Engineering a Quantum Many-body Hamiltonian with Trapped Ions

While fault-tolerant quantum computation might still be years away, analog quantum simulators offer a way to leverage current quantum technologies to study classically intractable quantum systems. Cutting edge quantum simulators such as those utilizing ultracold atoms are beginning to study physics which surpass what is classically tractable. As the system sizes of these quantum simulators increase, there are also concurrent gains in the complexity and types of Hamiltonians which can be simulated. In this work, I describe advances toward the realization of an adaptable, tunable quantum simulator capable of surpassing classical computation. We simulate long-ranged Ising and XY spin models which can have global arbitrary transverse and longitudinal fields in addition to individual transverse fields using a linear chain of up to 24 Yb+ 171 ions confined in a linear rf Paul trap. Each qubit is encoded in the ground state hyperfine levels of an ion. Spin-spin interactions are engineered by the application of spin-dependent forces from laser fields, coupling spin to motion. Each spin can be read independently using state-dependent fluorescence. The results here add yet more tools to an ever growing quantum simulation toolbox. One of many challenges has been the coherent manipulation of individual qubits. By using a surprisingly large fourth-order Stark shifts in a clock-state qubit, we demonstrate an ability to individually manipulate spins and apply independent Hamiltonian terms, greatly increasing the range of quantum simulations which can be implemented. As quantum systems grow beyond the capability of classical numerics, a constant question is how to verify a quantum simulation. Here, I present measurements which may provide useful metrics for large system sizes and demonstrate them in a system of up to 24 ions during a classically intractable simulation. The observed values are consistent with extremely large entangled states, as much as ~95% of the system entangled. Finally, we use many of these techniques in order to generate a spin Hamiltonian which fails to thermalize during experimental time scales due to a meta-stable state which is often called prethermal. The observed prethermal state is a new form of prethermalization which arises due to long-range interactions and open boundary conditions, even in the thermodynamic limit. This prethermalization is observed in a system of up to 22 spins. We expect that system sizes can be extended up to 30 spins with only minor upgrades to the current apparatus. These results emphasize that as the technology improves, the techniques and tools developed here can potentially be used to perform simulations which will surpass the capability of even the most sophisticated classical techniques, enabling the study of a whole new regime of quantum many-body physics.

Circadian rhythms, sleep and autonomic function in progressive supranuclear palsy: characteristic features and reciprocal interactions

Background: Progressive supranuclear palsy (PSP) is a rare neurodegenerative condition. The aims of this study were to evaluate the association between sleep, the circadian system and autonomic function in a cohort of PSP patients. Methods: Patients with PSP diagnosed according to consensus criteria were recruited prospectively and retrospectively and performed the following tests: body core temperature (BcT), sleep-wake cycle, systolic and diastolic blood pressure (SBP, DBP) continuous monitoring for 48 h under controlled environmental conditions; cardiovascular reflex tests (CRTs). The analysis of circadian rhythmicity was performed with the single cosinor method. For state-dependent analysis, the mean value of variables in each sleep stage was calculated as well as the difference to the value in wake. Results: PSP patients presented a reduced total duration of night sleep, with frequent and prolonged awakenings. During daytime, patients had very short naps, suggesting a state of profound sleep deprivation across the 24-h. REM sleep behaviour disorder was found in 15%, restless legs syndrome in 46%, periodic limb movements in 52% and obstructive sleep apnea in 54%. BcT presented the expected fall during night-time, however, compared to controls, mean values during day and night were higher. However BcT state-dependent modulation was maintained. Increased BcT could be attributed to an inability to properly reduce sympathetic activity favoured by the sleep deprivation. At CRTs, PSP presented mild cardiovascular adrenergic impairment and preserved cardiovagal function. 14% had non-neurogenic orthostatic hypotension. Only 2 PSP presented the expected BP dipping pattern, possibly as a consequence of sleep disruption. State-dependent analysis showed a partial loss of the state-dependent modulation for SBP. Discussion: This study showed that PSP presented abnormalities of sleep, circadian rhythms and cardiovascular autonomic function that are likely to be closely linked one to another.

