in Bose-Einstein Condensates in an Oblate, Purely Magnetic Potential

Vortex Nucleation in Bose-Einstein Condensates in an Oblate, Purely Magnetic Potential

Vortices in a trapped dilute Bose-Einstein condensate

A unifying theory of the magnetic and transport properties of La2−xSrxCuO4

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