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Non-Markovian quantum trajectories: An exact result
No full textWe analyze the non-Markovian stochastic Schrödinger equation describing a particle subject to spontaneous collapses in space (in the language of collapse models), or subject to a continuous measurement of its position (in the language of continuous quantum measurement). For the first time, we give the explicit general solution for the free particle case (H=p^2/2m) and discuss the main properties. We analyze the case of an exponential correlation function for the noise, giving a quantitative description of the dynamics and of its dependence on the correlation time
Non-Markovian dynamics for a free quantum particle subject to spontaneous collapse in space: general solution and main properties
No full textColored collapse models from the non-interferometric perspective
Get PDFModels of spontaneous wave function collapse describe the quantum-to-classical transition by assuming a progressive breakdown of the superposition principle when the mass of the system increases, providing a well-defined phenomenology in terms of a non-linearly and stochastically modified Schro ̈dinger equation, which can be tested experimentally. The most popular of such models is the continuous spontaneous localization (CSL) model: in its original version, the collapse is driven by a white noise, and more recently, generalizations in terms of colored noises, which are more realistic, have been formulated. We will analyze how current non-interferometric tests bound the model, depending on the spectrum of the noise. We will find that low frequency purely mechanical experiments provide the most stable and strongest bounds
Collapse dynamics are diffusive
Get PDFNon-interferometric experiments have been successfully employed to constrain
models of spontaneous wave function collapse, which predict a violation of the
quantum superposition principle for large systems. These experiments are
grounded on the fact that, according to these models, the dynamics is driven by
a noise that, besides collapsing the wave function in space, generates a
diffusive motion with characteristic signatures, which, though small, can be
tested. The non-interferometric approach might seem applicable only to those
models which implement the collapse through a noisy dynamics, not to any model,
which collapses the wave function in space. Here we show that this is not the
case: under reasonable assumptions, any collapse dynamics (in space) is
diffusive. Specifically, we prove that any space-translation invariant dynamics
which complies with the no-signaling constraint, if collapsing the wave
function in space, must change the average momentum of the system, and/or its
spread.Comment: 20 page
Minimum measurement time: lower bound on the frequency cutoff for collapse models
Get PDFThe CSL model predicts a progressive breakdown of the quantum superposition principle, with a noise randomly driving the state of the system towards a localized one, thus accounting for the emergence of a classical world within a quantum framework. In the original model the noise is supposed to be white, but since white noises do not exist in nature, it becomes relevant to identify some of its spectral properties. Experimental data set an upper bound on its frequencies, while in this paper we bound it from below. We do so in two ways: by considering a 'minimal' measurement setup, requiring that the collapse is completed within the measurement time; and in a measurement modeling-independent way, by requiring that the fluctuations average to zero before the measurement time
Present status and future challenges of non-interferometric tests of collapse models
No full textThe superposition principle is the cornerstone of quantum mechanics, leading to a variety of genuinely quantum effects. Whether the principle applies also to macroscopic systems or, instead, there is a progressive breakdown when moving to larger scales is a fundamental and still open question. Spontaneous wavefunction collapse models predict the latter option, thus questioning the universality of quantum mechanics. Technological advances allow to increasingly challenge collapse models and the quantum superposition principle, with a variety of different experiments. Among them, non-interferometric experiments proved to be the most effective in testing these models. We provide an overview of such experiments, including cold atoms, optomechanical systems, X-ray detection, bulk heating and comparisons with cosmological observations. We also discuss avenues for future dedicated experiments, which aim at further testing collapse models and the validity of quantum mechanics.</p
Optimal control for feedback cooling in cavityless levitated optomechanics
Get PDFWe consider feedback cooling in a cavityless levitated optomechanics setup, and we investigate the possibility to improve the feedback implementation. We apply optimal control theory to derive the optimal feedback signal both for quadratic (parametric) and linear (electric) feedback. We numerically compare optimal feedback against the typical feedback implementation used for experiments. In order to do so, we implement a state estimation scheme that takes into account the modulation of the laser intensity. We show that such an implementation allows us to increase the feedback strength, leading to faster cooling rates and lower center-of-mass temperatures
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Non-Markovian collapse models
No full text2008/2009We introduce the measurement problem in quantum mechanics and we briefly
discuss
the solutions proposed in literature. We then focus our
attention on models of spontaneous wavefunction collapse.
We describe the two most popular models (GRW, CSL) and list other proposals.
We analyze
in detail a third collapse
model (QMUPL), which is particularly simple (but physically meaningful) to
be studied in great mathematical detail. We discuss its main properties. We
also describe a "finite
temperature" version of this model, which includes dissipative terms.
