Quantum solitons in spin-orbit-coupled Bose-Bose mixtures

Recent experimental and theoretical results show that weakly interacting atomic Bose-Bose mixtures with attractive interspecies interaction are stabilized by beyond-mean-field effects. Here we consider the peculiar properties of these systems in a strictly one-dimensional configuration, taking also into account the nontrivial role of spin-orbit and Rabi couplings. We show that when the value of inter- and intraspecies interaction strengths are such that mean-field contributions to the energy cancel, a self-bound bright soliton fully governed by quantum fluctuations exists. We derive the phase diagram of the phase transition between a single-peak soliton and a multipeak (striped) soliton, produced by the interplay between spin-orbit, Rabi couplings and beyond-mean-field effects, which also affect the breathing mode frequency of the atomic cloud. Finally, we prove that a phase imprinting of the single-peak soliton leads to a self-confined propagating solitary wave even in the presence of spin-orbit coupling.Comment: 6 pages, 4 figures, published in Phys. Rev.

Zero-temperature equation of state of a two-dimensional bosonic quantum fluid with finite-range interaction

We derive the two-dimensional equation of state for a bosonic system of ultracold atoms interacting with a finite-range effective interaction. Within a functional integration approach, we employ an hydrodynamic parametrization of the bosonic field to calculate the superfluid equations of motion and the zero-temperature pressure. The ultraviolet divergences, naturally arising from the finite-range interaction, are regularized with an improved dimensional regularization technique.Comment: 10 pages, no figure

Bose-Einstein Condensation and Superfluidity in 3D and 2D bosons

The refinement and the combination of laser cooling and evaporative cooling in dilute systems of alkali atoms lead to the achievement of Bose-Einstein condensation in 1995. Nowadays there is a fruitful interplay between theoretical and experimental results: in this context, the study of uniform Bose gases plays an important role in the comprehension of the static and dynamic properties of a bosonic system. Here we use quantum field theory, within the approach of functional integration, to study an homogeneous system of weakly-interacting bosonic cold atoms. After characterizing their thermodynamical properties, we derive - at a gaussian level - the number density and the superfluid density in three and in two spatial dimensions, expressed as functions of the condensate density and the temperature. Since the equations derived are valid for a generic interaction potential, we implement these formulas for bosons with a zero-range interaction, providing also an extension of these results with the inclusion of a finite-range interaction.ope

Topological superfluid transition in bubble-trapped condensates

Ultracold quantum gases are highly controllable and, thus, capable of simulating difficult quantum many-body problems ranging from condensed matter physics to astrophysics. Although experimental realizations have so far been restricted to flat geometries, recently also curved quantum systems, with the prospect of exploring tunable geometries, are produced in microgravity facilities as ground-based experiments are technically limited. Here we analyze bubble-trapped condensates, in which the atoms are confined on the surface of a thin spherically-symmetric shell by means of external magnetic fields. A thermally-induced proliferation of vorticity yields a vanishing of superfluidity. We describe the occurrence of this topological transition by conceptually extending the theory of Berezinskii, Kosterlitz and Thouless for infinite uniform systems to such finite-size systems. Unexpectedly, we find universal scaling relations for the mean critical temperature and the finite width of the superfluid transition. Furthermore, we elucidate how they could be experimentally observed in finite-temperature hydrodynamic excitations.Comment: 8 pages, 3 figure

Sull’approssimazione diffusiva della Master Equation

La Master Equation è un’equazione integrodifferenziale che descrive l’evoluzione temporale di un ampio spettro di sistemi stocastici. Spesso se ne considera l’approssimazione diffusiva, valida nel limite di grandi lunghezze d’onda, che la trasforma in una pura equazione differenziale alle derivate parziali. Nel regime opposto, in presenza di forti discontinuità spaziali o pareti materiali, ci si attende quindi una discrepanza tra le predizioni ricavate risolvendo la Master Equation completa e quelle ottenute dalla sua approssimazione diffusiva. Il lavoro di tesi è consistito nell’evidenziare questa discrepanza attraverso l’investigazione numerica di alcuni semplici modelli costruiti ad hoc. Contrariamente alle aspettative, i risultati hanno mostrato che la dinamica diffusiva è anche in queste situazioni un’ottima approssimazione della Master Equation. È stata identificata a posteriori -dall’analisi della letteratura- una spiegazione di questo fatto; nell’ultima parte del lavoro viene fornita una nuova versione della dimostrazione.ope

