165 research outputs found
Three fermions in a box at the unitary limit: universality in a lattice model
We consider three fermions with two spin components interacting on a lattice
model with an infinite scattering length. Low lying eigenenergies in a cubic
box with periodic boundary conditions, and for a zero total momentum, are
calculated numerically for decreasing values of the lattice period. The results
are compared to the predictions of the zero range Bethe-Peierls model in
continuous space, where the interaction is replaced by contact conditions. The
numerical computation, combined with analytical arguments, shows the absence of
negative energy solution, and a rapid convergence of the lattice model towards
the Bethe-Peierls model for a vanishing lattice period. This establishes for
this system the universality of the zero interaction range limit.Comment: 6 page
Limits of sympathetic cooling of fermions by zero temperature bosons due to particle losses
It has been suggested by Timmermans [Phys. Rev. Lett. {\bf 87}, 240403
(2001)] that loss of fermions in a degenerate system causes strong heating. We
address the fundamental limit imposed by this loss on the temperature that may
be obtained by sympathetic cooling of fermions by bosons. Both a quantum
Boltzmann equation and a quantum Boltzmann \emph{master} equation are used to
study the evolution of the occupation number distribution. It is shown that, in
the thermodynamic limit, the Fermi gas cools to a minimal temperature , where
is a constant loss rate, is the
bare fermion--boson collision rate not including the reduction due to Fermi
statistics, and is the chemical potential. It
is demonstrated that, beyond the thermodynamic limit, the discrete nature of
the momentum spectrum of the system can block cooling. The unusual non-thermal
nature of the number distribution is illustrated from several points of view:
the Fermi surface is distorted, and in the region of zero momentum the number
distribution can descend to values significantly less than unity. Our model
explicitly depends on a constant evaporation rate, the value of which can
strongly affect the minimum temperature.Comment: 14 pages, 7 figures. Phys. Rev. A in pres
Stability analysis of sonic horizons in Bose-Einstein condensates
We examine the linear stability of various configurations in Bose-Einstein
condensates with sonic horizons. These configurations are chosen in analogy
with gravitational systems with a black hole horizon, a white hole horizon and
a combination of both. We discuss the role of different boundary conditions in
this stability analysis, paying special attention to their meaning in
gravitational terms. We highlight that the stability of a given configuration,
not only depends on its specific geometry, but especially on these boundary
conditions. Under boundary conditions directly extrapolated from those in
standard General Relativity, black hole configurations, white hole
configurations and the combination of both into a black hole--white hole
configuration are shown to be stable. However, we show that under other (less
stringent) boundary conditions, configurations with a single black hole horizon
remain stable, whereas white hole and black hole--white hole configurations
develop instabilities associated to the presence of the sonic horizons.Comment: 14 pages, 7 figures (reduced resolution
Anomalous spatial diffusion and multifractality in optical lattices
Transport of cold atoms in shallow optical lattices is characterized by slow,
nonstationary momentum relaxation. We here develop a projector operator method
able to derive in this case a generalized Smoluchowski equation for the
position variable. We show that this explicitly non-Markovian equation can be
written as a systematic expansion involving higher-order derivatives. We use
the latter to compute arbitrary moments of the spatial distribution and analyze
their multifractal properties.Comment: 5 pages, 3 figure
Quasicondensation reexamined
We study in detail the effect of quasicondensation. We show that this effect
is strictly related to dimensionality of the system. It is present in one
dimensional systems independently of interactions - exists in repulsive,
attractive or in non-interacting Bose gas in some range of temperatures below
characteristic temperature of the quantum degeneracy. Based on this observation
we analyze the quasicondensation in terms of a ratio of the two largest
eigenvalues of the single particle density matrix for the ideal gas. We show
that in the thermodynamic limit in higher dimensions the second largest
eigenvalue vanishes (as compared to the first one) with total number of
particles as whereas goes to zero only logarithmically in
one dimension. We also study the effect of quasicondensation for various
geometries of the system: from quasi-1D elongated one, through spherically
symmetric 3D case to quasi-2D pancake-like geometry
Quantum fluctuations in coupled dark solitons in trapped Bose-Einstein condensates
We show that the quantum fluctuations associated with the Bogoliubov
quasiparticle vacuum can be strongly concentrated inside dark solitons in a
trapped Bose Einstein condensate. We identify a finite number of anomalous
modes that are responsible for such quantum phenomena. The fluctuations in
these anomalous modes correspond to the `zero-point' oscillations in coupled
dark solitons.Comment: 4 pages, 3 figure
Non-diffusive phase spreading of a Bose-Einstein condensate at finite temperature
We show that the phase of a condensate in a finite temperature gas spreads
linearly in time at long times rather than in a diffusive way. This result is
supported by classical field simulations, and analytical calculations which are
generalized to the quantum case under the assumption of quantum ergodicity in
the system. This super-diffusive behavior is intimately related to conservation
of energy during the free evolution of the system and to fluctuations of energy
in the prepared initial state.Comment: 16 pages, 7 figure
Dynamics of a Bose-Einstein Condensate in an Anharmonic Trap
We present a theoretical model to describe the dynamics of Bose-Einstein
condensates in anharmonic trapping potentials. To first approximation the
center-of-mass motion is separated from the internal condensate dynamics and
the problem is reduced to the well known scaling solutions for the Thomas-Fermi
radii. We discuss the validity of this approach and analyze the model for an
anharmonic waveguide geometry which was recently realized in an experiment
\cite{Ott2002c}
Images of the Dark Soliton in a Depleted Condensate
The dark soliton created in a Bose-Einstein condensate becomes grey in course
of time evolution because its notch fills up with depleted atoms. This is the
result of quantum mechanical calculations which describes output of many
experimental repetitions of creation of the stationary soliton, and its time
evolution terminated by a destructive density measurement. However, such a
description is not suitable to predict the outcome of a single realization of
the experiment were two extreme scenarios and many combinations thereof are
possible: one will see (1) a displaced dark soliton without any atoms in the
notch, but with a randomly displaced position, or (2) a grey soliton with a
fixed position, but a random number of atoms filling its notch. In either case
the average over many realizations will reproduce the mentioned quantum
mechanical result. In this paper we use N-particle wavefunctions, which follow
from the number-conserving Bogoliubov theory, to settle this issue.Comment: 8 pages, 6 figures, references added in version accepted for
publication in J. Phys.
The N boson time dependent problem: an exact approach with stochastic wave functions
We present a numerically tractable method to solve exactly the evolution of a
N boson system with binary interactions. The density operator of the system rho
is obtained as the stochastic average of particular operators |Psi_1><Psi_2| of
the system. The states |Psi_{1,2}> are either Fock states |N:phi_{1,2}> or
coherent states |coh:phi_{1,2}> with each particle in the state phi_{1,2}. We
determine the conditions on the evolution of phi_{1,2} -which involves a
stochastic element- under which we recover the exact evolution of rho. We
discuss various possible implementations of these conditions. The well known
positive P-representation arises as a particular case of the coherent state
ansatz. We treat numerically two examples: a two-mode system and a
one-dimensional harmonically confined gas. These examples, together with an
analytical estimate of the noise, show that the Fock state ansatz is the most
promising one in terms of precision and stability of the numerical solution.Comment: 21 pages, 5 figures, submitted to Phys.Rev.
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