17 research outputs found
Quantum shutter approach to tunneling time scales with wave packets
The quantum shutter approach to tunneling time scales (G. Garc\'{\i
}a-Calder\'{o}n and A. Rubio, Phys. Rev. A \textbf{55}, 3361 (1997)), which
uses a cutoff plane wave as the initial condition, is extended in such a way
that a certain type of wave packet can be used as the initial condition. An
analytical expression for the time evolved wave function is derived. The
time-domain resonance, the peaked structure of the probability density (as the
function of time) at the exit of the barrier, originally found with the cutoff
plane wave initial condition, is studied with the wave packet initial
conditions. It is found that the time-domain resonance is not very sensitive to
the width of the packet when the transmission process is in the tunneling
regime.Comment: 6 page
Quantum matter wave dynamics with moving mirrors
When a stationary reflecting wall acting as a perfect mirror for an atomic
beam with well defined incident velocity is suddenly removed, the density
profile develops during the time evolution an oscillatory pattern known as
diffraction in time. The interference fringes are suppressed or their
visibility is diminished by several effects such as averaging over a
distribution of incident velocities, apodization of the aperture function,
atom-atom interactions, imperfect reflection or environmental noise. However,
when the mirror moves with finite velocity along the direction of propagation
of the beam, the visibility of the fringes is enhanced. For mirror velocities
below beam velocity, as used for slowing down the beam, the matter wave splits
into three regions separated by space-time points with classical analogues. For
mirror velocities above beam velocity a visibility enhancement occurs without a
classical counterpart. When the velocity of the beam approaches that of the
mirror the density oscillations rise by a factor 1.8 over the stationary value.Comment: 5.2 pages, 6 figure
Enhanced observability of quantum post-exponential decay using distant detectors
We study the elusive transition from exponential to post-exponential
(algebraic) decay of the probability density of a quantum particle emitted by
an exponentially decaying source, in one dimension. The main finding is that
the probability density at the transition time, and thus its observability,
increases with the distance of the detector from the source, up to a critical
distance beyond which exponential decay is no longer observed. Solvable models
provide explicit expressions for the dependence of the transition on resonance
and observational parameters, facilitating the choice of optimal conditions
Dynamics of a Tonks-Girardeau gas released from a hard-wall trap
We study the expansion dynamics of a Tonks-Girardeau gas released from a hard
wall trap. Using the Fermi-Bose map, the density profile is found analytically
and shown to differ from that one of a classical gas in the microcanonical
ensemble even at macroscopic level, for any observation time larger than a
critical time. The relevant time scale arises as a consequence of
fermionization.Comment: 4 pages, 6 figure
Time dependence of evanescent quantum waves
The time dependence of quantum evanescent waves generated by a point source
with an infinite or a limited frequency band is analyzed. The evanescent wave
is characterized by a forerunner (transient) related to the precise way the
source is switched on. It is followed by an asymptotic, monochromatic wave
which at long times reveals the oscillation frequency of the source. For a
source with a sharp onset the forerunner is exponentially larger than the
monochromatic solution and a transition from the transient regime to the
asymtotic regime occurs only at asymptotically large times. In this case, the
traversal time for tunneling plays already a role only in the transient regime.
To enhance the monochromatic solution compared to the forerunner we investigate
(a) frequency band limited sources and (b) the short time Fourier analysis (the
spectrogram) corresponding to a detector which is frequency band limited.
Neither of these two methods leads to a precise determination of the traversal
time. However, if they are limited to determine the traversal time only with a
precision of the traversal time itself both methods are successful: In this
case the transient behavior of the evanescent waves is at a time of the order
of the traversal time followed by a monochromatic wave which reveals the
frequency of the source.Comment: 16 text pages and 9 postscript figure
Doubly resonant ultrachirped pulses
Ultrachirped pulses for which the frequency chirp is of the order of the
transition frequency of a two-level atom are examined. When the chirp is large
enough, the resonance may be crossed twice, for positive and negative
quadrature frequencies. In this scenario the analytic signal and quadrature
decompositions of the field into amplitude and phase factors turn out to be
quite different. The corresponding interaction pictures are strictly
equivalent, but only as long as approximations are not applied. The domain of
validity of the formal rotating wave approximation is dramatically enhanced
using the analytic signal representation
Exact propagators for atom-laser interactions
A class of exact propagators describing the interaction of an -level atom
with a set of on-resonance -lasers is obtained by means of the Laplace
transform method. State-selective mirrors are described in the limit of strong
lasers. The ladder, V and configurations for a three-level atom are
discussed. For the two level case, the transient effects arising as result of
the interaction between both a semi-infinite beam and a wavepacket with the
on-resonance laser are examined.Comment: 13 pages, 6 figure
Dynamical description of the buildup process in resonant tunneling: Evidence of exponential and non-exponential contributions
The buildup process of the probability density inside the quantum well of a
double-barrier resonant structure is studied by considering the analytic
solution of the time dependent Schr\"{o}dinger equation with the initial
condition of a cutoff plane wave. For one level systems at resonance condition
we show that the buildup of the probability density obeys a simple charging up
law, where is the
stationary wave function and the transient time constant is exactly
two lifetimes. We illustrate that the above formula holds both for symmetrical
and asymmetrical potential profiles with typical parameters, and even for
incidence at different resonance energies. Theoretical evidence of a crossover
to non-exponential buildup is also discussed.Comment: 4 pages, 2 figure
Matter wave pulses characteristics
We study the properties of quantum single-particle wave pulses created by
sharp-edged or apodized shutters with single or periodic openings. In
particular, we examine the visibility of diffraction fringes depending on
evolution time and temperature; the purity of the state depending on the
opening-time window; the accuracy of a simplified description which uses
``source'' boundary conditions instead of solving an initial value problem; and
the effects of apodization on the energy width.Comment: 11 pages, 11 figure
Matter-wave diffraction in time with a linear potential
Diffraction in time of matter waves incident on a shutter which is removed at
time is studied in the presence of a linear potential. The solution is
also discussed in phase space in terms of the Wigner function. An alternative
configuration relevant to current experiments where particles are released from
a hard wall trap is also analyzed for single-particle states and for a
Tonks-Girardeau gas.Comment: 11 pages, 6 figure