91 research outputs found
Symbiotic gap and semi-gap solitons in Bose-Einstein condensates
Using the variational approximation and numerical simulations, we study
one-dimensional gap solitons in a binary Bose-Einstein condensate trapped in an
optical-lattice potential. We consider the case of inter-species repulsion,
while the intra-species interaction may be either repulsive or attractive.
Several types of gap solitons are found: symmetric or asymmetric; unsplit or
split, if centers of the components coincide or separate; intra-gap (with both
chemical potentials falling into a single bandgap) or inter-gap, otherwise. In
the case of the intra-species attraction, a smooth transition takes place
between solitons in the semi-infinite gap, the ones in the first finite
bandgap, and semi-gap solitons (with one component in a bandgap and the other
in the semi-infinite gap).Comment: 5 pages, 9 figure
One-dimensional superfluid Bose-Fermi mixture: mixing, demixing and bright solitons
We study a ultra-cold and dilute superfluid Bose-Fermi mixture confined in a
strictly one-dimensional atomic waveguide by using a set of coupled nonlinear
mean-field equations obtained from the Lieb-Liniger energy density for bosons
and the Gaudin-Yang energy density for fermions. We consider a finite
Bose-Fermi inter-atomic strength g_{bf} and both periodic and open boundary
conditions. We find that with periodic boundary conditions, i.e. in a quasi-1D
ring, a uniform Bose-Fermi mixture is stable only with a large fermionic
density. We predict that at small fermionic densities the ground state of the
system displays demixing if g_{bf}>0 and may become a localized Bose-Fermi
bright soliton for g_{bf}<0. Finally, we show, using variational and numerical
solution of the mean-field equations, that with open boundary conditions, i.e.
in a quasi-1D cylinder, the Bose-Fermi bright soliton is the unique ground
state of the system with a finite number of particles, which could exhibit a
partial mixing-demixing transition. In this case the bright solitons are
demonstrated to be dynamically stable. The experimental realization of these
Bose-Fermi bright solitons seems possible with present setups.Comment: 11 pages, 11 figure
Gap solitons in superfluid boson-fermion mixtures
Using coupled equations for the bosonic and fermionic order parameters, we
construct families of gap solitons (GSs) in a nearly one-dimensional Bose-Fermi
mixture trapped in a periodic optical-lattice (OL) potential, the boson and
fermion components being in the states of the BEC and BCS superfluid,
respectively. Fundamental GSs are compact states trapped, essentially, in a
single cell of the lattice. Full families of such solutions are constructed in
the first two bandgaps of the OL-induced spectrum, by means of variational and
numerical methods, which are found to be in good agreement. The families
include both intra-gap and inter-gap solitons, with the chemical potentials of
the boson and fermion components falling in the same or different bandgaps,
respectively.Nonfundamental states, extended over several lattice cells, are
constructed too. The GSs are stable against strong perturbations.Comment: 9 pages, 14 figure
Two phase transitions in (s+id)-wave Bardeen-Cooper-Schrieffer superconductivity
We establish universal behavior in temperature dependencies of some
observables in -wave BCS superconductivity in the presence of a weak
wave. There also could appear a second second-order phase transition. As
temperature is lowered past the usual critical temperature , a less
ordered superconducting phase is created in wave, which changes to a more
ordered phase in wave at (). The presence of two phase
transitions manifest in two jumps in specific heat at and . The
temperature dependencies of susceptibility, penetration depth, and thermal
conductivity also confirm the new phase transition.Comment: 6 pages, 5 post-script figures
Universal scaling in BCS superconductivity in two dimensions in non-s waves
The solutions of a renormalized BCS model are studied in two space dimensions
in , and waves for finite-range separable potentials. The gap
parameter, the critical temperature , the coherence length and the
jump in specific heat at as a function of zero-temperature condensation
energy exhibit universal scalings. In the weak-coupling limit, the present
model yields a small and large appropriate to those for high-
cuprates. The specific heat, penetration depth and thermal conductivity as a
function of temperature show universal scaling in and waves.Comment: 11 pages, LATEX, 4 postscript figures embedded using eps
