386 research outputs found
Time-dependent Gross-Pitaevskii equation for composite bosons as the strong-coupling limit of the fermionic BCS-RPA approximation
The linear response to a space- and time-dependent external disturbance of a
system of dilute condensed composite bosons at zero temperature, as obtained
from the linearized version of the time-dependent Gross-Pitaevskii equation, is
shown to result also from the strong-coupling limit of the time-dependent BCS
(or broken-symmetry RPA) approximation for the constituent fermions subject to
the same external disturbance. In this way, it is possible to connect
excited-state properties of the bosonic and fermionic systems by placing the
Gross-Pitaevskii equation in perspective with the corresponding fermionic
approximationsComment: 4 pages, 1 figur
Momentum distribution of a trapped Fermi gas with large scattering length
Using a scattering length parametrization of the BCS-BEC crossover as well as
the local density approximation for the density profile, we calculate the
momentum distribution of a harmonically trapped atomic Fermi gas at zero
temperature. Various interaction regimes are considered, including the BCS
phase, the unitarity limit and the molecular regime. We show that the relevant
parameter which characterizes the crossover is given by the dimensionless
combination , where is the number of atoms, is the
scattering length and is the oscillator length. The width of the
momentum distribution is shown to depend in a crucial way on the value and sign
of this parameter. Our predictions can be relevant for experiments on ultracold
atomic Fermi gases near a Feshbach resonance.Comment: 6 pages, 2 figures. Submitted to Phys. Rev. A. Added reference
Superfluid transition temperature in a trapped gas of Fermi atoms with a Feshbach resonance
We investigate strong coupling effects on the superfluid phase transition in
a gas of Fermi atoms with a Feshbach resonance. The Feshbach resonance
describes a composite quasi-Boson, which can give rise to an additional pairing
interaction between the Fermi atoms. This attractive interaction becomes
stronger as the threshold energy of the Feshbach resonance two-particle bound
state is lowered. In a recent paper, we showed that in the uniform Fermi gas,
this tunable pairing interaction naturally leads to a BCS-BEC crossover of the
Nozi`eres and Schmitt-Rink kind, in which the BCS-type superfluid phase
transition continuously changes into the BEC-type as the threshold energy is
decreased. In this paper, we extend our previous work by including the effect
of a harmonic trap potential, treated within the local density approximation
(LDA). We also give results for both weak and strong coupling to the Feshbach
resonance. We show that the BCS-BEC crossover phenomenon strongly modifies the
shape of the atomic density profile at the superfluid phase transition
temperature Tc, reflecting the change of the dominant particles going from
Fermi atoms to composite Bosons. In the BEC regime, these composite Bosons are
shown to first appear well above Tc. We also discuss the "phase diagram" above
Tc as a function of the tunable threshold energy. We introduce a characteristic
temperature T* describing the effective crossover in the normal phase from a
Fermi gas of atoms to a gas of stable molecules.Comment: 43 pages, 13 figures (submitted to PRA
Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs
We consider the low density limit of a Fermi gas in the BCS approximation. We
show that if the interaction potential allows for a two-particle bound state,
the system at zero temperature is well approximated by the Gross-Pitaevskii
functional, describing a Bose-Einstein condensate of fermion pairs.Comment: LaTeX2e, 17 page
Pairing of fermions in atomic traps and nuclei
Pairing gaps for fermionic atoms in harmonic oscillator traps are calculated
for a wide range of interaction strengths and particle number, and compared to
pairing in nuclei. Especially systems, where the pairing gap exceeds the level
spacing but is smaller than the shell splitting , are studied
which applies to most trapped Fermi atomic systems as well as to finite nuclei.
When solving the gap equation for a large trap with such multi-level pairing,
one finds that the matrix elements between nearby harmonic oscillator levels
and the quasi-particle energies lead to a double logarithm of the gap, and a
pronounced shell structure at magic numbers. It is argued that neutron and
proton pairing in nuclei belongs to the class of multi-level pairing, that
their shell structure follows naturally and that the gaps scale as - all in qualitative agreement with odd-even staggering of nuclear
binding energies. Pairing in large systems are related to that in the bulk
limit. For large nuclei the neutron and proton superfluid gaps approach the
asymptotic value in infinite nuclear matter: MeV.Comment: 11 pages, 5 figure
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Shrinking of a condensed fermionic cloud in a trap approaching the BEC limit
We determine the zero-temperature density profile of a cloud of fermionic
atoms in a trap subject to a mutual attractive interaction, as the strength of
the interaction is progressively increased. We find a significant decrease of
the size of the atomic cloud as it evolves from the weak-coupling (BCS) regime
of overlapping Cooper pairs to the strong-coupling (Bose-Einstein) regime of
non-overlapping bound-fermion pairs. Most significantly, we find a pronounced
increase of the value of the density at the center of the trap (even by an
order of magnitude) when evolving between the two regimes. Our results are
based on a generalized Thomas-Fermi approximation for the superfluid state,
that covers continuously all coupling regimes.Comment: 5 pages, 3 postscript figure
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Avaliação do desenvolvimento de maracujá-doce (Passiflora alata Dryander) propagado por estaquia e por semente em condições de pomar comercial
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