325 research outputs found
Fast generation of spin-squeezed states in bosonic Josephson junctions
We describe methods for fast production of highly coherent-spin-squeezed
many-body states in bosonic Josephson junctions (BJJs). We start from the known
mapping of the two-site Bose-Hubbard (BH) Hamiltonian to that of a single
effective particle evolving according to a Schr\"odinger-like equation in Fock
space. Since, for repulsive interactions, the effective potential in Fock space
is nearly parabolic, we extend recently derived protocols for shortcuts to
adiabatic evolution in harmonic potentials to the many-body BH Hamiltonian. The
best scaling of the squeezing parameter for large number of atoms N is \xi^2_S
~ 1/N.Comment: Improved and enlarged version, accepted at Phys. Rev.
A measurement-based approach to quantum arrival times
For a quantum-mechanically spread-out particle we investigate a method for
determining its arrival time at a specific location. The procedure is based on
the emission of a first photon from a two-level system moving into a
laser-illuminated region. The resulting temporal distribution is explicitly
calculated for the one-dimensional case and compared with axiomatically
proposed expressions. As a main result we show that by means of a deconvolution
one obtains the well known quantum mechanical probability flux of the particle
at the location as a limiting distribution.Comment: 11 pages, 4 figures, submitted to Phys. Rev.
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
Operator normalized quantum arrival times in the presence of interactions
We model ideal arrival-time measurements for free quantum particles and for
particles subject to an external interaction by means of a narrow and weak
absorbing potential. This approach is related to the operational approach of
measuring the first photon emitted from a two-level atom illuminated by a
laser. By operator-normalizing the resulting time-of-arrival distribution, a
distribution is obtained which for freely moving particles not only recovers
the axiomatically derived distribution of Kijowski for states with purely
positive momenta but is also applicable to general momentum components. For
particles interacting with a square barrier the mean arrival time and
corresponding ``tunneling time'' obtained at the transmission side of the
barrier becomes independent of the barrier width (Hartman effect) for
arbitrarily wide barriers, i.e., without the transition to the ultra-opaque,
classical-like regime dominated by wave packet components above the barrier.Comment: 10 pages, 5 figures, RevTe
Measurement as Absorption of Feynman Trajectories: Collapse of the Wave Function Can be Avoided
We define a measuring device (detector) of the coordinate of quantum particle
as an absorbing wall that cuts off the particle's wave function. The wave
function in the presence of such detector vanishes on the detector. The trace
the absorbed particles leave on the detector is identifies as the absorption
current density on the detector. This density is calculated from the solution
of Schr\"odinger's equation with a reflecting boundary at the detector. This
current density is not the usual Schr\"odinger current density. We define the
probability distribution of the time of arrival to a detector in terms of the
absorption current density. We define coordinate measurement by an absorbing
wall in terms of 4 postulates. We postulate, among others, that a quantum
particle has a trajectory. In the resulting theory the quantum mechanical
collapse of the wave function is replaced with the usual collapse of the
probability distribution after observation. Two examples are presented, that of
the slit experiment and the slit experiment with absorbing boundaries to
measure time of arrival. A calculation is given of the two dimensional
probability density function of a free particle from the measurement of the
absorption current on two planes.Comment: 20 pages, latex, no figure
Ramsey interferometry with oppositely detuned fields
We report a narrowing of the interference pattern obtained in an atomic
Ramsey interferometer if the two separated fields have different frequency and
their phase difference is controlled. The width of the Ramsey fringes depends
inversely on the free flight time of ground state atoms before entering the
first field region in addition to the time between the fields. The effect is
stable also for atomic wavepackets with initial position and momentum
distributions and for realistic mode functions.Comment: 6 pages, 6 figure
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
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
Ambiguities of arrival-time distributions in quantum theory
We consider the definition that might be given to the time at which a
particle arrives at a given place, both in standard quantum theory and also in
Bohmian mechanics. We discuss an ambiguity that arises in the standard theory
in three, but not in one, spatial dimension.Comment: LaTex, 12 pages, no figure
Scattering of two-level atoms by delta lasers: Exactly solvable models in atom optics
We study the scattering of two-level atoms at narrow laser fields, modeled by
a -shape intensity profile. The unique properties of these potentials
allow us to give simple analytic solutions for one or two field zones. Several
applications are studied: a single -laser may serve as a detector model
for atom detection and arrival-time measurements, either by means of
fluorescence or variations in occupation probabilities. We show that, in
principle, this ideal detector can measure the particle density, the quantum
mechanical flux, arrival time distributions or local kinetic energy densities.
Moreover, two spatially separated -lasers are used to investigate
quantized-motion effects on Ramsey interferometry.Comment: 11 pages, 5 figure
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