Dephasing-rephasing dynamics of one-dimensional tunneling quasicondensates

We study the quantum tunneling of two one-dimensional quasi-condensates made of alkali-metal atoms, considering two different tunneling configurations: side-by-side and head-to-tail. After deriving the quasiparticle excitation spectrum, we discuss the dynamics of the relative phase following a sudden coupling of the independent subsystems. In particular, we calculate the coherence factor of the system, which, due to the nonzero tunneling amplitude, it exhibits dephasing-rephasing oscillations instead of pure dephasing. These oscillations are enhanced by a higher tunneling energy, and by higher system densities. Our predictions provide a benchmark for future experiments at temperatures below T \lesssim 5 \, \mbox{nK}.Comment: 15 pages, 4 figure

Metabolomic analysis of mouse prefrontal cortex reveals upregulated analytes during wakefulness compared to sleep

By identifying endogenous molecules in brain extracellular fluid metabolomics can provide insight into the regulatory mechanisms and functions of sleep. Here we studied how the cortical metabolome changes during sleep, sleep deprivation and spontaneous wakefulness. Mice were implanted with electrodes for chronic sleep/wake recording and with microdialysis probes targeting prefrontal and primary motor cortex. Metabolites were measured using ultra performance liquid chromatography-high resolution mass spectrometry. Sleep/wake changes in metabolites were evaluated using partial least squares discriminant analysis, linear mixed effects model analysis of variance, and machine-learning algorithms. More than 30 known metabolites were reliably detected in most samples. When used by a logistic regression classifier, the profile of these metabolites across sleep, spontaneous wake, and enforced wake was sufficient to assign mice to their correct experimental group (pair-wise) in 80–100% of cases. Eleven of these metabolites showed significantly higher levels in awake than in sleeping mice. Some changes extend previous findings (glutamate, homovanillic acid, lactate, pyruvate, tryptophan, uridine), while others are novel (D-gluconate, N-acetyl-beta-alanine, N-acetylglutamine, orotate, succinate/methylmalonate). The upregulation of the de novo pyrimidine pathway, gluconate shunt and aerobic glycolysis may reflect a wake-dependent need to promote the synthesis of many essential components, from nucleic acids to synaptic membranes

Ultrastructural effects of sleep and wake on the parallel fiber synapses of the cerebellum

Multiple evidence in rodents shows that the strength of excitatory synapses in the cerebral cortex and hippocampus is greater after wake than after sleep. The widespread synaptic weakening afforded by sleep is believed to keep the cost of synaptic activity under control, promote memory consolidation, and prevent synaptic saturation, thus preserving the brain's ability to learn day after day. The cerebellum is highly plastic and the Purkinje cells, the sole output neurons of the cerebellar cortex, are endowed with a staggering number of excitatory parallel fiber synapses. However, whether these synapses are affected by sleep and wake is unknown. Here, we used serial block face scanning electron microscopy to obtain the full 3D reconstruction of more than 7000 spines and their parallel fiber synapses in the mouse posterior vermis. This analysis was done in mice whose cortical and hippocampal synapses were previously measured, revealing that average synaptic size was lower after sleep compared to wake with no major changes in synapse number. Here, instead, we find that while the average size of parallel fiber synapses does not change, the number of branched synapses is reduced in half after sleep compared to after wake, corresponding to similar to 16% of all spines after wake and similar to 8% after sleep. Branched synapses are harbored by two or more spines sharing the same neck and, as also shown here, are almost always contacted by different parallel fibers. These findings suggest that during wake, coincidences of firing over parallel fibers may translate into the formation of synapses converging on the same branched spine, which may be especially effective in driving Purkinje cells to fire. By contrast, sleep may promote the off-line pruning of branched synapses that were formed due to spurious coincidences

Beta oscillatory changes and retention of motor skills during practice in healthy subjects and in patients with Parkinson's disease

Recently we found that modulation depth of beta power during movement increases with practice over sensory-motor areas in normal subjects but not in patients with Parkinson's disease (PD). As such changes might reflect use-dependent modifications, we concluded that reduction of beta enhancement in PD represents saturation of cortical plasticity. A few questions remained open: What is the relation between these EEG changes and retention of motor skills? Would a second task exposure restore beta modulation enhancement in PD? Do practice-induced increases of beta modulation occur within each block? We thus recorded EEG in patients with PD and age-matched controls in two consecutive days during a 40-min reaching task divided in fifteen blocks of 56 movements each. The results confirmed that, with practice, beta modulation depth over the contralateral sensory-motor area significantly increased across blocks in controls but not in PD, while performance improved in both groups without significant correlations between behavioral and EEG data. The same changes were seen the following day in both groups. Also, beta modulation increased within each block with similar values in both groups and such increases were partially transferred to the successive block in controls, but not in PD. Retention of performance improvement was present in the controls but not in the patients and correlated with the increase in day 1 modulation depth. Therefore, the lack of practice-related increase beta modulation in PD is likely due to deficient potentiation mechanisms that permit between-block saving of beta power enhancement and trigger mechanisms of memory formation