These models are Markovian, i.e. the collapse mechanism is driven by a
white noise. Since the ultimate goal is to identify the noise responsible
for the
collapse with a random field in Nature, it becomes important to study
non-Markovian generalizations of collapse models, where the collapsing field
has a generic correlation function, likely with a cut off at high
frequencies.
Models of this kind have already been studied, as a generalization of the
CSL model. In this thesis
we describe in mathematical detail the generalization of the QMUPL model to
non-Markovian noises. After having proved, under suitable conditions, the
separation of the center-of-mass and relative
motions for a generic ensemble of particles, we focus our analysis on the
time evolution of the center of mass
of an isolated system (free particle case). We compute the explicit
expression of the Green's function via the path integral formalism, for a
generic Gaussian noise. We analyze in detail the case of an exponential
correlation function, providing the exact analytical solution.
We next study the
time evolution of average quantities, such as the mean position, momentum
(which satisfy Ehrefest's theorem) and energy (which is not conserved like
in the other collapse models). We also compute the non-Markovian master
equation
for an harmonic oscillator, according to this model, and compare
its structure to the well-known Lindblad structure of Markovian open quantum
systems.
We
eventually specialize to the case of
Gaussian wave functions, and prove that all basic facts about collapse
models (reduction process, amplification mechanism, etc.), which are known
to be true in the white noise case, hold also in
the more general case of non-Markovian dynamics.
We further analyze the evolution
of Gaussian wave function according to the three different realizations of
the QMUPL model so far developed (Markovian, non-Markovian and "finite
temperature"), comparing their fundamental features.
Finally, by analyzing different localization criteria, we set new lower
bounds on the
parameters of these models, and we compare them with the upper bounds coming
from known experimental data.Nel primo capitolo si introduce il problema della misura in Meccanica Quantistica e si discutono brevemente le soluzioni proposte nella letteratura. Nel capitolo 2 si discutono i modelli di collasso spontaneo della funzione d'onda, con particolare attenzione per i modelli GRW e CSL; si elencano altri modelli.
Si analizza in dettaglio anche il modello di riduzione QMUPL, il quale è particolarmente semplice (ma fisicamente significativo) da poter essere studiato dettagliatamente dal punto di vista matematico. Si discutono le sue proprietà principali. Si descrive inoltre una versione "a temperatura finita" di questo modello, che include termini dissipativi.
Questi modelli sono Markoviani, ovvero il meccanismo di collasso è guidato da un rumore bianco. Poichè parte significativa della ricerca consiste nell'identificare il rumore responsabile del collasso con un campo stocastico esistente in Natura, diventa importante studiare le generalizzazioni non-Markoviane dei modelli di riduzione, in cui il campo di collasso ha una funzione di correlazione generale, probabilmente con un cutoff ad alte frequenze.
Modelli di questo tipo, come la generalizzazione del modello CSL, sono già stati studiati.
In questa tesi si descrive in dettaglio la generalizzazione a rumori non-Markoviani del modello QMUPL. Dopo aver provato, sotto particolari condizioni, la separazione del moto del centro di massa da quello relativo per un generico ensemble di particelle, si pone attenzione all'evoluzione temporale del centro di massa di un sistema isolato (particella libera). Si dà l'espressione esplicita per la funzione di Green attraverso il formalismo del path-integral, per un generico rumore Gaussiano. Si analizza in particolare il caso della funzione di correlazione esponenziale, fornendo la soluzione analitica esatta delle equazioni.
Successivamente si studia l'evoluzione dei valori medi, in particolare della posizione, del momento (che soddsfa il teorema di Ehrenfest) e dell'energia (che non è conservata come negli altri modelli di riduzione). Si scrive inoltre la master equation non-Markoviana per un oscillatore armonico per questo modello, e si confronta la sua struttura con le ben nota struttura di Lindblad dei sistemi quantistici aperti Markoviani.
Ci si specializza al caso di funzioni d'onda Gaussiane, e si prova che tutte le nozioni di base sui modelli di riduzione (processo di collasso, meccanismo di amplificazione, ecc.), che sono note essere vere nel caso Markoviano, valgono anche nel caso più generale di dinamiche non-Markoviane.
Infine, si analizza l'evoluzione di funzioni d'onda Gaussiane secondo le tre differenti realizzazioni del modello QMUPL finora analizzate (Markoviana, non-Markoviana e "a temperatura finita"), confrontando le loro caratteristiche fondamentali.
Inoltre, analizzando differenti criteri di localizzazione, si individano nuovi limiti inferiori per i parametri di questi modelli, e si confrontano con i limiti superiori che vengono da dati sperimentali noti.XXII Ciclo198
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