36 research outputs found
A simple mean field equation for condensates in the BEC-BCS crossover regime
We present a mean field approach based on pairs of fermionic atoms to
describe condensates in the BEC-BCS crossover regime. By introducing an
effective potential, the mean field equation allows us to calculate the
chemical potential, the equation of states and the atomic correlation function.
The results agree surprisingly well with recent quantum Monte Carlo
calculations. We show that the smooth crossover from the bosonic mean field
repulsion between molecules to the Fermi pressure among atoms is associated
with the evolution of the atomic correlation function
Quantum stochastic description of collisions in a canonical Bose gas
We derive a stochastic process that describes the kinetics of a
one-dimensional Bose gas in a regime where three body collisions are important.
In this situation the system becomes non integrable offering the possibility to
investigate dissipative phenomena more simply compared to higher dimensional
gases. Unlike the quantum Boltzmann equation describing the average momentum
distribution, the stochastic approach allows a description of higher-order
correlation functions in a canonical ensemble. As will be shown, this ensemble
differs drastically from the grand canonical one. We illustrate the use of this
method by determining the time evolution of the momentum mode particle number
distribution and the static structure factor during the evaporative cooling
process.Comment: 4 pages, 4 figure
Ultra--cold gases and the detection of the Earth's rotation: Bogoliubov space and gravitomagnetism
The present work analyzes the consequences of the gravitomagnetic effect of
the Earth upon a bosonic gas in which the corresponding atoms have a
non--vanishing orbital angular momentum. Concerning the ground state of the
Bogoliubov space of this system we deduce the consequences, on the pressure and
on the speed of sound, of the gravitomagnetic effect. We prove that the effect
on a single atom is very small, but we also show that for some thermodynamical
properties the consequences scale as a non--trivial function of the number of
particles.Comment: 4 page
Solitons with Cubic and Quintic Nonlinearities Modulated in Space and Time
This work deals with soliton solutions of the nonlinear Schroedinger equation
with cubic and quintic nonlinearities. We extend the procedure put forward in a
recent Letter and we solve the equation in the presence of linear background,
and cubic and quintic interactions which are modulated in space and time. As a
result, we show how a simple parameter can be used to generate brightlike or
darklike localized nonlinear waves which oscillate in several distinct ways,
driven by the space and time dependence of the parameters that control the
trapping potential, and the cubic and quintic nonlinearities.Comment: 4 pages, 6 figures; version to appear in PRE, R
Collective excitations of a degenerate gas at the BEC-BCS crossover
We study collective excitation modes of a fermionic gas of Li atoms in
the BEC-BCS crossover regime. While measurements of the axial compression mode
in the cigar-shaped trap close to a Feshbach resonance confirm theoretical
expectations, the radial compression mode shows surprising features. In the
strongly interacting molecular BEC regime we observe a negative frequency shift
with increasing coupling strength. In the regime of a strongly interacting
Fermi gas, an abrupt change in the collective excitation frequency occurs,
which may be a signature for a transition from a superfluid to a collisionless
phase.Comment: Feshbach resonance position updated, few minor change
Spatial and Temporal Noise Spectra of Spatially Extended Systems with Order-Disorder Phase Transitions
The noise power spectra of spatially extended dynamical systems are
investigated, using as a model the Complex Ginzburg-Landau equation with a
stochastic term. Analytical and numerical investigations show that the spatial
spectra of the ordered state are similar to Bose-Einstein distribution, showing
1/k^2 asymptotics in the long wavelength limit. The temporal noise spectra of
the ordered state are obtained of 1/^alpha form, where alpha=2-D/2 with D the
spatial dimension of the system.Comment: to be printed in International Journal of Bifurcation and Chao
Fermi liquid near Pomeranchuk quantum criticality
We analyze the behavior of an itinerant Fermi system near a charge
nematic(n=2) Pomeranchuk instability in terms of the Landau Fermi liquid (FL)
theory. The main object of our study is the fully renormalized vertex function
, related to the Landau interaction function. We derive
for a model case of the long-range interaction in the nematic
channel. Already within the Random Phase Approximation (RPA), the vertex is
singular near the instability. The full vertex, obtained by resumming the
ladder series composed of the RPA vertices, differs from the RPA result by a
multiplicative renormalization factor , related to the
single-particle residue and effective mass renormalization . We
employ the Pitaevski-Landau identities, which express the derivatives of the
self-energy in terms of , to obtain and solve a set of coupled
non-linear equations for , , and . We show that near the
transition the system enters a critical FL regime, where and , where is the
charge Landau component which approaches -1 at the instability. We
construct the Landau function of the critical FL and show that all but
Landau components diverge at the critical point. We also show that in
the critical regime the one-loop result for the self-energy is asymptotically exact if one identifies the effective
interaction with the RPA form of .Comment: References added, discussion of the dynamic vertex is modifie
Effect of interactions on vortices in a nonequilibrium polariton condensate
We demonstrate the creation of vortices in a macroscopically occupied polariton state formed in a semiconductor microcavity. A weak external laser beam carrying orbital angular momentum (OAM) is used to imprint a vortex on the condensate arising from the polariton optical parametric oscillator (OPO). The vortex core radius is found to decrease with increasing pump power, and is determined by polariton-polariton interactions. As a result of OAM conservation in the parametric scattering process, the excitation consists of a vortex in the signal and a corresponding antivortex in the idler of the OPO. The experimental results are in good agreement with a theoretical model of a vortex in the polariton OPO
Critical points in a relativistic bosonic gas induced by the quantum structure of spacetime
It is well known that phase transitions arise if the interaction among
particles embodies an attractive as well as a repulsive contribution. In this
work it will be shown that the breakdown of Lorentz symmetry, characterized
through a deformation in the relation dispersion, plus the bosonic statistics
predict the emergence of critical points. In other words, in some quantum
gravity models the structure of spacetime implies the emergence of critical
points even when no interaction among the particle has been considered.Comment: 5 pages, no figure
Self Consistent Random Phase Approximation and the restoration of symmetries within the three-level Lipkin model
We show that it is possible to restore the symmetry associated with the
Goldstone mode within the Self Consistent Random Phase Approximation (SCRPA)
applied to the three-level Lipkin model. We determine one and two-body
densities as very convergent expansions in terms of the generators of the RPA
basis. We show that SCRPA excitations correspond to the heads of some
rotational bands in the exact spectrum. It turns out that the SCRPA eigenmodes
for N=2 coincide with exact solutions, given by the diagonalisation procedure