Seeing emotions in others: Improving cognitive and neuronal mechanisms of facial expression processing

In the conceptual framework of affective neuroscience, this thesis intends to advance the understanding of the plasticity mechanisms of other’s emotional facial expression representations. Chapter 1 outlines a description of the neurophysiological bases of Hebbian plasticity, reviews influential studies that adopted paired associative stimulation procedures, and introduces new lines of research where the impact of cortico-cortical paired associative stimulation protocols on higher order cognitive functions is investigated. The experiments in Chapter 2 aimed to test the modulatory influence of a perceptual-motor training, based on the execution of emotional expressions, on the subsequent emotion intensity judgements of others’ high (i.e., full visible) and low-intensity (i.e., masked) emotional expressions. As a result of the training-induced learning, participants showed a significant congruence effect, as indicated by relatively higher expression intensity ratings for the same emotion as the one that was previously trained. Interestingly, although judged as overall less emotionally intense, surgical facemasks did not prevent the emotion-specific effects of the training to occur, suggesting that covering the lower part of other’s face do not interact with the training-induced congruence effect. In Chapter 3 it was implemented a transcranial magnetic stimulation study targeting neural pathways involving re-entrant input from higher order brain regions into lower levels of the visual processing hierarchy. We focused on cortical visual networks within the temporo-occipital stream underpinning the processing of emotional faces and susceptible to plastic adaptations. Importantly, we tested the plasticity-induced effects in a state dependent manner, by administering ccPAS while presenting different facial expressions yet afferent to a specific emotion. Results indicated that the discrimination accuracy of emotion-specific expressions is enhanced following the ccPAS treatment, suggesting that a multi-coil TMS intervention might represent a suitable tool to drive brain remodeling at a neural network level, and consequently influence a specific behavior.

Induction of Hebbian associative plasticity through paired non-invasive brain stimulation of premotor-motor areas to elucidate the network's functional role

The ventral premotor cortex (PMv) is believed to play a pivotal role in a multitude of visuomotor behaviors, such as sensory-guided goal-directed visuomotor transformations, arbitrary visuomotor mapping, and hyper-learnt visuomotor associations underlying automatic imitative tendencies. All these functions are likely carried out through the copious projections connecting PMv to the primary motor cortex (M1). Yet, causal evidence investigating the functional relevance of the PMv-M1 network remains elusive and scarce. In the studies reported in this thesis we addressed this issue using a transcranial magnetic stimulation (TMS) protocol called cortico-cortical paired associative stimulation (ccPAS), which relies on multisite stimulation to induce Hebbian spike-timing dependent plasticity (STDP) by repeatedly stimulating the pathway connecting two target areas to manipulate their connectivity. Firstly, we show that ccPAS protocols informed by both short- and long-latency PMv-M1 interactions effectively modulate connectivity between the two nodes. Then, by pre-activating the network to apply ccPAS in a state-dependent manner, we were able to selectively target specific functional visuo-motor pathways, demonstrating the relevance of PMv-M1 connectivity to arbitrary visuomotor mapping. Subsequently, we addressed the PMv-to-M1 role in automatic imitation, and demonstrated that its connectivity manipulation has a corresponding impact on automatic imitative tendencies. Finally, by combining dual-coil TMS connectivity assessments and ccPAS in young and elderly individuals, we traced effective connectivity of premotor-motor networks and tested their plasticity and relevance to manual dexterity and force in healthy ageing. Our findings provide unprecedent causal evidence of the functional role of the PMv-to-M1 network in young and elderly individuals. The studies presented in this thesis suggest that ccPAS can effectively modulate the strength of connectivity between targeted areas, and coherently manipulate a networks’ behavioral output. Results open new research prospects into the causal role of cortico-cortical connectivity, and provide necessary information to the development of clinical interventions based on connectivity manipulation.

