32 research outputs found
Measurement of Time-of-Arrival in Quantum Mechanics
It is argued that the time-of-arrival cannot be precisely defined and
measured in quantum mechanics. By constructing explicit toy models of a
measurement, we show that for a free particle it cannot be measured more
accurately then , where is the initial kinetic
energy of the particle. With a better accuracy, particles reflect off the
measuring device, and the resulting probability distribution becomes distorted.
It is shown that a time-of-arrival operator cannot exist, and that approximate
time-of-arrival operators do not correspond to the measurements considered
here.Comment: References added. To appear in Phys. Rev.
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
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 distributions from position-momentum and energy-time joint measurements
The position-momentum quasi-distribution obtained from an Arthurs and Kelly
joint measurement model is used to obtain indirectly an ``operational''
time-of-arrival (TOA) distribution following a quantization procedure proposed
by Kocha\'nski and W\'odkiewicz [Phys. Rev. A 60, 2689 (1999)]. This TOA
distribution is not time covariant. The procedure is generalized by using other
phase-space quasi-distributions, and sufficient conditions are provided for
time covariance that limit the possible phase-space quasi-distributions
essentially to the Wigner function, which, however, provides a non-positive TOA
quasi-distribution. These problems are remedied with a different quantization
procedure which, on the other hand, does not guarantee normalization. Finally
an Arthurs and Kelly measurement model for TOA and energy (valid also for
arbitrary conjugate variables when one of the variables is bounded from below)
is worked out. The marginal TOA distribution so obtained, a distorted version
of Kijowski's distribution, is time covariant, positive, and normalized
Time-of-Arrival States
Although one can show formally that a time-of-arrival operator cannot exist,
one can modify the low momentum behaviour of the operator slightly so that it
is self-adjoint. We show that such a modification results in the difficulty
that the eigenstates are drastically altered. In an eigenstate of the modified
time-of-arrival operator, the particle, at the predicted time-of-arrival, is
found far away from the point of arrival with probability 1/2.Comment: 15 pages, 2 figure
Spacetime Coarse Grainings in the Decoherent Histories Approach to Quantum Theory
We investigate the possibility of assigning consistent probabilities to sets
of histories characterized by whether they enter a particular subspace of the
Hilbert space of a closed system during a given time interval. In particular we
investigate the case that this subspace is a region of the configuration space.
This corresponds to a particular class of coarse grainings of spacetime
regions. We consider the arrival time problem and the problem of time in
reparametrization invariant theories as for example in canonical quantum
gravity. Decoherence conditions and probabilities for those application are
derived. The resulting decoherence condition does not depend on the explicit
form of the restricted propagator that was problematic for generalizations such
as application in quantum cosmology. Closely related is the problem of
tunnelling time as well as the quantum Zeno effect. Some interpretational
comments conclude, and we discuss the applicability of this formalism to deal
with the arrival time problem.Comment: 23 pages, Few changes and added references in v
Heating rate and electrode charging measurements in a scalable, microfabricated, surface-electrode ion trap
We characterise the performance of a surface-electrode ion "chip" trap
fabricated using established semiconductor integrated circuit and
micro-electro-mechanical-system (MEMS) microfabrication processes which are in
principle scalable to much larger ion trap arrays, as proposed for implementing
ion trap quantum information processing. We measure rf ion micromotion parallel
and perpendicular to the plane of the trap electrodes, and find that on-package
capacitors reduce this to <~ 10 nm in amplitude. We also measure ion trapping
lifetime, charging effects due to laser light incident on the trap electrodes,
and the heating rate for a single trapped ion. The performance of this trap is
found to be comparable with others of the same size scale.Comment: 6 pages, 10 figure
Background-free detection of trapped ions
We demonstrate a Doppler cooling and detection scheme for ions with low-lying
D levels which almost entirely suppresses scattered laser light background,
while retaining a high fluorescence signal and efficient cooling. We cool a
single ion with a laser on the 2S1/2 to 2P1/2 transition as usual, but repump
via the 2P3/2 level. By filtering out light on the cooling transition and
detecting only the fluorescence from the 2P_3/2 to 2S1/2 decays, we suppress
the scattered laser light background count rate to 1 per second while
maintaining a signal of 29000 per second with moderate saturation of the
cooling transition. This scheme will be particularly useful for experiments
where ions are trapped in close proximity to surfaces, such as the trap
electrodes in microfabricated ion traps, which leads to high background scatter
from the cooling beam
Consistent histories, the quantum Zeno effect, and time of arrival
We present a decomposition of the general quantum mechanical evolution
operator, that corresponds to the path decomposition expansion, and interpret
its constituents in terms of the quantum Zeno effect (QZE). This decomposition
is applied to a finite dimensional example and to the case of a free particle
in the real line, where the possibility of boundary conditions more general
than those hitherto considered in the literature is shown. We reinterpret the
assignment of consistent probabilities to different regions of spacetime in
terms of the QZE. The comparison of the approach of consistent histories to the
problem of time of arrival with the solution provided by the probability
distribution of Kijowski shows the strength of the latter point of view
Weak measurement of arrival time
The arrival time probability distribution is defined by analogy with the
classical mechanics. The difficulty of requirement to have the values of
non-commuting operators is circumvented using the concept of weak measurements.
The proposed procedure is suitable to the free particles and to the particles
subjected to an external potential, as well. It is shown that such an approach
imposes an inherent limitation to the accuracy of the arrival time
determination.Comment: 3 figure