404 research outputs found
Topological Schr\"odinger cats: Non-local quantum superpositions of topological defects
Topological defects (such as monopoles, vortex lines, or domain walls) mark
locations where disparate choices of a broken symmetry vacuum elsewhere in the
system lead to irreconcilable differences. They are energetically costly (the
energy density in their core reaches that of the prior symmetric vacuum) but
topologically stable (the whole manifold would have to be rearranged to get rid
of the defect). We show how, in a paradigmatic model of a quantum phase
transition, a topological defect can be put in a non-local superposition, so
that - in a region large compared to the size of its core - the order parameter
of the system is "undecided" by being in a quantum superposition of conflicting
choices of the broken symmetry. We demonstrate how to exhibit such a
"Schr\"odinger kink" by devising a version of a double-slit experiment suitable
for topological defects. Coherence detectable in such experiments will be
suppressed as a consequence of interaction with the environment. We analyze
environment-induced decoherence and discuss its role in symmetry breaking.Comment: 7 pages, 4 figure
Sub-Planck spots of Schroedinger cats and quantum decoherence
Heisenberg's principle states that the product of uncertainties of
position and momentum should be no less than Planck's constant . This is
usually taken to imply that phase space structures associated with sub-Planck
() scales do not exist, or, at the very least, that they do not
matter. I show that this deeply ingrained prejudice is false: Non-local
"Schr\"odinger cat" states of quantum systems confined to phase space volume
characterized by `the classical action' develop spotty structure
on scales corresponding to sub-Planck . Such
structures arise especially quickly in quantum versions of classically chaotic
systems (such as gases, modelled by chaotic scattering of molecules), that are
driven into nonlocal Schr\"odinger cat -- like superpositions by the quantum
manifestations of the exponential sensitivity to perturbations. Most
importantly, these sub-Planck scales are physically significant: determines
sensitivity of a quantum system (or of a quantum environment) to perturbations.
Therefore sub-Planck controls the effectiveness of decoherence and
einselection caused by the environment. It may also be relevant in
setting limits on sensitivity of Schr\"odinger cats used as detectors.Comment: Published in Nature 412, 712-717 (2001
Consistent quantum mechanics admits no mereotopology
It is standardly assumed in discussions of quantum theory that physical
systems can be regarded as having well-defined Hilbert spaces. It is shown here
that a Hilbert space can be consistently partitioned only if its components are
assumed not to interact. The assumption that physical systems have well-defined
Hilbert spaces is, therefore, physically unwarranted.Comment: 10 pages; to appear in Axiomathe
Quantum Darwinism
Quantum Darwinism describes the proliferation, in the environment, of
multiple records of selected states of a quantum system. It explains how the
fragility of a state of a single quantum system can lead to the classical
robustness of states of their correlated multitude; shows how effective
`wave-packet collapse' arises as a result of proliferation throughout the
environment of imprints of the states of quantum system; and provides a
framework for the derivation of Born's rule, which relates probability of
detecting states to their amplitude. Taken together, these three advances mark
considerable progress towards settling the quantum measurement problem
A Stepwise Planned Approach to the Solution of Hilbert's Sixth Problem. III : Measurements and von Neumann Projection/Collapse Rule
Supmech, the universal mechanics developed in the previous two papers,
accommodates both quantum and classical mechanics as subdisciplines (a brief
outline is included for completeness); this feature facilitates, in a supmech
based treatment of quantum measurements, an unambiguous treatment of the
apparatus as a quantum system approximated well by a classical one. Taking
explicitly into consideration the fact that observations on the apparatus are
made when it has `settled down after the measurement interaction' and are
restricted to macroscopically distinguishable pointer readings, the unwanted
superpositions of (system + apparatus) states are shown to be suppressed; this
provides a genuinely physics based justification for the (traditionally
\emph{postulated}) von Neumann projection/collapse rule. The decoherence
mechanism brought into play by the stated observational constraints is free
from the objections against the traditional decoherence program.Comment: 29 pages; one section and two references added; results unchange
Measurement and Particle Statistics in the Szilard Engine
A Szilard Engine is a hypothetical device which is able to extract work from
a single thermal reservoir by measuring the position of particles within the
engine. We derive the amount of work that can be extracted from such a device
in the low temperature limit. Interestingly, we show this work is determined by