Predicting corticospinal excitability from pre-TMS EEG using convolutional neural networks

The amplitude of motor evoked potentials (MEPs) elicited by transcranial magnetic stimulation (TMS) of the primary motor cortex (M1) shows a large variability from trial to trial, although MEPs are evoked by the same repeated stimulus. A multitude of factors is believed to influence MEP amplitudes, such as cortical, spinal and motor excitability state. The goal of this work is to explore to which degree the variation in MEP amplitudes can be explained by the cortical state right before the stimulation. Specifically, we analyzed a dataset acquired on eleven healthy subjects comprising, for each subject, 840 single TMS pulses applied to the left M1 during acquisition of electroencephalography (EEG) and electromyography (EMG). An interpretable convolutional neural network, named SincEEGNet, was utilized to discriminate between low- and high-corticospinal excitability trials, defined according to the MEP amplitude, using in input the pre-TMS EEG. This data-driven approach enabled considering multiple brain locations and frequency bands without any a priori selection. Post-hoc interpretation techniques were adopted to enhance interpretation by identifying the more relevant EEG features for the classification. Results show that individualized classifiers successfully discriminated between low and high M1 excitability states in all participants. Outcomes of the interpretation methods suggest the importance of the electrodes situated over the TMS stimulation site, as well as the relevance of the temporal samples of the input EEG closer to the stimulation time. This novel decoding method allows causal investigation of the cortical excitability state, which may be relevant for personalizing and increasing the efficacy of therapeutic brain-state dependent brain stimulation (for example in patients affected by Parkinson’s disease).

A pore-size-dependent equation of state for multilayer adsorption in cylindrical mesopores

The chemical potential of adsorbed film inside cylindrical mesopores is dependent on the attractive interactions between the adsorbed molecules and adsorbent, the curvature of gas/adsorbed phase interface, and surface tension. A state equation of the adsorbed film is proposed to take into account the above factors. Nitrogen adsorption on model adsorbents, MCM-41, which exhibit uniform cylindrical channels, are used to verify the theoretical analysis. The proposed theory is capable of describing the important features of adsorption processes in cylindrical mesopores. According to this theory, at a given relative pressure, the smaller the pore radius is, the thicker the adsorbed film will be. The thickening of adsorbed films in the pores as the vapor pressure increases inevitably causes an increase in the interface curvature, which consequently leads to capillary condensation. Besides, this study confirmed that the interface tension depends substantially on the interface curvature in small mesopores. A quantitative relationship between the condensation pressure and the pore radius can be derived from the state equation and used to predict the pore radius from a condensation pressure, or vice versa.

Equation of state for the magnetic-color-flavor-locked phase and its implications for compact star models

Using the solutions of the gap equations of the magnetic-color-flavor-locked (MCFL) phase of paired quark matter in a magnetic field, and taking into consideration the separation between the longitudinal and transverse pressures due to the field-induced breaking of the spatial rotational symmetry, the equation of state of the MCFL phase is self-consistently determined. This result is then used to investigate the possibility of absolute stability, which turns out to require a field-dependent ""bag constant"" to hold. That is, only if the bag constant varies with the magnetic field, there exists a window in the magnetic field vs bag constant plane for absolute stability of strange matter. Implications for stellar models of magnetized (self-bound) strange stars and hybrid (MCFL core) stars are calculated and discussed.

A stress relaxation model for the viscoelastic solids based on the steady-state creep equation

Creep and stress relaxation are inherent mechanical behaviors of viscoelastic materials. It is considered that both are different performances of one identical physical phenomenon. The relationship between the decay stress and time during stress relaxation has been derived from the power law equation of the steady-state creep. The model was used to analyse the stress relaxation curves of various different viscoelastic materials (such as pure polycrystalline ice, polymers, foods, bones, metal, animal tissues, etc.). The calculated results using the theoretical model agree with the experimental data very well. Here we show that the new mathematical formula is not only simple but its parameters have the clear physical meanings. It is suitable to materials with a very broad scope and has a strong predictive ability.

