904 research outputs found
Classical-quantum correspondence in bosonic two-mode conversion systems: polynomial algebras and Kummer shapes
Bosonic quantum conversion systems can be modeled by many-particle
single-mode Hamiltonians describing a conversion of molecules of type A
into molecules of type B and vice versa. These Hamiltonians are analyzed in
terms of generators of a polynomially deformed algebra. In the
mean-field limit of large particle numbers, these systems become classical and
their Hamiltonian dynamics can again be described by polynomial deformations of
a Lie algebra, where quantum commutators are replaced by Poisson brackets. The
Casimir operator restricts the motion to Kummer shapes, deformed Bloch spheres
with cusp singularities depending on and . It is demonstrated that the
many-particle eigenvalues can be recovered from the mean-field dynamics using a
WKB type quantization condition. The many-particle state densities can be
semiclassically approximated by the time-periods of periodic orbits, which show
characteristic steps and singularities related to the fixed points, whose
bifurcation properties are analyzed.Comment: 13 pages, 13 figure
Quantum transport and localization in biased periodic structures under bi- and polychromatic driving
We consider the dynamics of a quantum particle in a one-dimensional periodic
potential (lattice) under the action of a static and time-periodic field. The
analysis is based on a nearest-neighbor tight-binding model which allows a
convenient closed form description of the transport properties in terms of
generalized Bessel functions. The case of bichromatic driving is analyzed in
detail and the intricate transport and localization phenomena depending on the
communicability of the two excitation frequencies and the Bloch frequency are
discussed. The case of polychromatic driving is also discussed, in particular
for flipped static fields, i.e. rectangular pulses, which can support an almost
dispersionless transport with a velocity independent of the field amplitude.Comment: 18 pages, 11 figur
Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices
Many features of Bloch oscillations in one-dimensional quantum lattices with
a static force can be described by quasiclassical considerations for example by
means of the acceleration theorem, at least for Hermitian systems. Here the
quasiclassical approach is extended to non-Hermitian lattices, which are of
increasing interest. The analysis is based on a generalised non-Hermitian phase
space dynamics developed recently. Applications to a single-band tight-binding
system demonstrate that many features of the quantum dynamics can be understood
from this classical description qualitatively and even quantitatively. Two
non-Hermitian and -symmetric examples are studied, a Hatano-Nelson lattice
with real coupling constants and a system with purely imaginary couplings, both
for initially localised states in space or in momentum. It is shown that the
time-evolution of the norm of the wave packet and the expectation values of
position and momentum can be described in a classical picture.Comment: 20 pages, 8 figures, typos corrected, slightly extended, accepted for
publication in New Journal of Physics in Focus Issue on Parity-Time Symmetry
in Optics and Photonic
Wannier-Stark resonances in optical and semiconductor superlattices
In this work, we discuss the resonance states of a quantum particle in a
periodic potential plus a static force. Originally this problem was formulated
for a crystal electron subject to a static electric field and it is nowadays
known as the Wannier-Stark problem. We describe a novel approach to the
Wannier-Stark problem developed in recent years. This approach allows to
compute the complex energy spectrum of a Wannier-Stark system as the poles of a
rigorously constructed scattering matrix and solves the Wannier-Stark problem
without any approximation. The suggested method is very efficient from the
numerical point of view and has proven to be a powerful analytic tool for
Wannier-Stark resonances appearing in different physical systems such as
optical lattices or semiconductor superlattices.Comment: 94 pages, 41 figures, typos corrected, references adde
Bloch oscillations of cold atoms in optical lattices
This work is devoted to Bloch oscillations (BO) of cold neutral atoms in
optical lattices. After a general introduction to the phenomenon of BO and its
realization in optical lattices, we study different extentions of this problem,
which account for recent developments in this field. These are two-dimensional
BO, decoherence of BO, and BO in correlated systems. Although these problems
are discussed in relation to the system of cold atoms in optical lattices, many
of the results are of general validity and can be well applied to other systems
showing the phenomenon of BO.Comment: submitted to the review section of IJMPB, few misprints are correcte
Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
We investigate an -particle Bose-Hubbard dimer with an additional
effective decay term in one of the sites. A mean-field approximation for this
non-Hermitian many-particle system is derived, based on a coherent state
approximation. The resulting nonlinear, non-Hermitian two-level dynamics, in
particular the fixed point structures showing characteristic modifications of
the self-trapping transition, are analyzed. The mean-field dynamics is found to
be in reasonable agreement with the full many-particle evolution.Comment: 4 pages, 3 figures, published versio
A quantum cable car for Wannier-Stark ladders
The paper studies the dynamics of transitions between the levels of a Wannier-Stark ladder induced by a resonant periodic driving. The analysis of the problem is done in terms of resonance quasienergy states, which take into account the metastable character of the Wannier-Stark states. It is shown that the periodic driving creates from a localized Wannier-Stark state an extended Bloch-like state with a spatial length varying in time as ~ t^1/2. Such a state can find applications in the field of atomic optics because it generates a coherent pulsed atomic beam
Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model
The dynamics of M-site, N-particle Bose-Hubbard systems is described in
quantum phase space constructed in terms of generalized SU(M) coherent states.
These states have a special significance for these systems as they describe
fully condensed states. Based on the differential algebra developed by Gilmore,
we derive an explicit evolution equation for the (generalized) Husimi-(Q)- and
Glauber-Sudarshan-(P)-distributions. Most remarkably, these evolution equations
turn out to be second order differential equations where the second order terms
scale as 1/N with the particle number. For large N the evolution reduces to a
(classical) Liouvillian dynamics. The phase space approach thus provides a
distinguished instrument to explore the mean-field many-particle crossover. In
addition, the thermodynamic Bloch equation is analyzed using similar
techniques.Comment: 11 pages, Revtex
Evidence for a Single-Spin Azimuthal Asymmetry in Semi-inclusive Pion Electroproduction
Single-spin asymmetries for semi-inclusive pion production in deep-inelastic scattering have been measured for the first time. A significant target-spin asymmetry of the distribution in the azimuthal angle φ of the pion relative to the lepton scattering plane was formed for π^+ electroproduction on a longitudinally polarized hydrogen target. The corresponding analyzing power in the sinφ moment of the cross section is 0.022±0.005±0.003. This result can be interpreted as the effect of terms in the cross section involving chiral-odd spin distribution functions in combination with a chiral-odd fragmentation function that is sensitive to the transverse polarization of the fragmenting quark
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