165 research outputs found
Asymptotic behaviour of the probability density in one dimension
We demonstrate that the probability density of a quantum state moving freely
in one dimension may decay faster than 1/t. Inverse quadratic and cubic
dependences are illustrated with analytically solvable examples. Decays faster
than 1/t allow the existence of dwell times and delay times.Comment: 5 pages, one eps figure include
Atomic time-of-arrival measurements with a laser of finite beam width
A natural approach to measure the time of arrival of an atom at a spatial
region is to illuminate this region with a laser and detect the first
fluorescence photons produced by the excitation of the atom and subsequent
decay. We investigate the actual physical content of such a measurement in
terms of atomic dynamical variables, taking into account the finite width of
the laser beam. Different operation regimes are identified, in particular the
ones in which the quantum current density may be obtained.Comment: 7 figure
Quantum optical time-of-arrival model in three dimensions
We investigate the three-dimensional formulation of a recently proposed
operational arrival-time model. It is shown that within typical conditions for
optical transitions the results of the simple one-dimensional version are
generally valid. Differences that may occur are consequences of Doppler and
momentum-transfer effects. Ways to minimize these are discussed.Comment: 14 pages, 5 figure
Bohmian transmission and reflection dwell times without trajectory sampling
Within the framework of Bohmian mechanics dwell times find a straightforward
formulation. The computation of associated probabilities and distributions
however needs the explicit knowledge of a relevant sample of trajectories and
therefore implies formidable numerical effort. Here a trajectory free
formulation for the average transmission and reflection dwell times within
static spatial intervals [a,b] is given for one-dimensional scattering
problems. This formulation reduces the computation time to less than 5% of the
computation time by means of trajectory sampling.Comment: 14 pages, 7 figures; v2: published version, significantly revised and
shortened (former sections 2 and 3 omitted, appendix A added, simplified
mathematics
Optimal atomic detection by control of detuning and spatial dependence of laser intensity
Atomic detection by fluorescence may fail because of reflection from the
laser or transmission without excitation. The detection probability for a given
velocity range may be improved by controlling the detuning and the spatial
dependence of the laser intensity. A simple optimization method is discussed
and exemplified
Ultra-fast propagation of Schr\"odinger waves in absorbing media
We identify the characteristic times of the evolution of a quantum wave
generated by a point source with a sharp onset in an absorbing medium. The
"traversal'' or "B\"uttiker-Landauer'' time (which grows linearly with the
distance to the source) for the Hermitian, non-absorbing case is substituted by
three different characteristic quantities. One of them describes the arrival of
a maximum of the density calculated with respect to position, but the maximum
with respect to time for a given position becomes independent of the distance
to the source and is given by the particle's ``survival time'' in the medium.
This later effect, unlike the Hartman effect, occurs for injection frequencies
under or above the cut-off, and for arbitrarily large distances. A possible
physical realization is proposed by illuminating a two-level atom with a
detuned laser
Improvement by laser quenching of an "atom diode": a one-way barrier for ultra-cold atoms
Different laser devices working as ``atom diodes'' or ``one-way barriers''
for ultra-cold atoms have been proposed recently. They transmit ground state
level atoms coming from one side, say from the left, but reflect them when they
come from the other side. We combine a previous model, consisting of the
stimulated Raman adiabatic passage (STIRAP) from the ground to an excited state
and a state-selective mirror potential, with a localized quenching laser which
produces spontaneous decay back to the ground state. This avoids backwards
motion, provides more control of the decay process and therefore a more compact
and useful device.Comment: 6 page
Bohmian arrival time without trajectories
The computation of detection probabilities and arrival time distributions
within Bohmian mechanics in general needs the explicit knowledge of a relevant
sample of trajectories. Here it is shown how for one-dimensional systems and
rigid inertial detectors these quantities can be computed without calculating
any trajectories. An expression in terms of the wave function and its spatial
derivative, both restricted to the boundary of the detector's spacetime volume,
is derived for the general case, where the probability current at the
detector's boundary may vary its sign.Comment: 20 pages, 12 figures; v2: reference added, extended introduction,
published versio
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