245 research outputs found
Phase Separation of a Fast Rotating Boson-Fermion Mixture in the Lowest-Landau-Level Regime
By minimizing the coupled mean-field energy functionals, we investigate the
ground-state properties of a rotating atomic boson-fermion mixture in a
two-dimensional parabolic trap. At high angular frequencies in the
mean-field-lowest-Landau-level regime, quantized vortices enter the bosonic
condensate, and a finite number of degenerate fermions form the
maximum-density-droplet state. As the boson-fermion coupling constant
increases, the maximum density droplet develops into a lower-density state
associated with the phase separation, revealing characteristics of a
Landau-level structure
Attractive ultracold bosons in a necklace optical potential
We study the ground state properties of the Bose-Hubbard model with
attractive interactions on a M-site one-dimensional periodic -- necklace-like
-- lattice, whose experimental realization in terms of ultracold atoms is
promised by a recently proposed optical trapping scheme, as well as by the
control over the atomic interactions and tunneling amplitudes granted by
well-established optical techniques. We compare the properties of the quantum
model to a semiclassical picture based on a number-conserving su(M) coherent
state, which results into a set of modified discrete nonlinear Schroedinger
equations. We show that, owing to the presence of a correction factor ensuing
from number conservation, the ground-state solution to these equations provides
a remarkably satisfactory description of its quantum counterpart not only -- as
expected -- in the weak-interaction, superfluid regime, but even in the deeply
quantum regime of large interactions and possibly small populations. In
particular, we show that in this regime, the delocalized, Schroedinger-cat-like
quantum ground state can be seen as a coherent quantum superposition of the
localized, symmetry-breaking ground-state of the variational approach. We also
show that, depending on the hopping to interaction ratio, three regimes can be
recognized both in the semiclassical and quantum picture of the system.Comment: 11 pages, 7 figures; typos corrected and references added; to appear
in Phys. Rev.
Effectively attractive Bose-Einstein condensates in a rotating toroidal trap
We examine an effectively attractive quasi-one-dimensional Bose-Einstein
condensate of atoms confined in a rotating toroidal trap, as the magnitude of
the coupling constant and the rotational frequency are varied. Using both a
variational mean-field approach, as well as a diagonalization technique, we
identify the phase diagram between a uniform and a localized state and we
describe the system in the two phases.Comment: 4 pages, 4 ps figures, RevTe
Metastable Quantum Phase Transitions in a Periodic One-dimensional Bose Gas: Mean-Field and Bogoliubov Analyses
We generalize the concept of quantum phase transitions, which is
conventionally defined for a ground state and usually applied in the
thermodynamic limit, to one for \emph{metastable states} in \emph{finite size
systems}. In particular, we treat the one-dimensional Bose gas on a ring in the
presence of both interactions and rotation. To support our study, we bring to
bear mean-field theory, i.e., the nonlinear Schr\"odinger equation, and linear
perturbation or Bogoliubov-de Gennes theory. Both methods give a consistent
result in the weakly interacting regime: there exist \emph{two topologically
distinct quantum phases}. The first is the typical picture of superfluidity in
a Bose-Einstein condensate on a ring: average angular momentum is quantized and
the superflow is uniform. The second is new: one or more dark solitons appear
as stationary states, breaking the symmetry, the average angular momentum
becomes a continuous quantity, and the phase of the condensate can be
continuously wound and unwound
Collective modes and the broken symmetry of a rotating attractive Bose gas in an anharmonic trap
We study the rotational properties of an attractively interacting Bose gas in
a quadratic + quartic potential. The low-lying modes of both rotational ground
state configurations, namely the vortex and the center of mass rotating states,
are solved. The vortex excitation spectrum is positive for weak interactions
but the lowest modes decrease rapidly to negative values when the interactions
become stronger. The broken rotational symmetry involved in the center of mass
rotating state induces the appearance of an extra zero-energy mode in the
Bogoliubov spectrum. The excitations of the center of mass rotational state
also demonstrate the coupling between the center of mass and relative motions.Comment: 4 pages, 3 eps figures (2 in color) v2: changes in Title, all
figures, in text (especially in Sec III) and in Reference
Quantization with Action-Angle Coherent States
For a single degree of freedom confined mechanical system with given energy,
we know that the motion is always periodic and action-angle variables are
convenient choice as conjugate phase-space variables. We construct action-angle
coherent states in view to provide a quantization scheme that yields precisely
a given observed energy spectrum for such a system. This construction
is based on a Bayesian approach: each family corresponds to a choice of
probability distributions such that the classical energy averaged with respect
to this probability distribution is precisely up to a constant shift. The
formalism is viewed as a natural extension of the Bohr-Sommerfeld rule and an
alternative to the canonical quantization. In particular, it also yields a
satisfactory angle operator as a bounded self-adjoint operator
Reflection of a Lieb-Liniger wave packet from the hard-wall potential
Nonequilibrium dynamics of a Lieb-Liniger system in the presence of the
hard-wall potential is studied. We demonstrate that a time-dependent wave
function, which describes quantum dynamics of a Lieb-Liniger wave packet
comprised of N particles, can be found by solving an -dimensional Fourier
transform; this follows from the symmetry properties of the many-body
eigenstates in the presence of the hard-wall potential. The presented formalism
is employed to numerically calculate reflection of a few-body wave packet from
the hard wall for various interaction strengths and incident momenta.Comment: revised version, improved notation, Fig. 5 adde
Evolution of the macroscopically entangled states in optical lattices
We consider dynamics of boson condensates in finite optical lattices under a
slow external perturbation which brings the system to the unstable equilibrium.
It is shown that quantum fluctuations drive the condensate into the maximally
entangled state. We argue that the truncated Wigner approximation being a
natural generalization of the Gross-Pitaevskii classical equations of motion is
adequate to correctly describe the time evolution including both collapse and
revival of the condensate.Comment: 14 pages, 10 figures, Discussion of reversibility of entanglement is
adde
Quantum corrections to the dynamics of interacting bosons: beyond the truncated Wigner approximation
We develop a consistent perturbation theory in quantum fluctuations around
the classical evolution of a system of interacting bosons. The zero order
approximation gives the classical Gross-Pitaevskii equations. In the next order
we recover the truncated Wigner approximation, where the evolution is still
classical but the initial conditions are distributed according to the Wigner
transform of the initial density matrix. Further corrections can be
characterized as quantum scattering events, which appear in the form of a
nonlinear response of the observable to an infinitesimal displacement of the
field along its classical evolution. At the end of the paper we give a few
numerical examples to test the formalism.Comment: published versio
Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media
We develop a complete mathematical theory for the symmetrical solutions of
the generalized nonlinear Schr\"odinger equation based on the new concept of
angular pseudomomentum. We consider the symmetric solitons of a generalized
nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus
of the field. We provide a rigorous proof of a set of mathematical results
justifying that these solitons can be classified according to the irreducible
representations of a discrete group. Then we extend this theory to
non-stationary solutions and study the relationship between angular momentum
and pseudomomentum. We illustrate these theoretical results with numerical
examples. Finally, we explore the possibilities of the generalization of the
previous framework to the quantum limit.Comment: 18 pages; submitted to Physica
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