222 research outputs found

### Causality, delocalization and positivity of energy

In a series of interesting papers G. C. Hegerfeldt has shown that quantum
systems with positive energy initially localized in a finite region,
immediately develop infinite tails. In our paper Hegerfeldt's theorem is
analysed using quantum and classical wave packets. We show that Hegerfeldt's
conclusion remains valid in classical physics. No violation of Einstein's
causality is ever involved. Using only positive frequencies, complex wave
packets are constructed which at $t = 0$ are real and finitely localized and
which, furthemore, are superpositions of two nonlocal wave packets. The
nonlocality is initially cancelled by destructive interference. However this
cancellation becomes incomplete at arbitrary times immediately afterwards. In
agreement with relativity the two nonlocal wave packets move with the velocity
of light, in opposite directions.Comment: 14 pages, 5 figure

### Cooperative quantum jumps for three dipole-interacting atoms

We investigate the effect of the dipole-dipole interaction on the quantum
jump statistics of three atoms. This is done for three-level systems in a V
configuration and in what may be called a D configuration. The transition rates
between the four different intensity periods are calculated in closed form.
Cooperative effects are shown to increase by a factor of 2 compared to two of
either three-level systems. This results in transition rates that are, for
distances of about one wavelength of the strong transition, up to 100% higher
than for independent systems. In addition the double and triple jump rates are
calculated from the transition rates. In this case cooperative effects of up to
170% for distances of about one wavelength and still up to 15% around 10
wavelengths are found. Nevertheless, for the parameters of an experiment with
Hg+ ions the effects are negligible, in agreement with the experimental data.
For three Ba+ ions this seems to indicate that the large cooperative effects
observed experimentally cannot be explained by the dipole-dipole interaction.Comment: 9 pages, 9 figures. Revised version, to be published in PR

### Symmetries and time operators

All covariant time operators with normalized probability distribution are
derived. Symmetry criteria are invoked to arrive at a unique expression for a
given Hamiltonian. As an application, a well known result for the arrival time
distribution of a free particle is generalized and extended. Interestingly, the
resulting arrival time distribution operator is connected to a particular,
positive, quantization of the classical current. For particles in a potential
we also introduce and study the notion of conditional arrival-time
distribution

### New classical properties of quantum coherent states

A noncommutative version of the Cramer theorem is used to show that if two quantum systems are prepared independently, and if their center of mass is found to be in a coherent state, then each of the component systems is also in a coherent state, centered around the position in phase space predicted by the classical theory. Thermal coherent states are also shown to possess properties similar to classical ones

### Discriminating between the von Neumann and L\"uders reduction rule

Given an ensemble of systems in an unknown state, as well as an observable
$\hat A$ and a physical apparatus which performs a measurement of $\hat A$ on
the ensemble, whose detailed working is unknown ('black box'), how can one test
whether the L\"uders or von Neumann reduction rule applies?Comment: 5 page

### Passage-time distributions from a spin-boson detector model

The passage-time distribution for a spread-out quantum particle to traverse a
specific region is calculated using a detailed quantum model for the detector
involved. That model, developed and investigated in earlier works, is based on
the detected particle's enhancement of the coupling between a collection of
spins (in a metastable state) and their environment. We treat the continuum
limit of the model, under the assumption of the Markov property, and calculate
the particle state immediately after the first detection. An explicit example
with 15 boson modes shows excellent agreement between the discrete model and
the continuum limit. Analytical expressions for the passage-time distribution
as well as numerical examples are presented. The precision of the measurement
scheme is estimated and its optimization discussed. For slow particles, the
precision goes like $E^{-3/4}$, which improves previous $E^{-1}$ estimates,
obtained with a quantum clock model.Comment: 11 pages, 6 figures; minor changes, references corrected; accepted
for publication in Phys. Rev.

### A wave-function Monte Carlo method for simulating conditional master equations

Wave-function Monte Carlo methods are an important tool for simulating
quantum systems, but the standard method cannot be used to simulate decoherence
in continuously measured systems. Here we present a new Monte Carlo method for
such systems. This was used to perform the simulations of a continuously
measured nano-resonator in [Phys. Rev. Lett. 102, 057208 (2009)].Comment: 4 pages, revtex 4, 1 eps figure. v2: correction to Eqs (3),(9), and
(11); v3 added further informatio

### Double jumps and transition rates for two dipole-interacting atoms

Cooperative effects in the fluorescence of two dipole-interacting atoms, with
macroscopic quantum jumps (light and dark periods), are investigated. The
transition rates between different intensity periods are calculated in closed
form and are used to determine the rates of double jumps between periods of
double intensity and dark periods, the mean duration of the three intensity
periods and the mean rate of their occurrence. We predict, to our knowledge for
the first time, cooperative effects for double jumps, for atomic distances from
one and to ten wave lengths of the strong transition. The double jump rate, as
a function of the atomic distance, can show oscillations of up to 30% at
distances of about a wave length, and oscillations are still noticeable at a
distance of ten wave lengths. The cooperative effects of the quantities and
their characteristic behavior turn out to be strongly dependent on the laser
detuning.Comment: Substantially revised versio

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