685 research outputs found
How to prepare quantum states that follow classical paths
We present an alternative quantization procedure for the one-dimensional
non-relativistic quantum mechanics. We show that, for the case of a free
particle and a particle in a box, the complete classical and quantum
correspondence can be obtained using this formulation. The resulting wave
packets do not disperse and strongly peak on the classical paths. Moreover, for
the case of the free particle, they satisfy minimum uncertainty relation.Comment: 10 pages, 3 figures, to appear in Europhysics Letter
Correlations in an expanding gas of hard-core bosons
We consider a longitudinal expansion of a one-dimensional gas of hard-core
bosons suddenly released from a trap. We show that the broken translational
invariance in the initial state of the system is encoded in correlations
between the bosonic occupation numbers in the momentum space. The correlations
are protected by the integrability and exhibit no relaxation during the
expansion
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.
Hubbard ring: currents induced by change of magnetic flux
We investigate currents in a quantum ring threaded by a magnetic flux which
can be varied in an arbitrary way from an initial value at time
to a final value at time . Dynamics of electrons in the ring is
described by the Hubbard and the extended Hubbard models. We demonstrate that
time dependence of the induced current bears information on electron
correlations. In the case of the Hubbard model with infinite on--site repulsion
we prove that the current for is independent of the flux variation
before . Additionally, this current is fully determined by a solution of
the initial equilibrium problem and the value of . Apart from
mesoscopic rings our results pose important implications for designing of
quantum motors built out as the ring--shaped optical lattice
Mesoscopic superposition and sub-Planck-scale structure in molecular wave packets
We demonstrate the possibility of realizing sub-Planck-scale structures in
the mesoscopic superposition of molecular wave packets involving vibrational
levels. The time evolution of the wave packet, taken here as the SU(2) coherent
state of the Morse potential describing hydrogen iodide molecules, produces
macroscopicquantum- superposition-like states, responsible for the above
phenomenon. We investigate the phase-space dynamics of the coherent state
through the Wigner function approach and identify the interference phenomena
behind the sub-Planck-scale structures. The optimal parameter ranges are
specified for observing these features.Comment: 4 pages, 3 figure
Production of high energy particles in laser and Coulomb fields and e^+e^- antenna
A strong laser field and the Coulomb field of a nucleus can produce
e^{+}e^{-} pairs. It is shown for the first time that there is a large
probability that electrons and positrons created in this process collide after
one or several oscillations of the laser field. These collisions can take place
at high energy resulting in several phenomena. The quasielastic collision
e^{+}e^{-} -> e^{+}e^{-} allows acceleration of leptons in the laser field to
higher energies. The inelastic collisions allow production of high energy
photons e^{+}e^{-}-> 2 gamma and muons, e^{+}e^{-} -> mu^{+}mu^{-}. The yield
of high-energy photons and muons produced via this mechanism exceeds
exponentially their production through conventional direct creation in laser
and Coulomb fields. A relation of the phenomena considered with the
antenna-mechanism of multiphoton absorption in atoms is discussed.Comment: 4 page
Reformulation of the strong-field approximation for light-matter interactions
We consider the interaction of hydrogen-like atoms with a strong laser field
and show that the strong field approximation and all its variants may be
grouped into a set of families of approximation schemes. This is done by
introducing an ansatz describing the electron wave packet as the sum of the
initial state wave function times a phase factor and a function which is the
perturbative solution in the Coulomb potential of an inhomogeneous
time-dependent Schr\"odinger equation. It is the phase factor that
characterizes a given family. In each of these families, the velocity and
length gauge version of the approximation scheme lead to the same results at
each order in the Coulomb potential. By contrast, irrespective of the gauge,
approximation schemes belonging to different families give different results.
Furthermore, this new formulation of the strong field approximations allows us
to gain deeper insight into the validity of the strong field approximation
schemes. In particular, we address two important questions: the role of the
Coulomb potential in the output channel and the convergence of the perturbative
series in the Coulomb potential. In all the physical situations we consider
here, our results are compared to those obtained by solving numerically the
time-dependent Schr\"odinger equation.Comment: 19 pages, 9 figures, submitted for publicatio
Joint measurements via quantum cloning
We explore the possibility of achieving optimal joint measurements of
noncommuting observables on a single quantum system by performing conventional
measurements of commuting self adjoint operators on optimal clones of the
original quantum system. We consider the case of both finite dimensional and
infinite dimensional Hilbert spaces. In the former we study the joint
measurement of three orthogonal components of a spin 1/2, in the latter we
consider the case of the joint measurements of any pair of noncommuting
quadratures of one mode of the electromagnetic field. We show that universally
covariant cloning is not ideal for joint measurements, and a suitable non
universally covariant cloning is needed.Comment: 8 page
Momentum Analysis in Strong-field Double Ionization
We provide a basis for the laser intensity dependence of the momentum
distributions of electrons and ions arising from strong-field non-sequential
double ionization (NSDI) at intensities in the range . To do this we use a completely classical method introduced previously
\cite{ho-etal05}. Our calculated results reproduce the features of experimental
observations at different laser intensities and depend on just two distinct
categories of electon trajectories.Comment: 5 pages, 7 figure
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
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