748 research outputs found
Quantum dynamics of Bose-Hubbard Hamiltonians beyond Hartree-Fock-Bogoliubov: The Bogoliubov backreaction approximation
e formulate a method for studying the quantum field dynamics of ultracold
Bose gases confined within optical lattice potentials, within the lowest
Bloch-band Bose-Hubbard model. Our formalism extends the two-sites results of
Phys. Rev. Lett. {\bf86}, 000568 (2001) to the general case of lattice
sites. The methodology is based on mapping the Bose-Hubbard Hamiltonian to an
pseudospin problem and truncating the resulting hierarchy of dynamical
equations for correlation functions, up to pair-correlations between
generators. Agreement with few-site exact many-particle calculations is
consistently better than the corresponding Hartree-Fock-Bogoliubov
approximation. Moreover, our approximation compares favorably with a more
elaborate two-particle irreducible effective action formalism, at a fraction of
the analytic and numerical effort.Comment: 8 pages, 7 figure
Vortex solitons in dipolar Bose-Einstein Condensates
We predict solitary vortices in quasi-planar condensates of dipolar atoms,
polarized parallel to the confinement direction, with the effective sign of the
dipole-dipole interaction inverted by means of a rapidly rotating field. Energy
minima corresponding to vortex solitons with topological charges {% \ell}=1
and 2 are predicted for moderately strong dipole-dipole interaction, using an
axisymmetric Gaussian ansatz. The stability of the solitons with is
confirmed by full 3D simulations, whereas their counterparts with are
found to be unstable against splitting into a set of four fragments
(quadrupole).Comment: 6 pages, 6 figure
Robust sub-shot-noise measurement via Rabi-Josephson oscillations in bimodal Bose-Einstein condensates
Mach-Zehnder atom interferometry requires hold-time phase-squeezing to attain
readout accuracy below the standard quantum limit. This increases its
sensitivity to phase-diffusion, restoring shot-noise scaling of the optimal
signal-to-noise ratio, , in the presence of interactions. The
contradiction between the preparations required for readout accuracy and
robustness to interactions, is removed by monitoring Rabi-Josephson
oscillations instead of relative-phase oscillations during signal acquisition.
Optimizing with a Gaussian squeezed input, we find that hold-time number
squeezing satisfies both demands and that sub-shot-noise scaling is retained
even for strong interactions.Comment: 6 pages, 4 figure
Synchronization with mismatched synaptic delays: A unique role of elastic neuronal latency
We show that the unavoidable increase in neuronal response latency to ongoing
stimulation serves as a nonuniform gradual stretching of neuronal circuit delay
loops and emerges as an essential mechanism in the formation of various types
of neuronal timers. Synchronization emerges as a transient phenomenon without
predefined precise matched synaptic delays. These findings are described in an
experimental procedure where conditioned stimulations were enforced on a
circuit of neurons embedded within a large-scale network of cortical cells
in-vitro, and are corroborated by neuronal simulations. They evidence a new
cortical timescale based on tens of microseconds stretching of neuronal circuit
delay loops per spike, and with realistic delays of a few milliseconds,
synchronization emerges for a finite fraction of neuronal circuit delays.Comment: 12 pages, 4 figures, 13 pages of Supplementary materia
Many-body effects on adiabatic passage through Feshbach resonances
We theoretically study the dynamics of an adiabatic sweep through a Feshbach
resonance, thereby converting a degenerate quantum gas of fermionic atoms into
a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero
temperature mean-field theory which accurately accounts for initial molecular
quantum fluctuations, triggering the association process. The structure of the
resulting semiclassical phase space is investigated, highlighting the dynamical
instability of the system towards association, for sufficiently small detuning
from resonance. It is shown that this instability significantly modifies the
finite-rate efficiency of the sweep, transforming the single-pair exponential
Landau-Zener behavior of the remnant fraction of atoms Gamma on sweep rate
alpha, into a power-law dependence as the number of atoms increases. The
obtained nonadiabaticity is determined from the interplay of characteristic
time scales for the motion of adiabatic eigenstates and for fast periodic
motion around them. Critical slowing-down of these precessions near the
instability leads to the power-law dependence. A linear power law is obtained when the initial molecular fraction is smaller than the 1/N
quantum fluctuations, and a cubic-root power law is
attained when it is larger. Our mean-field analysis is confirmed by exact
calculations, using Fock-space expansions. Finally, we fit experimental low
temperature Feshbach sweep data with a power-law dependence. While the
agreement with the experimental data is well within experimental error bars,
similar accuracy can be obtained with an exponential fit, making additional
data highly desirable.Comment: 9 pages, 9 figure
Nonlinear adiabatic passage from fermion atoms to boson molecules
We study the dynamics of an adiabatic sweep through a Feshbach resonance in a
quantum gas of fermionic atoms. Analysis of the dynamical equations, supported
by mean-field and many-body numerical results, shows that the dependence of the
remaining atomic fraction on the sweep rate varies from
exponential Landau-Zener behavior for a single pair of particles to a power-law
dependence for large particle number . The power-law is linear, , when the initial molecular fraction is smaller than the 1/N
quantum fluctuations, and when it is larger.
Experimental data agree better with a linear dependence than with an
exponential Landau-Zener fit, indicating that many-body effects are significant
in the atom-molecule conversion process.Comment: 5 pages, 4 figure
Diluted maximum-likelihood algorithm for quantum tomography
We propose a refined iterative likelihood-maximization algorithm for
reconstructing a quantum state from a set of tomographic measurements. The
algorithm is characterized by a very high convergence rate and features a
simple adaptive procedure that ensures likelihood increase in every iteration
and convergence to the maximum-likelihood state.
We apply the algorithm to homodyne tomography of optical states and quantum
tomography of entangled spin states of trapped ions and investigate its
convergence properties.Comment: v2: Convergence proof adde
Anisotropic solitons in dipolar Bose-Einstein Condensates
Starting with a Gaussian variational ansatz, we predict anisotropic bright
solitons in quasi-2D Bose-Einstein condensates consisting of atoms with dipole
moments polarized \emph{perpendicular} to the confinement direction. Unlike
isotropic solitons predicted for the moments aligned with the confinement axis
[Phys. Rev. Lett. \textbf{95}, 200404 (2005)], no sign reversal of the
dipole-dipole interaction is necessary to support the solitons. Direct 3D
simulations confirm their stability.Comment: 5 pages, 4 figure
Dynamics of a two-mode Bose-Einstein condensate beyond mean-field theory
We study the dynamics of a two-mode Bose-Einstein condensate in the vicinity
of a mean-field dynamical instability. Convergence to mean-field theory (MFT),
with increasing total number of particles , is shown to be logarithmically
slow. Using a density matrix formalism rather than the conventional
wavefunction methods, we derive an improved set of equations of motion for the
mean-field plus the fluctuations, which goes beyond MFT and provides accurate
predictions for the leading quantum corrections and the quantum break time. We
show that the leading quantum corrections appear as decoherence of the reduced
single-particle quantum state; we also compare this phenomenon to the effects
of thermal noise. Using the rapid dephasing near an instability, we propose a
method for the direct measurement of scattering lengths.Comment: 17 pages, 9 figures, Phys. Rev. A 64, 0136XX (2001
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