the information gain of the initial measurement rather than by the number and
type of particles which constitute the working substance. Our work provides
another clear connection between information gain and extractable work in
thermodynamical processes.Comment: 4 page
Breakdown of the adiabatic limit in low dimensional gapless systems
It is generally believed that a generic system can be reversibly transformed
from one state into another by sufficiently slow change of parameters. A
standard argument favoring this assertion is based on a possibility to expand
the energy or the entropy of the system into the Taylor series in the ramp
speed. Here we show that this argumentation is only valid in high enough
dimensions and can break down in low-dimensional gapless systems. We identify
three generic regimes of a system response to a slow ramp: (A) mean-field, (B)
non-analytic, and (C) non-adiabatic. In the last regime the limits of the ramp
speed going to zero and the system size going to infinity do not commute and
the adiabatic process does not exist in the thermodynamic limit. We support our
results by numerical simulations. Our findings can be relevant to
condensed-matter, atomic physics, quantum computing, quantum optics, cosmology
and others.Comment: 11 pages, 5 figures, to appear in Nature Physics (originally
submitted version
Fault Models for Quantum Mechanical Switching Networks
The difference between faults and errors is that, unlike faults, errors can
be corrected using control codes. In classical test and verification one
develops a test set separating a correct circuit from a circuit containing any
considered fault. Classical faults are modelled at the logical level by fault
models that act on classical states. The stuck fault model, thought of as a
lead connected to a power rail or to a ground, is most typically considered. A
classical test set complete for the stuck fault model propagates both binary
basis states, 0 and 1, through all nodes in a network and is known to detect
many physical faults. A classical test set complete for the stuck fault model
allows all circuit nodes to be completely tested and verifies the function of
many gates. It is natural to ask if one may adapt any of the known classical
methods to test quantum circuits. Of course, classical fault models do not
capture all the logical failures found in quantum circuits. The first obstacle
faced when using methods from classical test is developing a set of realistic
quantum-logical fault models. Developing fault models to abstract the test
problem away from the device level motivated our study. Several results are
established. First, we describe typical modes of failure present in the
physical design of quantum circuits. From this we develop fault models for
quantum binary circuits that enable testing at the logical level. The
application of these fault models is shown by adapting the classical test set
generation technique known as constructing a fault table to generate quantum
test sets. A test set developed using this method is shown to detect each of
the considered faults.Comment: (almost) Forgotten rewrite from 200
Spontaneous creation of Kibble-Zurek solitons in a Bose-Einstein condensate
When a system crosses a second-order phase transition on a finite timescale,
spontaneous symmetry breaking can cause the development of domains with
independent order parameters, which then grow and approach each other creating
boundary defects. This is known as Kibble-Zurek mechanism. Originally
introduced in cosmology, it applies both to classical and quantum phase
transitions, in a wide variety of physical systems. Here we report on the
spontaneous creation of solitons in Bose-Einstein condensates via the
Kibble-Zurek mechanism. We measure the power-law dependence of defects number
with the quench time, and provide a check of the Kibble-Zurek scaling with the
sonic horizon. These results provide a promising test bed for the determination
of critical exponents in Bose-Einstein condensates.Comment: 7 pages, 4 figure
Big bang simulation in superfluid 3He-B -- Vortex nucleation in neutron-irradiated superflow
We report the observation of vortex formation upon the absorption of a
thermal neutron in a rotating container of superfluid He-B. The nuclear
reaction n + He = p + H + 0.76MeV heats a cigar shaped region of the
superfluid into the normal phase. The subsequent cooling of this region back
through the superfluid transition results in the nucleation of quantized
vortices. Depending on the superflow velocity, sufficiently large vortex rings
grow under the influence of the Magnus force and escape into the container
volume where they are detected individually with nuclear magnetic resonance.
The larger the superflow velocity the smaller the rings which can expand. Thus
it is possible to obtain information about the morphology of the initial defect
network. We suggest that the nucleation of vortices during the rapid cool-down
into the superfluid phase is similar to the formation of defects during
cosmological phase transitions in the early universe.Comment: 4 pages, LaTeX file, 4 figures are available at
ftp://boojum.hut.fi/pub/publications/lowtemp/LTL-95009.p
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