616 research outputs found
Free expansion of lowest Landau level states of trapped atoms: a wavefunction microscope
We show that for any lowest-Landau-level state of a trapped, rotating,
interacting Bose gas, the particle distribution in coordinate space in a free
expansion (time of flight) experiment is related to that in the trap at the
time it is turned off by a simple rescaling and rotation. When the
lowest-Landau-level approximation is valid, interactions can be neglected
during the expansion, even when they play an essential role in the ground state
when the trap is present. The correlations in the density in a single snapshot
can be used to obtain information about the fluid, such as whether a transition
to a quantum Hall state has occurred.Comment: 5 pages, no figures. v2: discussion of neglect of interactions during
expansion improved, refs adde
Strongly correlated phases in rapidly rotating Bose gases
We consider a system of trapped spinless bosons interacting with a repulsive
potential and subject to rotation. In the limit of rapid rotation and small
scattering length, we rigorously show that the ground state energy converges to
that of a simplified model Hamiltonian with contact interaction projected onto
the Lowest Landau Level. This effective Hamiltonian models the bosonic analogue
of the Fractional Quantum Hall Effect (FQHE). For a fixed number of particles,
we also prove convergence of states; in particular, in a certain regime we show
convergence towards the bosonic Laughlin wavefunction. This is the first
rigorous justification of the effective FQHE Hamiltonian for rapidly rotating
Bose gases. We review previous results on this effective Hamiltonian and
outline open problems.Comment: AMSLaTeX, 23 page
Thomas-Fermi-Poisson theory of screening for latterally confined and unconfined two-dimensional electron systems in strong magnetic fields
We examine within the self-consistent Thomas-Fermi-Poisson approach the
low-temperature screening properties of a two-dimensional electron gas (2DEG)
subjected to strong perpendicular magnetic fields. Numerical results for the
unconfined 2DEG are compared with those for a simplified Hall bar geometry
realized by two different confinement models. It is shown that in the strongly
non-linear screening limit of zero temperature the total variation of the
screened potential is related by simple analytical expressions to the amplitude
of an applied harmonic modulation potential and to the strength of the magnetic
field.Comment: 12 pages, 12 figure
The excitation spectrum for weakly interacting bosons in a trap
We investigate the low-energy excitation spectrum of a Bose gas confined in a
trap, with weak long-range repulsive interactions. In particular, we prove that
the spectrum can be described in terms of the eigenvalues of an effective
one-particle operator, as predicted by the Bogoliubov approximation.Comment: LaTeX, 32 page
Rapidly Rotating Fermions in an Anisotropic Trap
We consider a cold gas of non-interacting fermions in a two dimensional
harmonic trap with two different trapping frequencies ,
and discuss the effect of rotation on the density profile. Depending on the
rotation frequency and the trap anisotropy , the
density profile assumes two qualitatively different shapes. For small
anisotropy (), the
density consists of elliptical plateaus of constant density, corresponding to
Landau levels and is well described by a two dimensional local density
approximation. For large anisotropy (), the density profile is Gaussian in the strong confining
direction and semicircular with prominent Friedel oscillations in the weak
direction. In this regime, a one dimensional local density approximation is
well suited to describe the system. The crossover between the two regimes is
smooth where the step structure between the Landau level edges turn into
Friedel oscillations. Increasing the temperature causes the step structure or
the Friedel oscillations to wash out leaving a Boltzmann gas density profile.Comment: 14 pages, 7 figure
Exclusion Statistics of Quasiparticles in Condensed States of Composite Fermion Excitations
The exclusion statistics of quasiparticles is found at any level of the
hierarchy of condensed states of composite fermion excitations (for which
experimental indications have recently been found). The hierarchy of condensed
states of excitations in boson Jain states is introduced and the statistics of
quasiparticles is found. The quantum Hall states of charged -anyons
( -- the exclusion statistics parameter) can be described as
incompressible states of -anyons ( -- an even number).Comment: 4 page
Spinor Bose-Einstein Condensates with Many Vortices
Vortex-lattice structures of antiferromagnetic spinor Bose-Einstein
condensates with hyperfine spin F=1 are investigated theoretically based on the
Ginzburg-Pitaevskii equations near . The Abrikosov lattice with clear
core regions are found {\em never stable} at any rotation drive .