MODELLING OF HIGH-PRESSURE PHASE EQUILIBRIUM IN SYSTEMS OF INTEREST IN THE FOOD ENGINEERING FIELD USING THE PENG-ROBINSON EQUATION OF STATE WITH TWO DIFFERENT MIXING RULES

In this work, thermodynamic models for fitting the phase equilibrium of binary systems were applied, aiming to predict the high pressure phase equilibrium of multicomponent systems of interest in the food engineering field, comparing the results generated by the models with new experimental data and with those from the literature. Two mixing rules were used with the Peng-Robinson equation of state, one with the mixing rule of van der Waals and the other with the composition-dependent mixing rule of Mathias et al. The systems chosen are of fundamental importance in food industries, such as the binary systems CO(2)-limonene, CO(2)-citral and CO(2)-linalool, and the ternary systems CO(2)-Limonene-Citral and CO(2)-Limonene-Linalool, where high pressure phase equilibrium knowledge is important to extract and fractionate citrus fruit essential oils. For the CO(2)-limonene system, some experimental data were also measured in this work. The results showed the high capability of the model using the composition-dependent mixing rule to model the phase equilibrium behavior of these systems.

Transport properties and equation of state of quark-nuclear matter

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Exact boundary control for the wave equation in a polyhedral time-dependent domain

We establish exact boundary controllability for the wave equation in a polyhedral domain where a part of the boundary moves slowly with constant speed in a small interval of time. The control on the moving part of the boundary is given by the conormal derivative associated with the wave operator while in the fixed part the control is of Neuman type. For initial state H-1 x L-2 we obtain controls in L-2. (C) 1999 Elsevier B.V. Ltd. All rights reserved.

Numerical study of the coupled time-dependent Gross-Pitaevskii equation: Application to Bose-Einstein condensation

The Bose-Einstein condensate of several types of trapped bosons at ultralow temperature was described using the coupled time dependent Gross-Pitaevskii equation. Both the stationary and time evolution problems were analyzed using this approach. The ground state stationary wave functions were found to be sharply peaked near the origin for attractive interatomic interaction for larger nonlinearity while for a repulsive interatomic interaction the wave function extends over a larger region of space.

Equivalence between Redfield- and master-equation approaches for a time-dependent quantum system and coherence control

We present a derivation of the Redfield formalism for treating the dissipative dynamics of a time-dependent quantum system coupled to a classical environment. We compare such a formalism with the master equation approach where the environments are treated quantum mechanically. Focusing on a time-dependent spin-1/2 system we demonstrate the equivalence between both approaches by showing that they lead to the same Bloch equations and, as a consequence, to the same characteristic times T(1) and T(2) (associated with the longitudinal and transverse relaxations, respectively). These characteristic times are shown to be related to the operator-sum representation and the equivalent phenomenological-operator approach. Finally, we present a protocol to circumvent the decoherence processes due to the loss of energy (and thus, associated with T(1)). To this end, we simply associate the time dependence of the quantum system to an easily achieved modulated frequency. A possible implementation of the protocol is also proposed in the context of nuclear magnetic resonance.

Excitation energies from ground-state density-functionals by means of generator coordinates

The generator-coordinate method is a flexible and powerful reformulation of the variational principle. Here we show that by introducing a generator coordinate in the Kohn-Sham equation of density-functional theory, excitation energies can be obtained from ground-state density functionals. As a viability test, the method is applied to ground-state energies and various types of excited-state energies of atoms and ions from the He and the Li isoelectronic series. Results are compared to a variety of alternative DFT-based approaches to excited states, in particular time-dependent density-functional theory with exact and approximate potentials.