Superfluid Fermi-Fermi mixture: phase diagram, stability, and soliton formation
We study the phase diagram for a dilute Bardeen-Cooper-Schrieffer superfluid
Fermi-Fermi mixture (of distinct mass) at zero temperature using energy
densities for the superfluid fermions in one (1D), two (2D), and three (3D)
dimensions. We also derive the dynamical time-dependent nonlinear
Euler-Lagrange equation satisfied by the mixture in one dimension using this
energy density. We obtain the linear stability conditions for the mixture in
terms of fermion densities of the components and the interspecies Fermi-Fermi
interaction. In equilibrium there are two possibilities. The first is that of a
uniform mixture of the two components, the second is that of two pure phases of
two components without any overlap between them. In addition, a mixed and a
pure phase, impossible in 1D and 2D, can be created in 3D. We also obtain the
conditions under which the uniform mixture is stable from an energetic
consideration. The same conditions are obtained from a modulational instability
analysis of the dynamical equations in 1D. Finally, the 1D dynamical equations
for the system are solved numerically and by variational approximation (VA) to
study the bright solitons of the system for attractive interspecies Fermi-Fermi
interaction in 1D. The VA is found to yield good agreement to the numerical
result for the density profile and chemical potential of the bright solitons.
The bright solitons are demonstrated to be dynamically stable. The experimental
realization of these Fermi-Fermi bright solitons seems possible with present
setups.Comment: 14 page
Lattice Discretization in Quantum Scattering
The utility of lattice discretization technique is demonstrated for solving
nonrelativistic quantum scattering problems and specially for the treatment of
ultraviolet divergences in these problems with some potentials singular at the
origin in two and three space dimensions. This shows that lattice
discretization technique could be a useful tool for the numerical solution of
scattering problems in general. The approach is illustrated in the case of the
Dirac delta function potential.Comment: 9 page
Quantum scattering in one dimension
A self-contained discussion of nonrelativistic quantum scattering is
presented in the case of central potentials in one space dimension, which will
facilitate the understanding of the more complex scattering theory in two and
three dimensions. The present discussion illustrates in a simple way the
concept of partial-wave decomposition, phase shift, optical theorem and
effective-range expansion.Comment: 8 page
Quenching of -H with an ultra-cold anti-hydrogen atom
In this work we report the results concerning calculations for
quantum-mechanical rotational transitions in molecular hydrogen, H, induced
by an ultra-cold ground state anti-hydrogen atom . The
calculations are accomplished using a non-reactive close-coupling
quantum-mechanical approach. The H molecule is treated as a rigid rotor.
The total elastic scattering cross section at energy
, state-resolved rotational transition cross sections
between states and and corresponding thermal
rate coefficients are computed in the temperature range 0.004 K 4 K. Satisfactory agreement with other calculations
(variational) has been obtained for .Comment: 24 pages, 3 tables, 8 figure
Cooper pair dispersion relation for weak to strong coupling
Cooper pairing in two dimensions is analyzed with a set of renormalized
equations to determine its binding energy for any fermion number density and
all coupling assuming a generic pairwise residual interfermion interaction. \
Also considered are Cooper pairs (CPs) with nonzero center-of-mass momentum
(CMM)--usually neglected in BCS theory--and their binding energy is expanded
analytically in powers of the CMM up to quadratic terms. A Fermi-sea-dependent
{\it linear} term in the CMM dominates the pair excitation energy in weak
coupling (also called the BCS regime) while the more familiar quadratic term
prevails in strong coupling (the Bose regime). The crossover, though strictly
unrelated to BCS theory {\it per se,} is studied numerically as it is expected
to play a central role in a model of superconductivity as a Bose-Einstein
condensation of CPs where the transition temperature vanishes for all
dimensionality for quadratic dispersion, but is {\it nonzero} for all
for linear dispersion.Comment: 11 pages plus 3 figures, revised version accepted in Physical Review
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