26 research outputs found
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
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
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
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
Spontaneous emission of atoms via collisions of Bose-Einstein condensates
The widely used Gross-Pitaevskii equation treats only coherent aspects of the
evolution of a Bose-Einstein condensate. However, inevitably some atoms scatter
out of the condensate. We have developed a method, based on the field theory
formulation, describing the dynamics of incoherent processes which are due to
elastic collisions. We can therefore treat processes of spontaneous emission of
atoms into the empty modes, as opposed to stimulated processes, which require
non-zero initial occupation.
In this article we study two counter-propagating plane waves of atoms,
calculating the full dynamics of mode occupation, as well as the statistics of
scattered atoms. The more realistic case of Gaussian wavepackets is also
analyzed.Comment: 5 pages, 2 figure
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
Bogoliubov space of a Bose--Einstein condensate and quantum spacetime fluctuations
In the present work we consider the role that metric fluctuations could have
upon the properties of a Bose--Einstein condensate. In particular we consider
the Bogoliubov space associated to it and show that there are, at least, two
independent ways in which the average size of these metric fluctuations could
be, experimentally, determined. Indeed, we prove that the pressure and the
speed of sound of the ground state define an expression allowing us to
determine the average size of these fluctuations. Afterwards, an
interferometric experiment involving Bogoliubov excitations of the condensate
and the pressure (or the speed of sound of the ground state) provides a second
and independent way in which this average size could be determined,
experimentally
Explosive instability due to 4-wave mixing
It is known that an explosive instability can occur when nonlinear waves
propagate in certain media that admit 3-wave mixing. The purpose of this paper
is to show that explosive instabilities can occur even in media that admit no
3-wave mixing. Instead, the instability is caused by 4-wave mixing: four
resonantly interacting wavetrains gain energy from a background, and all blow
up in a finite time. Unlike singularities associated with self-focussing, these
singularities can occur with no spatial structure - the waves blow up
everywhere in space, simultaneously
Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
We review recent developments in the physics of ultracold atomic and
molecular gases in optical lattices. Such systems are nearly perfect
realisations of various kinds of Hubbard models, and as such may very well
serve to mimic condensed matter phenomena. We show how these systems may be
employed as quantum simulators to answer some challenging open questions of
condensed matter, and even high energy physics. After a short presentation of
the models and the methods of treatment of such systems, we discuss in detail,
which challenges of condensed matter physics can be addressed with (i)
disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii)
spinor lattice gases, (iv) lattice gases in "artificial" magnetic fields, and,
last but not least, (v) quantum information processing in lattice gases. For
completeness, also some recent progress related to the above topics with
trapped cold gases will be discussed.Comment: Review article. v2: published version, 135 pages, 34 figure