39 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
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
An ansatz for the nonlinear Demkov-Kunike problem for cold molecule formation
We study nonlinear mean-field dynamics of ultracold molecule formation in the
case when the external field configuration is defined by the level-crossing
Demkov-Kunike model, characterized by a bell-shaped coupling and finite
variation of the detuning. Analyzing the fast sweep rate regime of the strong
interaction limit, which models a situation when the peak value of the coupling
is large enough and the resonance crossing is sufficiently fast, we construct a
highly accurate ansatz to describe the temporal dynamics of the molecule
formation in the mentioned interaction regime. The absolute error of the
constructed approximation is less than 3*10^-6 for the final transition
probability while at certain time points it might increase up to 10^-3.
Examining the role of the different terms in the constructed approximation, we
prove that in the fast sweep rate regime of the strong interaction limit the
temporal dynamics of the atom-molecule conversion effectively consists of the
process of resonance crossing, which is governed by a nonlinear equation,
followed by atom-molecular coherent oscillations which are basically described
by a solution of the linear problem, associated with the considered nonlinear
one.Comment: Accepted for publication in J. Contemp. Phys. (Armenian National
Academy of Sciences) 8 pages, 4 figure
Demkov-Kunike model for cold atom association: weak interaction regime
We study the nonlinear mean-field dynamics of molecule formation at coherent
photo- and magneto-association of an atomic Bose-Einstein condensate for the
case when the external field configuration is defined by the quasi-linear level
crossing Demkov-Kunike model, characterized by a bell-shaped pulse and finite
variation of the detuning. We present a general approach to construct an
approximation describing the temporal dynamics of the molecule formation in the
weak interaction regime and apply the developed method to the nonlinear
Demkov-Kunike problem. The presented approximation, written as a scaled
solution to the linear problem associated to the nonlinear one we treat,
contains fitting parameters which are determined through a variational
procedure. Assuming that the parameters involved in the solution of the linear
problem are not modified, we suggest an analytical expression for the scaling
parameter.Comment: 6 pages, 4 figure
Weak coupling regime of the Landau-Zener transition for association of an atomic Bose-Einstein condensate
In the framework of a basic semiclassical time-dependent nonlinear two-state
problem, we study the weak coupling limit of the nonlinear Landau-Zener
transition at coherent photo- and magneto-association of an atomic
Bose-Einstein condensate. Using an exact third-order nonlinear differential
equation for the molecular state probability, we develop a variational approach
which enables us to construct an accurate analytic approximation describing
time dynamics of the coupled atom-molecular system for the case of weak
coupling. The approximation is written in terms of the solution to an auxiliary
linear Landau-Zener problem with some effective Landau-Zener parameter. The
dependence of this effective parameter on the input Landau-Zener parameter is
found to be unexpected: as the generic Landau-Zener parameter increases, the
effective Landau-Zener parameter first monotonically increases (starting from
zero), reaches its maximal value and then monotonically decreases again
reaching zero at some point. The constructed approximation quantitatively well
describes many characteristics of the time dynamics of the system, in
particular, it provides a highly accurate formula for the final transition
probability to the molecular state. The present result for the final transition
probability improves the accuracy of the previous approximation by Ishkhanyan
et al. [Phys. Rev. A 69, 043612 (2004); J. Phys. A 38, 3505 (2005)] by order of
magnitude.Comment: 7 pages, 3 figure
Quadratic-nonlinear Landau-Zener transition for association of an atomic Bose-Einstein condensate with inter-particle elastic interactions included
We study the strong coupling limit of a quadratic-nonlinear Landau-Zener
problem for coherent photo- and magneto-association of cold atoms taking into
account the atom-atom, atom-molecule, and molecule-molecule elastic scattering.
Using an exact third-order nonlinear differential equation for the molecular
state probability, we develop a variational approach which enables us to
construct a highly accurate and simple analytic approximation describing the
time dynamics of the coupled atom-molecule system. We show that the
approximation describing time evolution of the molecular state probability can
be written as a sum of two distinct terms; the first one, being a solution to a
limit first-order nonlinear equation, effectively describes the process of the
molecule formation while the second one, being a scaled solution to the linear
Landau-Zener problem (but now with negative effective Landau-Zener parameter as
long as the strong coupling regime is considered), corresponds to the remaining
oscillations which come up when the process of molecule formation is over.Comment: 19 pages, 7 figures, accepted for publication in Eur. Phys. J.