737 research outputs found
High-fidelity trapped-ion quantum logic using near-field microwaves
We demonstrate a two-qubit logic gate driven by near-field microwaves in a
room-temperature microfabricated ion trap. We measure a gate fidelity of
99.7(1)\%, which is above the minimum threshold required for fault-tolerant
quantum computing. The gate is applied directly to Ca "atomic clock"
qubits (coherence time ) using the microwave
magnetic field gradient produced by a trap electrode. We introduce a
dynamically-decoupled gate method, which stabilizes the qubits against
fluctuating a.c.\ Zeeman shifts and avoids the need to null the microwave
field
Real clocks and the Zeno effect
Real clocks are not perfect. This must have an effect in our predictions for
the behaviour of a quantum system, an effect for which we present a unified
description encompassing several previous proposals. We study the relevance of
clock errors in the Zeno effect, and find that generically no Zeno effect can
be present (in such a way that there is no contradiction with currently
available experimental data). We further observe that, within the class of
stochasticities in time addressed here, there is no modification in emission
lineshapes.Comment: 12 a4 pages, no figure
Examining Neolithic Building and Activity Areas through Historic Cultural Heritage in Jordan: A Combined Ethnographic, Phytolith and Geochemical Investigation
The INEA project (Identifying activity areas in Neolithic
sites through Ethnographic Analysis of phytoliths and
geochemical residues, https://research.bournemouth.
ac.uk/2014/07/inea-project-2/) develops and applies
a method that combines the analysis of plant remains
(silica phytoliths) and geochemical residues to inform
on construction methods and the use of space in recently
abandoned historical villages and Neolithic settlements. It
is a collaborative project based at Bournemouth University,
in partnership with the Council for British Research in the
Levant
Free motion time-of-arrival operator and probability distribution
We reappraise and clarify the contradictory statements found in the
literature concerning the time-of-arrival operator introduced by Aharonov and
Bohm in Phys. Rev. {\bf 122}, 1649 (1961). We use Naimark's dilation theorem to
reproduce the generalized decomposition of unity (or POVM) from any
self-adjoint extension of the operator, emphasizing a natural one, which arises
from the analogy with the momentum operator on the half-line. General time
operators are set within a unifying perspective. It is shown that they are not
in general related to the time of arrival, even though they may have the same
form.Comment: 10 a4 pages, no figure
Time-of-arrival in quantum mechanics
We study the problem of computing the probability for the time-of-arrival of
a quantum particle at a given spatial position. We consider a solution to this
problem based on the spectral decomposition of the particle's (Heisenberg)
state into the eigenstates of a suitable operator, which we denote as the
``time-of-arrival'' operator. We discuss the general properties of this
operator. We construct the operator explicitly in the simple case of a free
nonrelativistic particle, and compare the probabilities it yields with the ones
estimated indirectly in terms of the flux of the Schr\"odinger current. We
derive a well defined uncertainty relation between time-of-arrival and energy;
this result shows that the well known arguments against the existence of such a
relation can be circumvented. Finally, we define a ``time-representation'' of
the quantum mechanics of a free particle, in which the time-of-arrival is
diagonal. Our results suggest that, contrary to what is commonly assumed,
quantum mechanics exhibits a hidden equivalence between independent (time) and
dependent (position) variables, analogous to the one revealed by the
parametrized formalism in classical mechanics.Comment: Latex/Revtex, 20 pages. 2 figs included using epsf. Submitted to
Phys. Rev.
