55 research outputs found
Causality, particle localization and positivity of the energy
Positivity of the Hamiltonian alone is used to show that particles, if
initially localized in a finite region, immediately develop infinite tails.Comment: To appear in: Irreversibility and Causality in Quantum Theory --
Semigroups and Rigged Hilbert Spaces, edited by A. Bohm, H.-D. Doebner and P.
Kielanowski, Springer Lecture Notes in Physics, Vol. 504 (1998
Cooperative fluorescence effects for dipole-dipole interacting systems with experimentally relevant level configurations
The mutual dipole-dipole interaction of atoms in a trap can affect their
fluorescence. Extremely large effects were reported for double jumps between
different intensity periods in experiments with two and three Ba^+ ions for
distances in the range of about ten wave lengths of the strong transition while
no effects were observed for Hg^+ at 15 wave lengths. In this theoretical paper
we study this question for configurations with three and four levels which
model those of Hg^+ and Ba^+, respectively. For two systems in the Hg^+
configuration we find cooperative effects of up to 30% for distances around one
or two wave lengths, about 5% around ten wave lengths, and, for larger
distances in agreement with experiments, practically none. This is similar for
two V systems. However, for two four-level configurations, which model two Ba^+
ions, cooperative effects are practically absent, and this latter result is at
odds with the experimental findings for Ba^+.Comment: 9 pages, 5 figures, RevTeX4, to be published in Phys. Rev.
Projection Postulate and Atomic Quantum Zeno Effect
The projection postulate has been used to predict a slow-down of the time
evolution of the state of a system under rapidly repeated measurements, and
ultimately a freezing of the state. To test this so-called quantum Zeno effect
an experiment was performed by Itano et al. (Phys. Rev. A 41, 2295 (1990)) in
which an atomic-level measurement was realized by means of a short laser pulse.
The relevance of the results has given rise to controversies in the literature.
In particular the projection postulate and its applicability in this experiment
have been cast into doubt. In this paper we show analytically that for a wide
range of parameters such a short laser pulse acts as an effective level
measurement to which the usual projection postulate applies with high accuracy.
The corrections to the ideal reductions and their accumulation over n pulses
are calculated. Our conclusion is that the projection postulate is an excellent
pragmatic tool for a quick and simple understanding of the slow-down of time
evolution in experiments of this type. However, corrections have to be
included, and an actual freezing does not seem possible because of the finite
duration of measurements.Comment: 25 pages, LaTeX, no figures; to appear in Phys. Rev.
Equivalent classes of closed three-level systems
Published versio
Hidden Quantum Markov Models and Open Quantum Systems with Instantaneous Feedback
Hidden Markov Models are widely used in classical computer science to model
stochastic processes with a wide range of applications. This paper concerns the
quantum analogues of these machines --- so-called Hidden Quantum Markov Models
(HQMMs). Using the properties of Quantum Physics, HQMMs are able to generate
more complex random output sequences than their classical counterparts, even
when using the same number of internal states. They are therefore expected to
find applications as quantum simulators of stochastic processes. Here, we
emphasise that open quantum systems with instantaneous feedback are examples of
HQMMs, thereby identifying a novel application of quantum feedback control.Comment: 10 Pages, proceedings for the Interdisciplinary Symposium on Complex
Systems in Florence, September 2014, minor correction
Resonance fluorescence of a trapped three-level atom
We investigate theoretically the spectrum of resonance fluorescence of a
harmonically trapped atom, whose internal transitions are --shaped and
driven at two-photon resonance by a pair of lasers, which cool the
center--of--mass motion. For this configuration, photons are scattered only due
to the mechanical effects of the quantum interaction between light and atom. We
study the spectrum of emission in the final stage of laser--cooling, when the
atomic center-of-mass dynamics is quantum mechanical and the size of the wave
packet is much smaller than the laser wavelength (Lamb--Dicke limit). We use
the spectral decomposition of the Liouville operator of the master equation for
the atomic density matrix and apply second order perturbation theory. We find
that the spectrum of resonance fluorescence is composed by two narrow sidebands
-- the Stokes and anti-Stokes components of the scattered light -- while all
other signals are in general orders of magnitude smaller. For very low
temperatures, however, the Mollow--type inelastic component of the spectrum
becomes visible. This exhibits novel features which allow further insight into
the quantum dynamics of the system. We provide a physical model that interprets
our results and discuss how one can recover temperature and cooling rate of the
atom from the spectrum. The behaviour of the considered system is compared with
the resonance fluorescence of a trapped atom whose internal transition consists
of two-levels.Comment: 11 pages, 4 Figure
Resonance Fluorescence Spectrum of a Trapped Ion Undergoing Quantum Jumps
We experimentally investigate the resonance fluorescence spectrum of single
171Yb and 172Yb ions which are laser cooled to the Lamb-Dicke regime in a
radiofrequency trap. While the fluorescence scattering of 172Yb is continuous,
the 171Yb fluorescence is interrupted by quantum jumps because a nonvanishing
rate of spontaneous transitions leads to electron shelving in the metastable
hyperfine sublevel 2D3/2(F=2). The average duration of the resulting dark
periods can be varied by changing the intensity of a repumping laser field.
Optical heterodyne detection is employed to analyze the fluorescence spectrum
near the Rayleigh elastic scattering peak. It is found that the stochastic
modulation of the fluorescence emission by quantum jumps gives rise to a
Lorentzian component in the fluorescence spectrum, and that the linewidth of
this component varies according to the average duration of the dark
fluorescence periods. The experimental observations are in quantitative
agreement with theoretical predictions.Comment: 14 pages including 4 figures, pdf file, fig.1 replace
Dissipation-assisted quantum gates with cold trapped ions
It is shown that a two-qubit phase gate and SWAP operation between ground
states of cold trapped ions can be realised in one step by simultaneously
applying two laser fields. Cooling during gate operations is possible without
perturbing the computation and the scheme does not require a second ion species
for sympathetic cooling. On the contrary, the cooling lasers even stabilise the
desired time evolution of the system. This affords gate operation times of
nearly the same order of magnitude as the inverse coupling constant of the ions
to a common vibrational mode.Comment: 4 pages, 5 figures, substantially revised versio
Microscopic theory of atom-molecule oscillations in a Bose-Einstein condensate
In a recent experiment at JILA [E.A. Donley et al., Nature (London) 417, 529
(2002)] an initially pure condensate of Rb-85 atoms was exposed to a specially
designed time dependent magnetic field pulse in the vicinity of a Feshbach
resonance. The production of new components of the gas as well as their
oscillatory behavior have been reported. We apply a microscopic theory of the
gas to identify these components and determine their physical properties. Our
time dependent studies allow us to explain the observed dynamic evolution of
all fractions, and to identify the physical relevance of the pulse shape. Based
on ab initio predictions, our theory strongly supports the view that the
experiments have produced a molecular condensate.Comment: 18 pages, 20 figure
Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions
This paper is aimed to show the essential role played by the theory of
quasi-analytic functions in the study of the determinacy of the moment problem
on finite and infinite-dimensional spaces. In particular, the quasi-analytic
criterion of self-adjointness of operators and their commutativity are crucial
to establish whether or not a measure is uniquely determined by its moments.
Our main goal is to point out that this is a common feature of the determinacy
question in both the finite and the infinite-dimensional moment problem, by
reviewing some of the most known determinacy results from this perspective. We
also collect some properties of independent interest concerning the
characterization of quasi-analytic classes associated to log-convex sequences.Comment: 28 pages, Stochastic and Infinite Dimensional Analysis, Chapter 9,
Trends in Mathematics, Birkh\"auser Basel, 201
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