117 research outputs found
Retrodictive states and two-photon quantum imaging
We use retrodictive quantum theory to analyse two-photon quantum imaging
systems. The formalism is particularly suitable for calculating conditional
probability distributions.Comment: 5 pages, 3 figure
The fundamental cycle of concept construction underlying various theoretical frameworks
In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning
Retrodiction with two-level atoms: atomic previvals
In the Jaynes-Cummings model a two-level atom interacts with a single-mode
electromagnetic field. Quantum mechanics predicts collapses and revivals in the
probability that a measurement will show the atom to be excited at various
times after the initial preparation of the atom and field. In retrodictive
quantum mechanics we seek the probability that the atom was prepared in a
particular state given the initial state of the field and the outcome of a
later measurement on the atom. Although this is not simply the time reverse of
the usual predictive problem, we demonstrate in this paper that retrodictive
collapses and revivals also exist. We highlight the differences between
predictive and retrodictive evolutions and describe an interesting situation
where the prepared state is essentially unretrodictable.Comment: 15 pages, 3 (5) figure
Retrodiction as a tool for micromaser field measurements
We use retrodictive quantum theory to describe cavity field measurements by
successive atomic detections in the micromaser. We calculate the state of the
micromaser cavity field prior to detection of sequences of atoms in either the
excited or ground state, for atoms that are initially prepared in the excited
state. This provides the POM elements, which describe such sequences of
measurements.Comment: 20 pages, 4(8) figure
Photodetachment study of the 1s3s4s ^4S resonance in He^-
A Feshbach resonance associated with the 1s3s4s ^{4}S state of He^{-} has
been observed in the He(1s2s ^{3}S) + e^- (\epsilon s) partial photodetachment
cross section. The residual He(1s2s ^{3}S) atoms were resonantly ionized and
the resulting He^+ ions were detected in the presence of a small background. A
collinear laser-ion beam apparatus was used to attain both high resolution and
sensitivity. We measured a resonance energy E_r = 2.959 255(7) eV and a width
\Gamma = 0.19(3) meV, in agreement with a recent calculation.Comment: LaTeX article, 4 pages, 3 figures, 21 reference
Electron affinity of Li: A state-selective measurement
We have investigated the threshold of photodetachment of Li^- leading to the
formation of the residual Li atom in the state. The excited residual
atom was selectively photoionized via an intermediate Rydberg state and the
resulting Li^+ ion was detected. A collinear laser-ion beam geometry enabled
both high resolution and sensitivity to be attained. We have demonstrated the
potential of this state selective photodetachment spectroscopic method by
improving the accuracy of Li electron affinity measurements an order of
magnitude. From a fit to the Wigner law in the threshold region, we obtained a
Li electron affinity of 0.618 049(20) eV.Comment: 5 pages,6 figures,22 reference
Master Equation for Retrodiction of Quantum Communication Signals
We derive the master equation that governs the evolution of the measured
state backwards in time in an open system. This allows us to determine
probabilities for a given set of preparation events from the results of
subsequent measurements, which has particular relevance to quantum
communication.Comment: 14 pages, no figure
Toy Model for a Relational Formulation of Quantum Theory
In the absence of an external frame of reference physical degrees of freedom
must describe relations between systems. Using a simple model, we investigate
how such a relational quantum theory naturally arises by promoting reference
systems to the status of dynamical entities. Our goal is to demonstrate using
elementary quantum theory how any quantum mechanical experiment admits a purely
relational description at a fundamental level, from which the original
"non-relational" theory emerges in a semi-classical limit. According to this
thesis, the non-relational theory is therefore an approximation of the
fundamental relational theory. We propose four simple rules that can be used to
translate an "orthodox" quantum mechanical description into a relational
description, independent of an external spacial reference frame or clock. The
techniques used to construct these relational theories are motivated by a
Bayesian approach to quantum mechanics, and rely on the noiseless subsystem
method of quantum information science used to protect quantum states against
undesired noise. The relational theory naturally predicts a fundamental
decoherence mechanism, so an arrow of time emerges from a time-symmetric
theory. Moreover, there is no need for a "collapse of the wave packet" in our
model: the probability interpretation is only applied to diagonal density
operators. Finally, the physical states of the relational theory can be
described in terms of "spin networks" introduced by Penrose as a combinatorial
description of geometry, and widely studied in the loop formulation of quantum
gravity. Thus, our simple bottom-up approach (starting from the semi-classical
limit to derive the fully relational quantum theory) may offer interesting
insights on the low energy limit of quantum gravity.Comment: References added, extended discussio
Massively parallel quantum chemistry: PFAS on over 1 million cloud vCPUs
Accurate solutions to the electronic Schr\"odinger equation can provide
valuable insight for electron interactions within molecular systems,
accelerating the molecular design and discovery processes in many different
applications. However, the availability of such accurate solutions are limited
to small molecular systems due to both the extremely high computational
complexity and the challenge of operating and executing these workloads on
high-performance compute clusters. This work presents a massively scalable
cloud-based quantum chemistry platform by implementing a highly parallelizable
quantum chemistry method that provides a polynomial-scaling approximation to
full configuration interaction (FCI). Our platform orchestrates more than one
million virtual CPUs on the cloud to analyze the bond-breaking behaviour of
carbon-fluoride bonds of per- and polyfluoroalkyl substances (PFAS) with
near-exact accuracy within the chosen basis set. This is the first quantum
chemistry calculation utilizing more than one million virtual CPUs on the cloud
and is the most accurate electronic structure computation of PFAS bond breaking
to date
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