Controlling trapping potentials and stray electric fields in a microfabricated ion trap through design and compensation
Recent advances in quantum information processing with trapped ions have
demonstrated the need for new ion trap architectures capable of holding and
manipulating chains of many (>10) ions. Here we present the design and detailed
characterization of a new linear trap, microfabricated with scalable
complementary metal-oxide-semiconductor (CMOS) techniques, that is well-suited
to this challenge. Forty-four individually controlled DC electrodes provide the
many degrees of freedom required to construct anharmonic potential wells,
shuttle ions, merge and split ion chains, precisely tune secular mode
frequencies, and adjust the orientation of trap axes. Microfabricated
capacitors on DC electrodes suppress radio-frequency pickup and excess
micromotion, while a top-level ground layer simplifies modeling of electric
fields and protects trap structures underneath. A localized aperture in the
substrate provides access to the trapping region from an oven below, permitting
deterministic loading of particular isotopic/elemental sequences via
species-selective photoionization. The shapes of the aperture and
radio-frequency electrodes are optimized to minimize perturbation of the
trapping pseudopotential. Laboratory experiments verify simulated potentials
and characterize trapping lifetimes, stray electric fields, and ion heating
rates, while measurement and cancellation of spatially-varying stray electric
fields permits the formation of nearly-equally spaced ion chains.Comment: 17 pages (including references), 7 figure
Complete moduli of cubic threefolds and their intermediate Jacobians
The intermediate Jacobian map, which associates to a smooth cubic threefold
its intermediate Jacobian, does not extend to the GIT compactification of the
space of cubic threefolds, not even as a map to the Satake compactification of
the moduli space of principally polarized abelian fivefolds. A much better
"wonderful" compactification of the space of cubic threefolds was constructed
by the first and fourth authors --- it has a modular interpretation, and
divisorial normal crossing boundary. We prove that the intermediate Jacobian
map extends to a morphism from the wonderful compactification to the second
Voronoi toroidal compactification of the moduli of principally polarized
abelian fivefolds --- the first and fourth author previously showed that it
extends to the Satake compactification. Since the second Voronoi
compactification has a modular interpretation, our extended intermediate
Jacobian map encodes all of the geometric information about the degenerations
of intermediate Jacobians, and allows for the study of the geometry of cubic
threefolds via degeneration techniques. As one application we give a complete
classification of all degenerations of intermediate Jacobians of cubic
threefolds of torus rank 1 and 2.Comment: 56 pages; v2: multiple updates and clarification in response to
detailed referee's comment
Time in Quantum Mechanics and Quantum Field Theory
W. Pauli pointed out that the existence of a self-adjoint time operator is
incompatible with the semibounded character of the Hamiltonian spectrum. As a
result, people have been arguing a lot about the time-energy uncertainty
relation and other related issues. In this article, we show in details that
Pauli's definition of time operator is erroneous in several respects.Comment: 20 page
Time of arrival in the presence of interactions
We introduce a formalism for the calculation of the time of arrival t at a
space point for particles traveling through interacting media. We develop a
general formulation that employs quantum canonical transformations from the
free to the interacting cases to construct t in the context of the Positive
Operator Valued Measures. We then compute the probability distribution in the
times of arrival at a point for particles that have undergone reflection,
transmission or tunneling off finite potential barriers. For narrow Gaussian
initial wave packets we obtain multimodal time distributions of the reflected
packets and a combination of the Hartman effect with unexpected retardation in
tunneling. We also employ explicitly our formalism to deal with arrivals in the
interaction region for the step and linear potentials.Comment: 20 pages including 5 eps figure
Localization of Events in Space-Time
The present paper deals with the quantum coordinates of an event in
space-time, individuated by a quantum object. It is known that these
observables cannot be described by self-adjoint operators or by the
corresponding spectral projection-valued measure. We describe them by means of
a positive-operator-valued (POV) measure in the Minkowski space-time,
satisfying a suitable covariance condition with respect to the Poincare' group.
This POV measure determines the probability that a measurement of the
coordinates of the event gives results belonging to a given set in space-time.
We show that this measure must vanish on the vacuum and the one-particle
states, which cannot define any event. We give a general expression for the
Poincare' covariant POV measures. We define the baricentric events, which lie
on the world-line of the centre-of-mass, and we find a simple expression for
the average values of their coordinates. Finally, we discuss the conditions
which permit the determination of the coordinates with an arbitrary accuracy.Comment: 31 pages, latex, no figure
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