Instead, each component prefers to shift the core
locations from the others to realize almost uniform order-parameter amplitude
with complicated magnetic-moment configurations. This system is characterized
by many competing metastable structures so that quite a variety of vortices may
be realized with a small change in external parameters.Comment: 4 page
Control of Autophagosome Axonal Retrograde Flux by Presynaptic Activity Unveiled Using Botulinum Neurotoxin Type A
Botulinum neurotoxin type A (BoNT/A) is a highly potent neurotoxin that elicits flaccid paralysis by enzymatic cleavage of the exocytic machinery component SNAP25 in motor nerve terminals. However, recent evidence suggests that the neurotoxic activity of BoNT/A is not restricted to the periphery, but also reaches the CNS after retrograde axonal transport. Because BoNT/A is internalized in recycling synaptic vesicles, it is unclear which compartment facilitates this transport. Using live-cell confocal and single-molecule imaging of rat hippocampal neurons cultured in microfluidic devices, we show that the activity-dependent uptake of the binding domain of the BoNT/A heavy chain (BoNT/A-Hc) is followed by a delayed increase in retrograde axonal transport of BoNT/A-Hc carriers. Consistent with a role of presynaptic activity in initiating transport of the active toxin, activity-dependent uptake of BoNT/A in the terminal led to a significant increase in SNAP25 cleavage detected in the soma chamber compared with nonstimulated neurons. Surprisingly, most endocytosed BoNT/A-Hc was incorporated into LC3-positive autophagosomes generated in the nerve terminals, which then underwent retrograde transport to the cell soma, where they fused with lysosomes both in vitro and in vivo. Blocking autophagosome formation or acidification with wortmannin or bafilomycin A1, respectively, inhibited the activity-dependent retrograde trafficking of BoNT/A-Hc. Our data demonstrate that both the presynaptic formation of autophagosomes and the initiation of their retrograde trafficking are tightly regulated by presynaptic activity
Vortex lattice of a Bose-Einstein Condensate in a rotating anisotropic trap
We study the vortex lattices in a Bose-Einstein Condensate in a rotating
anisotropic harmonic trap. We first investigate the single particle
wavefunctions obtained by the exact solution of the problem and give simple
expressions for these wavefunctions in the small anisotropy limit. Depending on
the strength of the interactions, a few or a large number of vortices can be
formed. In the limit of many vortices, we calculate the density profile of the
cloud and show that the vortex lattice stays triangular. We also find that the
vortex lattice planes align themselves with the weak axis of the external
potential. For a small number of vortices, we numerically solve the
Gross-Pitaevskii equation and find vortex configurations that are very
different from the vortex configurations in an axisymmetric rotating trap.Comment: 15 pages,4 figure
The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate
We study the Gross-Pitaevskii (GP) energy functional for a fast rotating
Bose-Einstein condensate on the unit disc in two dimensions. Writing the
coupling parameter as 1 / \eps^2 we consider the asymptotic regime \eps
\to 0 with the angular velocity proportional to
(\eps^2|\log\eps|)^{-1} . We prove that if \Omega = \Omega_0
(\eps^2|\log\eps|)^{-1} and then a minimizer of
the GP energy functional has no zeros in an annulus at the boundary of the disc
that contains the bulk of the mass. The vorticity resides in a complementary
`hole' around the center where the density is vanishingly small. Moreover, we
prove a lower bound to the ground state energy that matches, up to small
errors, the upper bound obtained from an optimal giant vortex trial function,
and also that the winding number of a GP minimizer around the disc is in accord
with the phase of this trial function.Comment: 52 pages, PDFLaTex. Minor corrections, sign convention modified. To
be published in Commun. Math. Phy
- …