7,580 research outputs found
Density and spin response of a strongly-interacting Fermi gas in the attractive and quasi-repulsive regime
Recent experimental advances in ultra-cold Fermi gases allow for exploring
response functions under different dynamical conditions. In particular, the
issue of obtaining a "quasi-repulsive" regime starting from a Fermi gas with an
attractive inter-particle interaction while avoiding the formation of the
two-body bound state is currently debated. Here, we provide a calculation of
the density and spin response for a wide range of temperature and coupling both
in the attractive and quasi-repulsive regime, whereby the system is assumed to
evolve non-adiabatically toward the "upper branch" of the Fermi gas. A
comparison is made with the available experimental data for these two
quantities.Comment: 8 pages, 7 figures, to appear on Phys. Rev. Let
Size shrinking of composite bosons for increasing density in the BCS to Bose-Einstein crossover
We consider a system of fermions in the continuum case at zero temperature,
in the strong-coupling limit of a short-range attraction when composite bosons
form as bound-fermion pairs. We examine the density dependence of the size of
the composite bosons at leading order in the density ("dilute limit"), and show
on general physical grounds that this size should decrease with increasing
density, both in three and two dimensions. We then compare with the analytic
zero-temperature mean-field solution, which indeed exhibits the size shrinking
of the composite bosons both in three and two dimensions. We argue,
nonetheless, that the two-dimensional mean-field solution is not consistent
with our general result in the "dilute limit", to the extent that mean field
treats the scattering between composite bosons in the Born approximation which
is known to break down at low energy in two dimensions.Comment: Revised version to be published on Eur. Phys. Jour. B, 7 pages, 1
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Extracting the condensate density from projection experiments with Fermi gases
A debated issue in the physics of the BCS-BEC crossover with trapped Fermi
atoms is to identify characteristic properties of the superfluid phase.
Recently, a condensate fraction was measured on the BCS side of the crossover
by sweeping the system in a fast (nonadiabatic) way from the BCS to the BEC
sides, thus ``projecting'' the initial many-body state onto a molecular
condensate. We analyze here the theoretical implications of these projection
experiments, by identifying the appropriate quantum-mechanical operator
associated with the measured quantities and relating them to the many-body
correlations occurring in the BCS-BEC crossover. Calculations are presented
over wide temperature and coupling ranges, by including pairing fluctuations on
top of mean field.Comment: 4 pages, 4 figure
The influence of long-range hopping on ferromagnetism in the Hubbard model
The phase diagram of the Hubbard model in an external magnetic field is
examined by extrapolation of small-cluster exact-diagonalization calculations.
Using a general expression for the hopping matrix elements () the influence of long-range hopping (band asymmetry) on
ferromagnetism in this model is studied. It is found that the long-range
hopping (nonzero ) stabilizes ferromagnetism in an external magnetic field
for . In the opposite limit the fully polarized ferromagnetic
state is generally suppressed with increasing . The critical value of
magnetic field below which the ferromagnetic state becomes unstable is
calculated numerically.Comment: 8 pages, 3 Postscript figures, Late
From superconducting fluctuations to the bosonic limit in the response functions above the critical temperature
We investigate the density, current, and spin response functions above the
critical temperature for a system of three-dimensional fermions interacting via
an attractive short-range potential. In the strong-coupling (bosonic) limit of
this interaction, we identify the dominant diagrammatic contributions for a
``dilute'' system of composite bosons which form as bound-fermion pairs, and
compare them with the usual (Aslamazov-Larkin, Maki-Thompson, and
density-of-states) terms occurring in the theory of superconducting
fluctuations above the critical temperature for a clean system in the
weak-coupling limit. We show that, at the zeroth order in the diluteness
parameter for the composite bosons, the Aslamazov-Larkin term still represents
formally the dominant contribution to the density and current response
functions, while the Maki-Thompson and density-of-states terms are strongly
suppressed. Corrections to the Aslamazov-Larkin term are then considered at the
next order in the diluteness parameter for the composite bosons. The spin
response function is also examined, and it is found to be exponentially
suppressed in the bosonic limit only when appropriate sets of diagrams are
considered simultaneously.Comment: 10 pages, 6 figure
Gap equation with pairing correlations beyond mean field and its equivalence to a Hugenholtz-Pines condition for fermion pairs
The equation for the gap parameter represents the main equation of the
pairing theory of superconductivity. Although it is formally defined through a
single-particle property, physically it reflects the pairing correlations
between opposite-spin fermions. Here, we exploit this physical connection and
cast the gap equation in an alternative form which explicitly highlights these
two-particle correlations, by showing that it is equivalent to a
Hugenholtz-Pines condition for fermion pairs. At a formal level, a direct
connection is established in this way between the treatment of the condensate
fraction in condensate systems of fermions and bosons. At a practical level,
the use of this alternative form of the gap equation is expected to make easier
the inclusion of pairing fluctuations beyond mean field. As a proof-of-concept
of the new method, we apply the modified form of the gap equation to the
long-pending problem about the inclusion of the Gorkov-Melik-Barkhudarov
correction across the whole BCS-BEC crossover, from the BCS limit of strongly
overlapping Cooper pairs to the BEC limit of dilute composite bosons, and for
all temperatures in the superfluid phase. Our numerical calculations yield
excellent agreement with the recently determined experimental values of the gap
parameter for an ultra-cold Fermi gas in the intermediate regime between BCS
and BEC, as well as with the available quantum Monte Carlo data in the same
regime.Comment: 24 pages, 13 figure
Temperature dependence of a vortex in a superfluid Fermi gas
The temperature dependence of an isolated quantum vortex, embedded in an
otherwise homogeneous fermionic superfluid of infinite extent, is determined
via the Bogoliubov-de Gennes (BdG) equations across the BCS-BEC crossover.
Emphasis is given to the BCS side of this crossover, where it is physically
relevant to extend this study up to the critical temperature for the loss of
the superfluid phase, such that the size of the vortex increases without bound.
To this end, two novel techniques are introduced. The first one solves the BdG
equations with "free boundary conditions", which allows one to determine with
high accuracy how the vortex profile matches its asymptotic value at a large
distance from the center, thus avoiding a common practice of constraining the
vortex in a cylinder with infinite walls. The second one improves on the
regularization procedure of the self-consistent gap equation when the
inter-particle interaction is of the contact type, and permits to considerably
reduce the time needed for its numerical integration, by drawing elements from
the derivation of the Gross-Pitaevskii equation for composite bosons starting
from the BdG equations.Comment: 18 pgaes, 16 figure
Low density ferromagnetism in the Hubbard model
A single-band Hubbard model with nearest and next-nearest neighbour hopping
is studied for , 2, 3, using both analytical and numerical techniques. In
one dimension, saturated ferromagnetism is found above a critical value of
for a band structure with two minima and for small and intermediate densities.
This is an extension of a scenario recently proposed by M\"uller--Hartmann. For
three dimensions and non-pathological band structures, it is proven that such a
scenario does not work.Comment: 4 pages, 3 postscript figure
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